HF (Hartree-Fock) method
In this post we introduce one of the most fundamental methods in quantum chemistry: the Hartree–Fock (HF) method. Our aim is to lay out clearly how one goes from the many‑electron Schrödinger equation to a self‑consistent field (SCF) solution using the variational principle, and then demonstrate a complete calculation with PySCF.
HF Calculation with Aspirin
We now illustrate a complete HF calculation using PySCF. Aspirin(C9H8O4) is chosen as an example because it is a moderately sized organic molecule. Its geometry is defined by the Cartesian coordinates provided below. The 6‑31G basis set is used here since it offers a good compromise between computational cost and the level of detail needed to describe organic molecules accurately.
Note that we set `spin=0` for a closed‑shell configuration (each orbital doubly occupied) and disable symmetry for simplicity in geometry optimizations.
from pyscf import gto
# C10H7O6? what's this
aspirin_xyz = """
O 13.907 16.130 0.624
C 13.254 15.778 1.723
O 13.911 15.759 2.749
C 11.830 15.316 1.664
C 11.114 15.381 0.456
C 9.774 15.001 0.429
C 9.120 14.601 1.580
C 9.752 14.568 2.802
C 11.088 14.922 2.923
O 11.823 14.906 4.090
C 12.477 13.770 4.769
O 12.686 13.870 5.971
C 12.890 12.509 4.056
H 13.394 16.144 -0.175
H 11.602 15.729 -0.469
H 9.219 15.017 -0.524
H 8.060 14.298 1.521
H 9.182 14.254 3.693
H 13.384 11.651 4.568
H 11.987 12.110 3.536
H 13.544 12.808 3.204
"""
# Create the molecule object
mol = gto.M(
atom=aspirin_xyz,
basis='6-31G', # sto-3g
charge=0,
spin=0, # Closed-shell system spin=0! all electrons should paired
symmetry=False # Disable symmetry for easier geometry optimization.
)
- **Geometry:** The Cartesian coordinates represent an equilibrium geometry (or a reasonable guess thereof) for the aspirin molecule.
- **Basis Set Choice:** The 6‑31G basis set is used because it provides a more refined description of the electron density than minimal basis sets (e.g., STO‑3G) and is well suited for organic molecules.
- **Spin:** Setting `spin=0` ensures that the molecule is treated as a closed‑shell system, which is appropriate for most ground‑state organic molecules.
Initial HF Calculation
We then create an RHF (restricted HF) object and run the SCF procedure. Under RHF, the total HF energy is computed as: \[ E_{\text{HF}} = \sum_{ij} D_{ij}(H^{\text{core}}_{ij} + F_{ij}) + E_{\text{nuc}}, \] where \(E_{\text{nuc}}\) is the nuclear repulsion energy.
from pyscf import scf
import numpy as np
# Create RHF object and run initial SCF
mf = scf.RHF(mol)
print("Running initial HF calculation...")
mf.kernel() # This performs the SCF iterations and computes the HF energy.
Running initial HF calculation...
converged SCF energy = -644.598358849661
The `kernel()` method builds the Fock matrix from the current density, solves the Roothaan–Hall equations, updates the density matrix, and repeats until convergence. The reported energy (e.g., -831.53 a.u.) includes contributions from the electronic energy and the nuclear repulsion.
Geometry Optimization
The next step is to optimize the molecular geometry to find the structure corresponding to the minimum HF energy. PySCF’s geometric optimizer computes forces on the nuclei (the gradients of the energy with respect to nuclear positions) and updates the coordinates iteratively.
from pyscf.geomopt.geometric_solver import optimize
print("\nPerforming geometry optimization (this may take some time)...")
mol_eq = optimize(mf) # The optimizer adjusts the geometry until the forces are below a set threshold.
geometric-optimize called with the following command line:
/home/olivier/git/notes/.venv/lib/python3.12/site-packages/ipykernel_launcher.py -f /home/olivier/.local/share/jupyter/runtime/emacs-kernel-DnpXXm.json
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-=# geomeTRIC started. Version: 1.1 #=-
Current date and time: 2025-02-16 22:38:55
#========================================================#
#| Arguments passed to driver run_optimizer(): |#
#========================================================#
customengine <pyscf.geomopt.geometric_solver.PySCFEngine object at 0x7a8c24bfca70>
input /tmp/tmp9m32njzk/31a48c52-dd48-400d-a80c-805c9153004e
logIni /home/olivier/git/notes/.venv/lib/python3.12/site-packages/pyscf/geomopt/log.ini
----------------------------------------------------------
Custom engine selected.
Bonds will be generated from interatomic distances less than 1.20 times sum of covalent radii
63 internal coordinates being used (instead of 63 Cartesians)
Internal coordinate system (atoms numbered from 1):
Distance 1-2
Distance 1-14
Distance 2-3
Distance 2-4
Distance 4-5
Distance 4-9
Distance 5-6
Distance 5-15
Distance 6-7
Distance 6-16
Distance 7-8
Distance 7-17
Distance 8-9
Distance 8-18
Distance 9-10
Distance 10-11
Distance 11-12
Distance 11-13
Distance 13-19
Distance 13-20
Distance 13-21
Angle 2-1-14
Angle 1-2-4
Angle 3-2-4
Angle 2-4-9
Angle 5-4-9
Angle 4-5-15
Angle 6-5-15
Angle 5-6-16
Angle 7-6-16
Angle 6-7-17
Angle 8-7-17
Angle 7-8-18
Angle 9-8-18
Angle 4-9-10
Angle 8-9-10
Angle 9-10-11
Angle 10-11-13
Angle 12-11-13
Angle 11-13-19
Angle 11-13-20
Angle 11-13-21
Angle 19-13-20
Angle 19-13-21
Angle 20-13-21
Out-of-Plane 2-1-3-4
Out-of-Plane 4-2-5-9
Out-of-Plane 5-4-6-15
Out-of-Plane 6-5-7-16
Out-of-Plane 7-6-8-17
Out-of-Plane 8-7-9-18
Out-of-Plane 9-4-8-10
Out-of-Plane 11-10-12-13
Dihedral 14-1-2-3
Dihedral 14-1-2-4
Dihedral 1-2-4-5
Dihedral 1-2-4-9
Dihedral 3-2-4-5
Dihedral 3-2-4-9
Dihedral 2-4-5-6
Dihedral 2-4-5-15
Dihedral 9-4-5-6
Dihedral 9-4-5-15
Dihedral 2-4-9-8
Dihedral 2-4-9-10
Dihedral 5-4-9-8
Dihedral 5-4-9-10
Dihedral 4-5-6-7
Dihedral 4-5-6-16
Dihedral 15-5-6-7
Dihedral 15-5-6-16
Dihedral 5-6-7-8
Dihedral 5-6-7-17
Dihedral 16-6-7-8
Dihedral 16-6-7-17
Dihedral 6-7-8-9
Dihedral 6-7-8-18
Dihedral 17-7-8-9
Dihedral 17-7-8-18
Dihedral 7-8-9-4
Dihedral 7-8-9-10
Dihedral 18-8-9-4
Dihedral 18-8-9-10
Dihedral 4-9-10-11
Dihedral 8-9-10-11
Dihedral 9-10-11-12
Dihedral 9-10-11-13
Dihedral 10-11-13-19
Dihedral 10-11-13-20
Dihedral 10-11-13-21
Dihedral 12-11-13-19
Dihedral 12-11-13-20
Dihedral 12-11-13-21
Translation-X 1-21
Translation-Y 1-21
Translation-Z 1-21
Rotation-A 1-21
Rotation-B 1-21
Rotation-C 1-21
<class 'geometric.internal.Distance'> : 21
<class 'geometric.internal.Angle'> : 24
<class 'geometric.internal.OutOfPlane'> : 8
<class 'geometric.internal.Dihedral'> : 40
<class 'geometric.internal.TranslationX'> : 1
<class 'geometric.internal.TranslationY'> : 1
<class 'geometric.internal.TranslationZ'> : 1
<class 'geometric.internal.RotationA'> : 1
<class 'geometric.internal.RotationB'> : 1
<class 'geometric.internal.RotationC'> : 1
> ===== Optimization Info: ====
> Job type: Energy minimization
> Maximum number of optimization cycles: 300
> Initial / maximum trust radius (Angstrom): 0.100 / 0.300
> Convergence Criteria:
> Will converge when all 5 criteria are reached:
> |Delta-E| < 1.00e-06
> RMS-Grad < 3.00e-04
> Max-Grad < 4.50e-04
> RMS-Disp < 1.20e-03
> Max-Disp < 1.80e-03
> === End Optimization Info ===
Performing geometry optimization (this may take some time)...
Geometry optimization cycle 1
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
O 13.907000 16.130000 0.624000 -0.000000 0.000000 0.000000
C 13.254000 15.778000 1.723000 0.000000 0.000000 0.000000
O 13.911000 15.759000 2.749000 0.000000 0.000000 -0.000000
C 11.830000 15.316000 1.664000 0.000000 0.000000 0.000000
C 11.114000 15.381000 0.456000 0.000000 0.000000 0.000000
C 9.774000 15.001000 0.429000 0.000000 0.000000 0.000000
C 9.120000 14.601000 1.580000 0.000000 -0.000000 0.000000
C 9.752000 14.568000 2.802000 0.000000 0.000000 0.000000
C 11.088000 14.922000 2.923000 0.000000 0.000000 0.000000
O 11.823000 14.906000 4.090000 0.000000 0.000000 0.000000
C 12.477000 13.770000 4.769000 0.000000 0.000000 0.000000
O 12.686000 13.870000 5.971000 0.000000 0.000000 0.000000
C 12.890000 12.509000 4.056000 0.000000 0.000000 0.000000
H 13.394000 16.144000 -0.175000 0.000000 0.000000 0.000000
H 11.602000 15.729000 -0.469000 0.000000 0.000000 0.000000
H 9.219000 15.017000 -0.524000 -0.000000 0.000000 0.000000
H 8.060000 14.298000 1.521000 0.000000 0.000000 -0.000000
H 9.182000 14.254000 3.693000 0.000000 0.000000 0.000000
H 13.384000 11.651000 4.568000 0.000000 0.000000 -0.000000
H 11.987000 12.110000 3.536000 0.000000 0.000000 0.000000
H 13.544000 12.808000 3.204000 -0.000000 0.000000 0.000000
converged SCF energy = -644.59835884967
--------------- RHF_Scanner gradients ---------------
x y z
0 O 0.0077066244 -0.0080762717 0.0352394550
1 C -0.0082593893 0.0232080256 -0.0543968146
2 O 0.0089199032 -0.0004100472 0.0077272459
3 C 0.0350278833 -0.0054873925 -0.0286106109
4 C -0.0104035920 0.0020038214 -0.0142259932
5 C 0.0129108701 -0.0003903338 0.0238740981
6 C 0.0236588736 0.0028974060 0.0187973309
7 C -0.0082295442 0.0055352649 -0.0423792636
8 C -0.0502668156 -0.0029301814 0.0706972187
9 O 0.0010715863 0.0443684306 -0.0265716327
10 C -0.0075913411 -0.0073478077 -0.0569618070
11 O 0.0159323247 -0.0152545519 0.0488097448
12 C 0.0141653948 0.0012185458 0.0691666098
13 H -0.0071411222 -0.0026661848 0.0031722420
14 H 0.0126955352 0.0083354671 -0.0159984813
15 H -0.0113871805 -0.0005867260 -0.0181183866
16 H -0.0211480252 -0.0066995958 -0.0010669822
17 H -0.0140852288 -0.0070342709 0.0152067942
18 H 0.0136980946 -0.0341567810 -0.0081995172
19 H -0.0138820124 -0.0020322586 -0.0102612489
20 H 0.0066071612 0.0055054418 -0.0159000014
----------------------------------------------
cycle 1: E = -644.59835885 dE = -644.598 norm(grad) = 0.190974
Step 0 : Gradient = 4.167e-02/8.680e-02 (rms/max) Energy = -644.5983588497
Hessian Eigenvalues: 2.30000e-02 2.30000e-02 2.30000e-02 ... 6.04748e-01 9.35782e-01 9.60601e-01
Geometry optimization cycle 2
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
O 13.887728 16.087817 0.623270 -0.019272 -0.042183 -0.000730
C 13.291734 15.736841 1.779615 0.037734 -0.041159 0.056615
O 13.920391 15.706813 2.817142 0.009391 -0.052187 0.068142
C 11.868087 15.289830 1.705949 0.038087 -0.026170 0.041949
C 11.124937 15.330293 0.530331 0.010937 -0.050707 0.074331
C 9.787678 14.959117 0.455237 0.013678 -0.041883 0.026237
C 9.149625 14.567953 1.612511 0.029625 -0.033047 0.032511
C 9.823010 14.554864 2.825504 0.071010 -0.013136 0.023504
C 11.148110 14.915889 2.905704 0.060110 -0.006111 -0.017296
O 11.822241 14.903732 4.095607 -0.000759 -0.002268 0.005607
C 12.418901 13.788919 4.737648 -0.058099 0.018919 -0.031352
O 12.557183 13.888964 5.927418 -0.128817 0.018964 -0.043582
C 12.827769 12.599799 3.932242 -0.062231 0.090799 -0.123758
H 13.356658 16.103139 -0.162917 -0.037342 -0.040861 0.012083
H 11.597742 15.663792 -0.384385 -0.004258 -0.065208 0.084615
H 9.255895 14.975246 -0.488452 0.036895 -0.041754 0.035548
H 8.109129 14.267222 1.578494 0.049129 -0.030778 0.057494
H 9.297572 14.260229 3.726161 0.115572 0.006229 0.033161
H 13.284117 11.766941 4.462683 -0.099883 0.115941 -0.105317
H 11.958136 12.225292 3.372224 -0.028864 0.115292 -0.163776
H 13.511357 12.929308 3.138014 -0.032643 0.121308 -0.065986
converged SCF energy = -644.630341823445
--------------- RHF_Scanner gradients ---------------
x y z
0 O -0.0042347351 -0.0051297160 0.0020894250
1 C 0.0060749775 0.0177140227 -0.0184511568
2 O -0.0048697580 -0.0054403830 0.0197893337
3 C 0.0316638257 -0.0047878202 -0.0241791846
4 C -0.0108674790 -0.0029537322 0.0116857059
5 C -0.0009605749 -0.0003034364 0.0024754355
6 C 0.0122269267 0.0030057686 0.0019275145
7 C 0.0068753960 0.0040804477 -0.0149823585
8 C -0.0343131076 0.0007430473 0.0397635791
9 O 0.0065020139 0.0227091106 -0.0144821310
10 C 0.0013515999 -0.0122293887 -0.0210026411
11 O -0.0010362496 0.0016354384 0.0076702464
12 C 0.0079993507 -0.0023399170 0.0421789372
13 H -0.0031493368 -0.0010710496 -0.0009992973
14 H 0.0052545768 0.0035678300 -0.0039308840
15 H -0.0058884377 -0.0010672346 -0.0073580413
16 H -0.0078049600 -0.0026254150 -0.0012950929
17 H -0.0059114003 -0.0032301738 0.0057110730
18 H 0.0056280420 -0.0149341395 -0.0076046824
19 H -0.0057740025 0.0002462104 -0.0085279621
20 H 0.0012333323 0.0024105303 -0.0104778184
----------------------------------------------
cycle 2: E = -644.630341823 dE = -0.031983 norm(grad) = 0.101919
Step 1 : Displace = 1.047e-01/2.024e-01 (rms/max) Trust = 1.000e-01 (=) Grad = 2.224e-02/5.253e-02 (rms/max) E (change) = -644.6303418234 (-3.198e-02) Quality = 0.889
Hessian Eigenvalues: 2.29704e-02 2.30000e-02 2.30000e-02 ... 6.53380e-01 9.29238e-01 9.76077e-01
Geometry optimization cycle 3
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
O 13.901368 16.066581 0.586212 0.013640 -0.021236 -0.037058
C 13.303520 15.682953 1.748341 0.011786 -0.053888 -0.031274
O 14.102437 15.700339 2.646360 0.182046 -0.006474 -0.170781
C 11.871823 15.239259 1.764365 0.003736 -0.050571 0.058416
C 11.169410 15.296172 0.573619 0.044473 -0.034122 0.043288
C 9.836854 14.920838 0.533108 0.049176 -0.038280 0.077871
C 9.162985 14.516687 1.665782 0.013360 -0.051266 0.053271
C 9.860269 14.502560 2.870986 0.037259 -0.052303 0.045482
C 11.181931 14.869199 2.909570 0.033821 -0.046690 0.003866
O 11.753933 14.857266 4.150243 -0.068307 -0.046467 0.054636
C 12.302678 13.784058 4.782064 -0.116223 -0.004861 0.044416
O 12.412554 13.720539 5.961909 -0.144629 -0.168425 0.034491
C 12.740904 12.744318 3.824770 -0.086865 0.144520 -0.107472
H 13.387338 16.116183 -0.206423 0.030680 0.013044 -0.043506
H 11.623345 15.618032 -0.334724 0.025602 -0.045760 0.049661
H 9.325776 14.947453 -0.397737 0.069881 -0.027794 0.090715
H 8.139914 14.227102 1.630134 0.030785 -0.040119 0.051641
H 9.376785 14.223893 3.776492 0.079214 -0.036336 0.050331
H 13.167893 11.930551 4.358583 -0.116224 0.163610 -0.104101
H 11.918807 12.400359 3.213512 -0.039330 0.175067 -0.158712
H 13.457474 13.157659 3.132833 -0.053883 0.228351 -0.005181
converged SCF energy = -644.629042111964
--------------- RHF_Scanner gradients ---------------
x y z
0 O 0.0210108707 -0.0016516759 0.0236810792
1 C -0.0280616440 0.0007972413 -0.0004064105
2 O 0.0161110118 0.0114251554 -0.0357783956
3 C -0.0206562187 -0.0220698456 0.0095952666
4 C 0.0164976078 0.0088456874 -0.0038770105
5 C 0.0017580884 -0.0016350089 0.0119293474
6 C -0.0162842868 -0.0021076642 -0.0120399046
7 C 0.0163878443 0.0008511323 0.0142922498
8 C -0.0028103075 0.0062279424 -0.0044763548
9 O 0.0017387305 -0.0253940392 -0.0184495700
10 C -0.0073422309 0.0147459339 0.0296660513
11 O 0.0020438837 -0.0097257334 -0.0227315948
12 C -0.0016316139 0.0069754719 0.0098319668
13 H -0.0011423591 -0.0015831525 0.0029541457
14 H -0.0005649170 0.0002715948 0.0027262876
15 H 0.0041085304 -0.0009003423 0.0072495681
16 H 0.0054662638 0.0010461195 0.0008679362
17 H 0.0015536550 0.0007173019 -0.0057826990
18 H -0.0048137192 0.0094312361 -0.0034789668
19 H 0.0023985000 0.0041938689 -0.0030667918
20 H -0.0057676892 -0.0004612237 -0.0027062004
----------------------------------------------
cycle 3: E = -644.629042112 dE = 0.00129971 norm(grad) = 0.0959025
Step 2 : Displace = 1.416e-01/2.500e-01 (rms/max) Trust = 1.414e-01 (+) Grad = 2.093e-02/4.087e-02 (rms/max) E (change) = -644.6290421120 (+1.300e-03) Quality = -0.059
Hessian Eigenvalues: 2.29631e-02 2.30000e-02 2.30000e-02 ... 8.95559e-01 9.40628e-01 1.05154e+00
Geometry optimization cycle 4
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
O 13.876008 16.070512 0.582825 -0.025360 0.003932 -0.003387
C 13.302911 15.674573 1.756347 -0.000609 -0.008380 0.008005
O 14.031557 15.636995 2.715706 -0.070880 -0.063344 0.069346
C 11.868039 15.252747 1.732587 -0.003784 0.013488 -0.031778
C 11.146783 15.321916 0.545367 -0.022627 0.025745 -0.028252
C 9.811166 14.958422 0.500023 -0.025689 0.037584 -0.033085
C 9.152758 14.549756 1.642980 -0.010227 0.033069 -0.022801
C 9.850899 14.516969 2.843927 -0.009370 0.014408 -0.027059
C 11.181273 14.873805 2.883516 -0.000659 0.004606 -0.026055
O 11.768763 14.851888 4.124673 0.014830 -0.005378 -0.025570
C 12.331898 13.778404 4.767184 0.029220 -0.005654 -0.014880
O 12.418853 13.792841 5.958283 0.006299 0.072302 -0.003626
C 12.796489 12.687177 3.869630 0.055585 -0.057141 0.044860
H 13.345979 16.135093 -0.198587 -0.041359 0.018910 0.007836
H 11.596836 15.648853 -0.365359 -0.026509 0.030820 -0.030634
H 9.291588 14.997618 -0.430112 -0.034188 0.050165 -0.032375
H 8.124401 14.267210 1.614166 -0.015513 0.040108 -0.015969
H 9.367077 14.232985 3.751119 -0.009708 0.009092 -0.025372
H 13.224217 11.904339 4.457435 0.056324 -0.026211 0.098852
H 11.986144 12.299522 3.267738 0.067337 -0.100837 0.054226
H 13.524360 13.070376 3.170550 0.066886 -0.087283 0.037716
converged SCF energy = -644.64002379418
--------------- RHF_Scanner gradients ---------------
x y z
0 O 0.0050291094 -0.0010770078 -0.0000768337
1 C -0.0094588660 0.0051243508 0.0023054543
2 O 0.0058416881 0.0028586701 -0.0052911382
3 C -0.0077897484 -0.0161396336 0.0038283473
4 C 0.0094280382 0.0064325620 -0.0032742721
5 C -0.0010759759 -0.0015272725 0.0066534438
6 C -0.0091910647 -0.0005421665 -0.0087227488
7 C 0.0098846343 -0.0000316583 0.0097434028
8 C -0.0043321077 0.0085430050 -0.0034328530
9 O 0.0036127533 -0.0127612699 -0.0066577891
10 C -0.0028191447 0.0026762900 0.0108935572
11 O -0.0009166542 -0.0014852311 -0.0081468751
12 C 0.0005006420 0.0010807245 0.0070418016
13 H -0.0003888044 -0.0008905135 -0.0000965606
14 H -0.0006091641 0.0004456207 0.0020603074
15 H 0.0024864567 -0.0007875046 0.0040219925
16 H 0.0035680799 0.0005317539 0.0005998332
17 H 0.0007400775 0.0002562350 -0.0035567660
18 H -0.0027063596 0.0053535683 -0.0026082600
19 H 0.0026233654 0.0027677783 -0.0027001228
20 H -0.0044269553 -0.0008283008 -0.0025839207
----------------------------------------------
cycle 4: E = -644.640023794 dE = -0.0109817 norm(grad) = 0.0426708
Step 3 : Displace = 6.803e-02/1.335e-01 (rms/max) Trust = 7.071e-02 (-) Grad = 9.312e-03/1.833e-02 (rms/max) E (change) = -644.6400237942 (-1.098e-02) Quality = 0.936
Hessian Eigenvalues: 2.29390e-02 2.30000e-02 2.30000e-02 ... 9.18311e-01 9.39256e-01 1.18565e+00
Geometry optimization cycle 5
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
O 13.955435 16.038391 0.699322 0.079427 -0.032121 0.116497
C 13.289309 15.592589 1.797103 -0.013603 -0.081984 0.040756
O 13.956025 15.473408 2.793691 -0.075533 -0.163587 0.077985
C 11.839898 15.245746 1.688972 -0.028142 -0.007001 -0.043615
C 11.070174 15.312609 0.523308 -0.076609 -0.009307 -0.022059
C 9.727935 14.985408 0.447884 -0.083231 0.026986 -0.052139
C 9.104056 14.587878 1.618411 -0.048703 0.038122 -0.024570
C 9.808467 14.533366 2.809009 -0.042432 0.016397 -0.034918
C 11.153236 14.863491 2.849074 -0.028036 -0.010313 -0.034442
O 11.762728 14.861292 4.085450 -0.006036 0.009404 -0.039223
C 12.377703 13.803814 4.733377 0.045805 0.025409 -0.033807
O 12.477203 13.864384 5.927885 0.058350 0.071543 -0.030398
C 12.877736 12.683518 3.879169 0.081247 -0.003659 0.009539
H 13.482326 16.187434 -0.106066 0.136347 0.052341 0.092520
H 11.518934 15.625796 -0.396640 -0.077902 -0.023057 -0.031281
H 9.197283 15.041109 -0.482985 -0.094305 0.043491 -0.052873
H 8.064002 14.326628 1.609617 -0.060399 0.059418 -0.004548
H 9.323938 14.260362 3.725196 -0.043139 0.027377 -0.025924
H 13.336003 11.936732 4.506749 0.111786 0.032393 0.049314
H 12.071486 12.235152 3.309503 0.085342 -0.064370 0.041766
H 13.604125 13.062894 3.171971 0.079765 -0.007482 0.001421
converged SCF energy = -644.639799546805
--------------- RHF_Scanner gradients ---------------
x y z
0 O 0.0068218389 -0.0010103985 0.0055510841
1 C -0.0078933416 -0.0016597115 0.0085568068
2 O 0.0030881531 0.0041600705 -0.0048038665
3 C 0.0111069223 -0.0020975225 -0.0116601277
4 C -0.0133915481 -0.0041610680 0.0164228477
5 C -0.0079908819 0.0005202483 -0.0121641466
6 C 0.0075227016 0.0025767209 -0.0016535335
7 C 0.0008345268 -0.0009820370 0.0001188793
8 C -0.0050916323 0.0049646460 -0.0001667162
9 O 0.0097993570 0.0012711632 -0.0034264353
10 C -0.0019959534 -0.0029251257 -0.0006793375
11 O -0.0007416361 0.0004593540 0.0022474724
12 C 0.0009869749 -0.0000323148 0.0043512216
13 H 0.0030654595 -0.0008673012 0.0023978506
14 H -0.0049120769 -0.0008004138 0.0017552489
15 H -0.0015469525 -0.0004876277 -0.0017344752
16 H 0.0002783023 0.0000490616 -0.0007307797
17 H -0.0003083160 -0.0002555425 0.0004125072
18 H 0.0007198524 -0.0004825152 -0.0000998348
19 H 0.0001232096 0.0007930735 -0.0017689993
20 H -0.0004749592 0.0009672404 -0.0029256664
----------------------------------------------
cycle 5: E = -644.639799547 dE = 0.000224247 norm(grad) = 0.0392387
Step 4 : Displace = 1.014e-01/1.938e-01 (rms/max) Trust = 1.000e-01 (+) Grad = 8.563e-03/2.160e-02 (rms/max) E (change) = -644.6397995468 (+2.242e-04) Quality = -0.055
Hessian Eigenvalues: 2.09240e-02 2.29991e-02 2.30000e-02 ... 9.28905e-01 1.00469e+00 1.08567e+00
Geometry optimization cycle 6
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
O 13.880660 16.059960 0.620659 -0.074774 0.021569 -0.078663
C 13.292799 15.606528 1.758769 0.003490 0.013939 -0.038333
O 13.984774 15.485444 2.737852 0.028749 0.012037 -0.055839
C 11.845886 15.248734 1.705014 0.005988 0.002988 0.016042
C 11.106648 15.333473 0.523073 0.036473 0.020864 -0.000235
C 9.765736 15.003681 0.453806 0.037802 0.018273 0.005922
C 9.122170 14.593866 1.611990 0.018114 0.005988 -0.006421
C 9.813127 14.526635 2.808201 0.004660 -0.006730 -0.000808
C 11.158832 14.855008 2.864951 0.005596 -0.008483 0.015878
O 11.754567 14.844848 4.107840 -0.008160 -0.016444 0.022390
C 12.365693 13.784950 4.756851 -0.012010 -0.018864 0.023474
O 12.452971 13.845060 5.952173 -0.024231 -0.019324 0.024288
C 12.876294 12.662372 3.910168 -0.001442 -0.021146 0.030998
H 13.352545 16.200317 -0.152644 -0.129782 0.012882 -0.046578
H 11.568862 15.654506 -0.389687 0.049928 0.028710 0.006953
H 9.240071 15.067370 -0.479242 0.042788 0.026262 0.003743
H 8.081066 14.334695 1.587386 0.017064 0.008067 -0.022231
H 9.319341 14.246108 3.717529 -0.004597 -0.014255 -0.007667
H 13.327315 11.917816 4.547154 -0.008688 -0.018916 0.040406
H 12.075947 12.210542 3.334773 0.004461 -0.024610 0.025270
H 13.612696 13.040087 3.213383 0.008571 -0.022807 0.041412
converged SCF energy = -644.64297212751
--------------- RHF_Scanner gradients ---------------
x y z
0 O 0.0005503326 -0.0007864461 -0.0004735939
1 C 0.0000605210 0.0010951415 0.0031776917
2 O -0.0016644381 0.0019638126 -0.0005403400
3 C 0.0051247133 -0.0043011583 -0.0060814081
4 C -0.0028405972 0.0006978641 0.0057794855
5 C -0.0025949452 0.0003874414 -0.0049563724
6 C 0.0039432296 0.0012002222 0.0008348553
7 C -0.0005647097 -0.0009048725 -0.0016997783
8 C -0.0050340575 0.0032602282 0.0057860156
9 O 0.0061688309 0.0008310514 -0.0009686962
10 C -0.0016904070 -0.0025033249 -0.0012893516
11 O -0.0010069930 0.0005319642 0.0017240546
12 C 0.0012609872 -0.0005786563 0.0034092023
13 H 0.0004704578 -0.0009265770 -0.0004102328
14 H -0.0010183361 0.0008191747 -0.0002933455
15 H -0.0005084220 -0.0002639987 -0.0014044431
16 H -0.0005655346 -0.0002660277 -0.0001958426
17 H -0.0003531832 -0.0002665107 0.0005267979
18 H 0.0009935250 -0.0009921525 0.0002436131
19 H -0.0002114558 0.0004518774 -0.0013397220
20 H -0.0005195182 0.0005509469 -0.0018285892
----------------------------------------------
cycle 6: E = -644.642972128 dE = -0.00317258 norm(grad) = 0.0186603
Step 5 : Displace = 5.318e-02/1.380e-01 (rms/max) Trust = 5.000e-02 (-) Grad = 4.072e-03/9.041e-03 (rms/max) E (change) = -644.6429721275 (-3.173e-03) Quality = 0.903
Hessian Eigenvalues: 2.09223e-02 2.29993e-02 2.30000e-02 ... 9.29249e-01 1.05179e+00 1.19928e+00
Geometry optimization cycle 7
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
O 13.879653 16.105494 0.659777 -0.001008 0.045534 0.039119
C 13.303626 15.543289 1.754697 0.010827 -0.063239 -0.004073
O 13.993936 15.300262 2.713024 0.009162 -0.185182 -0.024828
C 11.845772 15.235396 1.687060 -0.000114 -0.013338 -0.017954
C 11.118110 15.325504 0.498194 0.011462 -0.007969 -0.024880
C 9.774344 15.003342 0.470683 0.008608 -0.000339 0.016877
C 9.099890 14.590720 1.610651 -0.022281 -0.003146 -0.001339
C 9.801871 14.511087 2.797847 -0.011255 -0.015549 -0.010354
C 11.151738 14.827090 2.829414 -0.007095 -0.027918 -0.035537
O 11.733303 14.846782 4.077615 -0.021264 0.001934 -0.030225
C 12.381314 13.819461 4.738871 0.015621 0.034511 -0.017981
O 12.505900 13.917457 5.927656 0.052929 0.072397 -0.024518
C 12.873704 12.670001 3.916531 -0.002590 0.007629 0.006363
H 13.336353 16.365520 -0.070618 -0.016192 0.165203 0.082027
H 11.579702 15.626010 -0.421182 0.010840 -0.028496 -0.031495
H 9.244738 15.077557 -0.457389 0.004667 0.010186 0.021853
H 8.055307 14.350118 1.579931 -0.025759 0.015423 -0.007454
H 9.319249 14.240160 3.715064 -0.000092 -0.005948 -0.002465
H 13.339906 11.957543 4.576938 0.012591 0.039727 0.029784
H 12.061040 12.187618 3.387951 -0.014907 -0.022924 0.053178
H 13.598546 13.021591 3.197285 -0.014149 -0.018496 -0.016099
converged SCF energy = -644.644200175235
--------------- RHF_Scanner gradients ---------------
x y z
0 O -0.0018980364 0.0013059855 -0.0037631630
1 C 0.0043098876 -0.0022797858 0.0025027301
2 O -0.0042178634 0.0001259381 0.0039237191
3 C 0.0005910444 0.0000793331 -0.0006693443
4 C 0.0021317857 0.0039732583 -0.0060593823
5 C 0.0057758309 -0.0010328345 0.0112639342
6 C -0.0076953300 -0.0012748401 -0.0013680729
7 C 0.0010098734 -0.0004847777 0.0007110476
8 C -0.0021690047 -0.0009074669 -0.0036115471
9 O 0.0028071749 0.0015753357 -0.0040456916
10 C -0.0019246376 -0.0010004834 0.0015052348
11 O -0.0009020083 -0.0003444431 -0.0004065007
12 C 0.0009562496 0.0001935417 -0.0002675589
13 H 0.0016969145 -0.0014530743 -0.0006440058
14 H -0.0002505036 0.0007826883 -0.0001187819
15 H 0.0006314950 -0.0001082279 0.0010274442
16 H -0.0008374111 -0.0003870830 0.0008989809
17 H -0.0008702443 -0.0000143354 -0.0001896157
18 H 0.0003390303 0.0003670321 0.0000176386
19 H 0.0002227817 0.0000730410 0.0001548133
20 H 0.0002929715 0.0008111980 -0.0008618787
----------------------------------------------
cycle 7: E = -644.644200175 dE = -0.00122805 norm(grad) = 0.0207981
Step 6 : Displace = 7.042e-02/1.858e-01 (rms/max) Trust = 7.071e-02 (+) Grad = 4.539e-03/1.270e-02 (rms/max) E (change) = -644.6442001752 (-1.228e-03) Quality = 0.782
Hessian Eigenvalues: 5.76773e-03 2.29931e-02 2.29998e-02 ... 9.30423e-01 1.06722e+00 1.19714e+00
Geometry optimization cycle 8
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
O 13.825912 16.242233 0.637630 -0.053741 0.136739 -0.022147
C 13.315505 15.564083 1.697472 0.011879 0.020794 -0.057224
O 14.065933 15.245372 2.587169 0.071997 -0.054890 -0.125855
C 11.858170 15.243668 1.675354 0.012398 0.008272 -0.011705
C 11.126339 15.327623 0.486890 0.008229 0.002120 -0.011304
C 9.785767 14.998364 0.445245 0.011423 -0.004978 -0.025438
C 9.136167 14.574439 1.595018 0.036278 -0.016281 -0.015633
C 9.840692 14.487659 2.780373 0.038821 -0.023428 -0.017475
C 11.189359 14.806958 2.815391 0.037621 -0.020131 -0.014024
O 11.759165 14.841961 4.068867 0.025862 -0.004821 -0.008748
C 12.407097 13.828671 4.748942 0.025783 0.009210 0.010072
O 12.584619 13.984763 5.924315 0.078718 0.067306 -0.003341
C 12.812297 12.611383 3.976845 -0.061407 -0.058618 0.060314
H 13.235116 16.589487 -0.015687 -0.101237 0.223968 0.054930
H 11.593458 15.627074 -0.428897 0.013756 0.001063 -0.007714
H 9.250193 15.074929 -0.478373 0.005455 -0.002628 -0.020984
H 8.094081 14.328923 1.570909 0.038775 -0.021195 -0.009022
H 9.363235 14.208761 3.696788 0.043986 -0.031399 -0.018275
H 13.267320 11.923730 4.668683 -0.072587 -0.033813 0.091745
H 11.957807 12.132541 3.518095 -0.103233 -0.055076 0.130143
H 13.529769 12.879377 3.218970 -0.068777 -0.142214 0.021686
converged SCF energy = -644.646482230912
--------------- RHF_Scanner gradients ---------------
x y z
0 O -0.0011472387 0.0013876674 -0.0013495901
1 C 0.0015739338 -0.0027894973 -0.0022112396
2 O 0.0006006449 0.0030233211 0.0016886757
3 C -0.0046808849 0.0013220671 0.0060433285
4 C 0.0016137011 0.0025275831 -0.0028248820
5 C 0.0012556225 -0.0003586758 0.0032274255
6 C -0.0019817731 0.0000355396 -0.0010740402
7 C 0.0003205054 0.0002699192 0.0025095441
8 C 0.0035727701 -0.0039283896 -0.0055627464
9 O -0.0019092411 0.0008562867 -0.0004425666
10 C 0.0001757392 -0.0004978109 0.0005882520
11 O -0.0019122441 0.0000325884 -0.0013779114
12 C 0.0009111133 -0.0012259781 -0.0033343585
13 H 0.0016855618 -0.0020072010 -0.0008417088
14 H -0.0011568022 0.0003888497 0.0003993167
15 H 0.0005061554 0.0001503732 0.0010427686
16 H 0.0007197227 0.0001379118 0.0001960257
17 H 0.0003851455 0.0002613467 -0.0003021029
18 H -0.0005812367 0.0012540391 -0.0002656119
19 H 0.0003540635 -0.0005230881 0.0017035720
20 H -0.0003052585 -0.0003168524 0.0021878496
----------------------------------------------
cycle 8: E = -644.646482231 dE = -0.00228206 norm(grad) = 0.0154428
Step 7 : Displace = 1.026e-01/2.468e-01 (rms/max) Trust = 1.000e-01 (+) Grad = 3.370e-03/7.758e-03 (rms/max) E (change) = -644.6464822309 (-2.282e-03) Quality = 0.984
Hessian Eigenvalues: 4.66789e-03 2.29998e-02 2.30002e-02 ... 9.29352e-01 1.12749e+00 1.26015e+00
Geometry optimization cycle 9
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
O 13.765479 16.360741 0.712917 -0.060433 0.118508 0.075287
C 13.319217 15.508563 1.666013 0.003713 -0.055520 -0.031459
O 14.107991 15.011163 2.433867 0.042058 -0.234209 -0.153302
C 11.860181 15.218118 1.675350 0.002012 -0.025550 -0.000004
C 11.144010 15.279417 0.474945 0.017671 -0.048206 -0.011945
C 9.802732 14.961135 0.401508 0.016966 -0.037229 -0.043737
C 9.163906 14.564668 1.569120 0.027738 -0.009771 -0.025898
C 9.847942 14.492924 2.767842 0.007250 0.005266 -0.012530
C 11.199081 14.802270 2.826435 0.009722 -0.004688 0.011044
O 11.777059 14.867970 4.077275 0.017895 0.026009 0.008408
C 12.468997 13.877839 4.747376 0.061900 0.049168 -0.001566
O 12.784208 14.055388 5.891539 0.199590 0.070625 -0.032776
C 12.750747 12.618230 3.988481 -0.061550 0.006847 0.011635
H 13.124593 16.877547 0.241998 -0.110522 0.288060 0.257685
H 11.649563 15.535683 -0.435130 0.056105 -0.091391 -0.006233
H 9.274856 15.016905 -0.529321 0.024663 -0.058024 -0.050948
H 8.120537 14.323383 1.543166 0.026456 -0.005540 -0.027743
H 9.353387 14.231767 3.680736 -0.009848 0.023006 -0.016053
H 13.243204 11.935868 4.661871 -0.024115 0.012138 -0.006812
H 11.836165 12.158261 3.638008 -0.121642 0.025720 0.119913
H 13.404145 12.824158 3.156004 -0.125625 -0.055219 -0.062966
converged SCF energy = -644.649130588746
--------------- RHF_Scanner gradients ---------------
x y z
0 O -0.0030178454 0.0006138127 -0.0004041548
1 C 0.0015241671 -0.0010313803 -0.0056606095
2 O 0.0005877234 -0.0004774756 0.0032812418
3 C -0.0041291419 0.0029822123 0.0070336149
4 C -0.0020083872 0.0008493340 0.0038772882
5 C -0.0036871982 0.0011567315 -0.0088497187
6 C 0.0071391782 0.0009676407 0.0021694365
7 C -0.0031753865 -0.0001413679 -0.0016810524
8 C 0.0064433357 -0.0062613985 0.0008447955
9 O -0.0015148749 -0.0013201165 -0.0029988123
10 C -0.0033415966 0.0084510155 0.0024570191
11 O 0.0028277230 -0.0066605483 0.0024544871
12 C -0.0003525448 0.0020210284 -0.0039981969
13 H 0.0014336751 -0.0013276027 -0.0009024943
14 H -0.0017250330 -0.0011050971 -0.0002814907
15 H -0.0003302121 0.0004233667 -0.0005245386
16 H 0.0010846334 0.0005686878 -0.0009532442
17 H 0.0014756300 0.0004781035 0.0003381792
18 H -0.0002413640 0.0005120127 0.0002113050
19 H 0.0000956535 -0.0006378363 0.0020685221
20 H 0.0009118652 -0.0000611226 0.0015184230
----------------------------------------------
cycle 9: E = -644.649130589 dE = -0.00264836 norm(grad) = 0.0244679
Step 8 : Displace = 1.396e-01/3.986e-01 (rms/max) Trust = 1.414e-01 (+) Grad = 5.339e-03/9.657e-03 (rms/max) E (change) = -644.6491305887 (-2.648e-03) Quality = 0.809
Hessian Eigenvalues: 3.41395e-03 2.09769e-02 2.30001e-02 ... 9.46592e-01 1.14215e+00 1.23708e+00
Geometry optimization cycle 10
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
O 13.718378 16.601673 0.852722 -0.047100 0.240932 0.139805
C 13.333941 15.551836 1.609079 0.014724 0.043273 -0.056935
O 14.176926 14.917828 2.197915 0.068936 -0.093336 -0.235952
C 11.885909 15.231501 1.619901 0.025728 0.013383 -0.055449
C 11.167061 15.251933 0.422104 0.023052 -0.027485 -0.052841
C 9.832941 14.894050 0.386350 0.030209 -0.067084 -0.015158
C 9.193145 14.509000 1.560232 0.029239 -0.055668 -0.008888
C 9.893302 14.479954 2.751626 0.045360 -0.012971 -0.016216
C 11.239328 14.817890 2.782963 0.040247 0.015619 -0.043472
O 11.864631 14.900860 4.011259 0.087572 0.032890 -0.066017
C 12.569374 13.907524 4.663900 0.100377 0.029686 -0.083476
O 13.062875 14.221736 5.711898 0.278667 0.166348 -0.179640
C 12.605547 12.539355 4.052884 -0.145200 -0.078875 0.064403
H 13.044092 17.236822 0.637141 -0.080501 0.359275 0.395143
H 11.678368 15.488530 -0.492970 0.028805 -0.047153 -0.057840
H 9.296298 14.909849 -0.541937 0.021443 -0.107056 -0.012615
H 8.153962 14.242750 1.543101 0.033425 -0.080633 -0.000066
H 9.415246 14.220099 3.674765 0.061859 -0.011668 -0.005970
H 13.122231 11.882379 4.736392 -0.120973 -0.053489 0.074521
H 11.604657 12.155665 3.895432 -0.231508 -0.002596 0.257424
H 13.139788 12.560766 3.115242 -0.264356 -0.263392 -0.040763
converged SCF energy = -644.650368151425
--------------- RHF_Scanner gradients ---------------
x y z
0 O 0.0027585235 -0.0053731964 0.0036903313
1 C -0.0079519678 0.0032699682 -0.0077476419
2 O 0.0050666136 0.0030442480 0.0000192325
3 C 0.0019714654 0.0052307310 0.0006397721
4 C -0.0032998318 0.0018591949 -0.0001220110
5 C 0.0026681305 0.0011684081 -0.0014977569
6 C -0.0003843049 -0.0014528092 0.0038090021
7 C -0.0034851725 0.0003938501 -0.0038905926
8 C 0.0047783779 -0.0051135637 0.0036714229
9 O 0.0016568811 0.0016717155 0.0083506343
10 C -0.0009804007 -0.0045224933 -0.0081212065
11 O -0.0023422316 0.0064517627 0.0004573192
12 C -0.0009024359 -0.0010104434 -0.0037419118
13 H -0.0000544927 -0.0001887811 0.0015648328
14 H 0.0010631498 -0.0028537396 -0.0011562548
15 H -0.0005077729 0.0003226003 -0.0003310965
16 H -0.0006633878 -0.0000498750 -0.0003844319
17 H 0.0007623850 0.0000521020 0.0003837130
18 H -0.0000239717 -0.0012747792 0.0007405840
19 H -0.0008104044 -0.0011882220 0.0018770093
20 H 0.0006808479 -0.0004366780 0.0017890505
----------------------------------------------
cycle 10: E = -644.650368151 dE = -0.00123756 norm(grad) = 0.0251935
Step 9 : Displace = 2.163e-01/5.280e-01 (rms/max) Trust = 2.000e-01 (+) Grad = 5.498e-03/1.157e-02 (rms/max) E (change) = -644.6503681514 (-1.238e-03) Quality = 0.333
Hessian Eigenvalues: 8.15754e-03 1.81599e-02 2.30002e-02 ... 9.35083e-01 1.12063e+00 1.21828e+00
Geometry optimization cycle 11
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
O 13.725315 16.553205 0.829866 0.006937 -0.048468 -0.022856
C 13.337431 15.554633 1.657532 0.003490 0.002797 0.048453
O 14.165787 14.963071 2.305067 -0.011139 0.045243 0.107152
C 11.891075 15.215560 1.641726 0.005166 -0.015940 0.021825
C 11.184045 15.225248 0.439986 0.016984 -0.026685 0.017881
C 9.849151 14.864380 0.397928 0.016210 -0.029670 0.011578
C 9.201375 14.508676 1.574158 0.008231 -0.000325 0.013926
C 9.879550 14.504586 2.781336 -0.013752 0.024633 0.029709
C 11.221605 14.845111 2.802815 -0.017723 0.027222 0.019852
O 11.853786 14.914917 4.028091 -0.010845 0.014057 0.016833
C 12.548605 13.907322 4.679182 -0.020768 -0.000203 0.015281
O 13.028776 14.159998 5.748308 -0.034099 -0.061738 0.036410
C 12.609745 12.574212 4.004022 0.004198 0.034857 -0.048862
H 13.044547 17.143531 0.524450 0.000455 -0.093290 -0.112691
H 11.692930 15.487945 -0.467887 0.014562 -0.000585 0.025082
H 9.320616 14.864048 -0.534160 0.024318 -0.045801 0.007776
H 8.163957 14.239983 1.551698 0.009995 -0.002767 0.008598
H 9.389009 14.260050 3.701973 -0.026237 0.039951 0.027207
H 13.117823 11.884384 4.657620 -0.004408 0.002005 -0.078772
H 11.617019 12.198404 3.790712 0.012363 0.042739 -0.104721
H 13.155851 12.652736 3.075579 0.016063 0.091970 -0.039662
converged SCF energy = -644.651315336923
--------------- RHF_Scanner gradients ---------------
x y z
0 O 0.0009457569 -0.0028667175 0.0007949800
1 C -0.0026187112 0.0036608134 -0.0009066494
2 O 0.0020613120 0.0003886217 0.0000913846
3 C 0.0025598242 -0.0011373478 0.0001236882
4 C -0.0010106199 -0.0001270629 0.0009804686
5 C -0.0005171342 -0.0002567781 -0.0021214471
6 C 0.0033333878 0.0006677433 0.0007729866
7 C -0.0024123573 -0.0013750890 0.0040929668
8 C -0.0013078194 0.0027136993 -0.0041569159
9 O -0.0009486667 -0.0009847545 -0.0020919041
10 C -0.0009907508 0.0001648471 -0.0003962690
11 O 0.0012106347 -0.0009504656 0.0010935378
12 C 0.0004969682 0.0004511470 0.0004325687
13 H -0.0006015191 0.0001902245 0.0000804084
14 H 0.0003555981 0.0002261128 0.0001990814
15 H -0.0000289730 0.0001559149 -0.0000578809
16 H 0.0004206058 0.0000604356 0.0001238875
17 H -0.0000971164 -0.0003681235 0.0004257607
18 H -0.0000892276 -0.0002977356 -0.0000620123
19 H -0.0002099587 -0.0000354826 0.0000913583
20 H -0.0005512334 -0.0002800022 0.0004900012
----------------------------------------------
cycle 11: E = -644.651315337 dE = -0.000947185 norm(grad) = 0.0112456
Step 10 : Displace = 6.690e-02/1.428e-01 (rms/max) Trust = 2.000e-01 (=) Grad = 2.454e-03/5.134e-03 (rms/max) E (change) = -644.6513153369 (-9.472e-04) Quality = 0.814
Hessian Eigenvalues: 8.11180e-03 1.91140e-02 2.23785e-02 ... 9.40091e-01 1.08443e+00 1.22557e+00
Geometry optimization cycle 12
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
O 13.740265 16.470453 0.845753 0.014950 -0.082752 0.015887
C 13.326309 15.470228 1.663589 -0.011121 -0.084405 0.006057
O 14.134635 14.851869 2.308547 -0.031153 -0.111202 0.003479
C 11.867263 15.178773 1.654519 -0.023812 -0.036787 0.012793
C 11.164412 15.214806 0.450303 -0.019633 -0.010442 0.010318
C 9.819244 14.894267 0.395717 -0.029907 0.029887 -0.002210
C 9.148690 14.553311 1.561136 -0.052686 0.044635 -0.013022
C 9.841125 14.532741 2.761198 -0.038426 0.028155 -0.020137
C 11.191838 14.828428 2.816174 -0.029768 -0.016683 0.013359
O 11.805816 14.897714 4.051922 -0.047970 -0.017203 0.023831
C 12.524637 13.906157 4.702751 -0.023969 -0.001164 0.023569
O 12.927899 14.151317 5.803785 -0.100878 -0.008682 0.055477
C 12.712311 12.608026 3.984684 0.102566 0.033815 -0.019338
H 13.076552 17.075426 0.533375 0.032005 -0.068106 0.008925
H 11.679337 15.478061 -0.453078 -0.013593 -0.009885 0.014810
H 9.300316 14.914664 -0.541097 -0.020300 0.050617 -0.006937
H 8.103643 14.316243 1.538731 -0.060313 0.076260 -0.012968
H 9.335646 14.308353 3.678000 -0.053363 0.048304 -0.023973
H 13.227821 11.930333 4.643527 0.109997 0.045949 -0.014093
H 11.763080 12.178042 3.694136 0.146061 -0.020362 -0.096576
H 13.307163 12.762788 3.096328 0.151312 0.110052 0.020749
converged SCF energy = -644.651182473653
--------------- RHF_Scanner gradients ---------------
x y z
0 O -0.0005099807 0.0007899600 -0.0009225055
1 C 0.0019756256 -0.0026878495 0.0013128912
2 O -0.0012873995 -0.0000397027 0.0000461645
3 C -0.0036190321 -0.0017536418 0.0030326628
4 C 0.0002961064 -0.0004134750 0.0000217612
5 C 0.0005871126 -0.0003648295 0.0010891183
6 C -0.0057791021 -0.0009327089 -0.0004305884
7 C 0.0048209650 0.0017763859 -0.0070404046
8 C 0.0013654435 0.0010127318 0.0023041546
9 O 0.0019723150 -0.0001871839 0.0016835889
10 C -0.0001840073 0.0012737934 0.0010825996
11 O -0.0004052249 -0.0008653338 -0.0010476975
12 C 0.0001301012 -0.0000959366 0.0011679095
13 H 0.0002756010 0.0002324496 -0.0003032978
14 H -0.0005403303 0.0009909055 0.0005167742
15 H -0.0001437078 -0.0001862103 0.0006359039
16 H -0.0002030813 0.0000298264 -0.0004951607
17 H 0.0003317734 0.0002920878 -0.0009072244
18 H 0.0001478210 0.0006905117 -0.0005496294
19 H 0.0007724922 0.0002844502 -0.0003835922
20 H -0.0000034911 0.0001537698 -0.0008134282
----------------------------------------------
cycle 12: E = -644.651182474 dE = 0.000132863 norm(grad) = 0.0134531
Step 11 : Displace = 9.166e-02/1.914e-01 (rms/max) Trust = 2.828e-01 (+) Grad = 2.936e-03/8.716e-03 (rms/max) E (change) = -644.6511824737 (+1.329e-04) Quality = -0.251
Hessian Eigenvalues: 8.38391e-03 1.93613e-02 2.17806e-02 ... 9.41000e-01 1.08517e+00 1.22214e+00
Geometry optimization cycle 13
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
O 13.728569 16.530583 0.864581 -0.011696 0.060130 0.018829
C 13.331019 15.496761 1.646460 0.004710 0.026533 -0.017129
O 14.147014 14.865441 2.269629 0.012380 0.013572 -0.038917
C 11.876136 15.190276 1.634894 0.008873 0.011503 -0.019625
C 11.171448 15.219824 0.431469 0.007036 0.005017 -0.018834
C 9.829418 14.886940 0.391726 0.010174 -0.007327 -0.003991
C 9.175456 14.538180 1.565476 0.026766 -0.015131 0.004339
C 9.857197 14.513050 2.770641 0.016072 -0.019691 0.009442
C 11.206534 14.821804 2.798131 0.014696 -0.006624 -0.018043
O 11.829324 14.902260 4.027864 0.023507 0.004547 -0.024058
C 12.542913 13.912188 4.685672 0.018277 0.006030 -0.017079
O 12.983202 14.177470 5.768174 0.055304 0.026153 -0.035611
C 12.668567 12.586656 4.003934 -0.043744 -0.021371 0.019250
H 13.055578 17.141619 0.585798 -0.020974 0.066193 0.052423
H 11.681911 15.476973 -0.476730 0.002574 -0.001087 -0.023653
H 9.300740 14.901427 -0.540224 0.000424 -0.013237 0.000872
H 8.132036 14.293604 1.544454 0.028392 -0.022638 0.005723
H 9.359653 14.282358 3.690865 0.024008 -0.025995 0.012865
H 13.178895 11.913787 4.672954 -0.048925 -0.016546 0.029427
H 11.696938 12.178662 3.757255 -0.066142 0.000620 0.063120
H 13.245450 12.692137 3.096977 -0.061712 -0.070651 0.000649
converged SCF energy = -644.651594470222
--------------- RHF_Scanner gradients ---------------
x y z
0 O -0.0006979588 0.0007195201 -0.0003597014
1 C 0.0013418444 -0.0015623918 -0.0012021302
2 O -0.0007822309 0.0003194428 0.0006007595
3 C -0.0004337944 0.0006673252 0.0012474542
4 C -0.0000655686 0.0002269905 -0.0013597016
5 C 0.0000173410 0.0000707120 -0.0003774633
6 C 0.0021626804 0.0007115140 0.0002181259
7 C -0.0015051286 -0.0006164622 0.0019590401
8 C 0.0003064683 -0.0011397166 -0.0010411765
9 O -0.0009953508 0.0001833272 0.0001306773
10 C 0.0006746726 0.0004141644 0.0000295279
11 O -0.0004350110 -0.0003653069 -0.0002687185
12 C -0.0003556031 -0.0002224532 -0.0002785395
13 H 0.0003757386 0.0002063020 0.0000999819
14 H -0.0002932524 -0.0000422385 -0.0000202591
15 H 0.0001766136 0.0000444952 -0.0000753497
16 H 0.0003047172 0.0000281873 0.0000978191
17 H -0.0000322958 0.0000534290 0.0002166841
18 H 0.0000719277 0.0003730724 0.0000039544
19 H 0.0001050021 -0.0000797106 0.0002155075
20 H 0.0000591885 0.0000097979 0.0001635076
----------------------------------------------
cycle 13: E = -644.65159447 dE = -0.000411997 norm(grad) = 0.00541847
Step 12 : Displace = 4.964e-02/9.473e-02 (rms/max) Trust = 4.583e-02 (-) Grad = 1.182e-03/2.546e-03 (rms/max) E (change) = -644.6515944702 (-4.120e-04) Quality = 0.790
Hessian Eigenvalues: 8.62711e-03 2.03085e-02 2.17380e-02 ... 9.41174e-01 1.08573e+00 1.22983e+00
Geometry optimization cycle 14
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
O 13.719629 16.563771 0.858815 -0.008940 0.033188 -0.005766
C 13.337475 15.532772 1.650336 0.006455 0.036011 0.003876
O 14.166221 14.908970 2.265166 0.019207 0.043529 -0.004463
C 11.888820 15.202742 1.635329 0.012684 0.012466 0.000435
C 11.179321 15.216657 0.435840 0.007873 -0.003166 0.004371
C 9.840014 14.868962 0.394941 0.010597 -0.017978 0.003215
C 9.184167 14.518718 1.567426 0.008711 -0.019462 0.001951
C 9.876119 14.512365 2.767642 0.018922 -0.000685 -0.002998
C 11.222147 14.835125 2.800660 0.015612 0.013320 0.002529
O 11.851981 14.911182 4.027169 0.022657 0.008922 -0.000695
C 12.551590 13.909434 4.683515 0.008677 -0.002753 -0.002157
O 13.020011 14.170200 5.755766 0.036809 -0.007270 -0.012408
C 12.630462 12.577316 4.007651 -0.038105 -0.009340 0.003717
H 13.034146 17.160263 0.577549 -0.021432 0.018644 -0.008249
H 11.689224 15.473906 -0.473317 0.007312 -0.003067 0.003413
H 9.313643 14.872572 -0.538720 0.012903 -0.028855 0.001504
H 8.143298 14.261056 1.549477 0.011263 -0.032548 0.005023
H 9.382906 14.277006 3.689095 0.023252 -0.005352 -0.001770
H 13.131088 11.889267 4.669429 -0.047807 -0.024519 -0.003525
H 11.642833 12.197730 3.777230 -0.054106 0.019068 0.019975
H 13.192905 12.661987 3.089000 -0.052545 -0.030150 -0.007977
converged SCF energy = -644.651546342369
--------------- RHF_Scanner gradients ---------------
x y z
0 O 0.0003003056 -0.0011960939 -0.0003852555
1 C -0.0012935570 0.0023466940 0.0014094003
2 O 0.0008679551 -0.0002421832 -0.0003972762
3 C 0.0017452030 -0.0001822919 -0.0020169190
4 C -0.0008602767 -0.0003143364 0.0008209103
5 C 0.0007927753 0.0002489778 0.0004106152
6 C -0.0024331454 -0.0008550643 0.0004598892
7 C 0.0009226091 0.0007916143 -0.0022753687
8 C 0.0005244337 0.0004674335 0.0013969835
9 O -0.0000697771 -0.0004654628 -0.0005638950
10 C -0.0003436744 0.0002483195 -0.0002871430
11 O 0.0007183459 -0.0004398578 0.0010045510
12 C 0.0002405084 0.0002626156 0.0000739332
13 H -0.0003643112 0.0000055361 0.0001910876
14 H 0.0004216824 0.0000384078 0.0000339881
15 H -0.0002559577 -0.0000632601 0.0000406226
16 H -0.0004179882 -0.0001095212 -0.0001168462
17 H 0.0000606492 -0.0000402247 -0.0001708731
18 H 0.0000654232 -0.0003462747 0.0001414314
19 H -0.0003818514 -0.0000260577 0.0001015789
20 H -0.0002393519 -0.0001289697 0.0001285852
----------------------------------------------
cycle 14: E = -644.651546342 dE = 4.81279e-05 norm(grad) = 0.00640214
Step 13 : Displace = 3.432e-02/6.274e-02 (rms/max) Trust = 6.481e-02 (+) Grad = 1.397e-03/3.028e-03 (rms/max) E (change) = -644.6515463424 (+4.813e-05) Quality = -0.468
Hessian Eigenvalues: 8.61999e-03 1.92962e-02 2.18228e-02 ... 9.42804e-01 1.08735e+00 1.22058e+00
Geometry optimization cycle 15
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
O 13.724766 16.545134 0.866047 0.005136 -0.018637 0.007232
C 13.332349 15.514924 1.654239 -0.005126 -0.017847 0.003903
O 14.155682 14.886064 2.270641 -0.010539 -0.022906 0.005475
C 11.880761 15.196112 1.639303 -0.008059 -0.006630 0.003974
C 11.177309 15.214931 0.436318 -0.002012 -0.001726 0.000478
C 9.836496 14.873926 0.393754 -0.003519 0.004964 -0.001187
C 9.180759 14.527680 1.567243 -0.003408 0.008963 -0.000184
C 9.864393 14.516155 2.772289 -0.011726 0.003790 0.004646
C 11.211278 14.833580 2.803504 -0.010869 -0.001544 0.002845
O 11.841549 14.910294 4.029693 -0.010432 -0.000888 0.002524
C 12.547843 13.911657 4.682253 -0.003747 0.002223 -0.001262
O 13.005813 14.176955 5.757490 -0.014198 0.006755 0.001724
C 12.648243 12.584271 3.999899 0.017781 0.006956 -0.007752
H 13.045442 17.147569 0.582871 0.011295 -0.012694 0.005322
H 11.690507 15.469260 -0.471613 0.001283 -0.004646 0.001705
H 9.310704 14.879529 -0.540074 -0.002939 0.006957 -0.001354
H 8.138933 14.275411 1.546562 -0.004366 0.014355 -0.002915
H 9.367232 14.283901 3.692393 -0.015674 0.006895 0.003298
H 13.153870 11.900032 4.661297 0.022782 0.010765 -0.008132
H 11.667992 12.192506 3.760145 0.025160 -0.005224 -0.017085
H 13.216079 12.682108 3.085746 0.023174 0.020121 -0.003254
converged SCF energy = -644.65163298869
--------------- RHF_Scanner gradients ---------------
x y z
0 O 0.0005217513 -0.0006786884 -0.0003028146
1 C -0.0009388361 0.0010183338 0.0008227217
2 O 0.0002778342 0.0001637303 -0.0004518093
3 C 0.0000826452 -0.0007489825 -0.0000961205
4 C -0.0000308711 0.0000714391 0.0002154056
5 C -0.0001494704 0.0000900108 -0.0003115063
6 C 0.0003716954 -0.0000673881 0.0001286198
7 C -0.0001747436 -0.0000080770 0.0001077549
8 C -0.0000369710 0.0005068715 -0.0001755861
9 O 0.0006394472 -0.0002525417 0.0005462653
10 C -0.0003072054 -0.0004784112 -0.0003888137
11 O -0.0002209734 0.0006395749 -0.0001420781
12 C 0.0000966494 -0.0000340014 0.0001640573
13 H -0.0001830272 0.0000140273 0.0001610988
14 H 0.0001925330 0.0000060449 -0.0000276304
15 H -0.0000233663 -0.0000011345 -0.0000705322
16 H 0.0000030929 0.0000012155 -0.0000170334
17 H 0.0000263560 -0.0000420538 0.0000564191
18 H 0.0000354879 -0.0001179827 -0.0000433836
19 H -0.0000517628 -0.0000059466 0.0000084598
20 H -0.0001302653 -0.0000760403 -0.0001834940
----------------------------------------------
cycle 15: E = -644.651632989 dE = -8.66463e-05 norm(grad) = 0.00263092
Step 14 : Displace = 1.740e-02/3.168e-02 (rms/max) Trust = 1.716e-02 (-) Grad = 5.741e-04/1.611e-03 (rms/max) E (change) = -644.6516329887 (-8.665e-05) Quality = 0.897
Hessian Eigenvalues: 8.61649e-03 1.92553e-02 2.14779e-02 ... 9.63784e-01 1.07924e+00 1.23322e+00
Geometry optimization cycle 16
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
O 13.726721 16.544399 0.878142 0.001955 -0.000735 0.012095
C 13.333785 15.497173 1.644343 0.001436 -0.017752 -0.009896
O 14.150735 14.857742 2.258098 -0.004947 -0.028322 -0.012543
C 11.878693 15.190200 1.632277 -0.002068 -0.005912 -0.007026
C 11.171987 15.214769 0.430767 -0.005322 -0.000162 -0.005550
C 9.829623 14.880380 0.392407 -0.006873 0.006454 -0.001347
C 9.174003 14.534555 1.565661 -0.006756 0.006874 -0.001582
C 9.861543 14.515426 2.768190 -0.002850 -0.000729 -0.004099
C 11.210313 14.825014 2.796424 -0.000965 -0.008566 -0.007081
O 11.836185 14.906737 4.024579 -0.005364 -0.003557 -0.005114
C 12.546464 13.914447 4.684422 -0.001379 0.002790 0.002169
O 12.993506 14.176209 5.764984 -0.012308 -0.000746 0.007494
C 12.661750 12.587828 4.003318 0.013507 0.003557 0.003419
H 13.049617 17.153287 0.604396 0.004175 0.005718 0.021526
H 11.681650 15.468795 -0.478768 -0.008857 -0.000465 -0.007155
H 9.301407 14.891886 -0.539757 -0.009297 0.012357 0.000316
H 8.130705 14.289087 1.547133 -0.008228 0.013676 0.000570
H 9.365441 14.286114 3.689457 -0.001791 0.002213 -0.002935
H 13.163373 11.909263 4.673112 0.009503 0.009231 0.011815
H 11.687532 12.189118 3.752164 0.019540 -0.003387 -0.007982
H 13.242968 12.689570 3.098650 0.026889 0.007462 0.012904
converged SCF energy = -644.65162009982
--------------- RHF_Scanner gradients ---------------
x y z
0 O -0.0009175957 0.0011727377 -0.0003379718
1 C 0.0016424912 -0.0019012848 -0.0012759589
2 O -0.0007354193 -0.0000407202 0.0010269615
3 C -0.0004973560 0.0009014375 0.0010150212
4 C 0.0000168308 0.0001253819 -0.0006894888
5 C 0.0002598872 -0.0000731525 0.0004134475
6 C -0.0001508215 0.0001266419 -0.0001530332
7 C 0.0000448909 0.0000085247 0.0002785483
8 C 0.0004917519 -0.0007661274 -0.0005868671
9 O -0.0011754854 0.0000937974 -0.0009741958
10 C 0.0008750090 0.0011227096 0.0006039748
11 O 0.0000890700 -0.0012575566 0.0000983718
12 C -0.0003859591 -0.0000722178 -0.0001168042
13 H 0.0003278279 0.0002495728 0.0000677687
14 H -0.0002168425 -0.0001412145 0.0000837037
15 H 0.0000746281 0.0000101877 0.0001296018
16 H 0.0001048874 0.0000282349 0.0000296501
17 H -0.0000174097 0.0000484062 -0.0000344454
18 H 0.0000341866 0.0003021891 -0.0000468035
19 H 0.0000961962 -0.0000521420 0.0002243467
20 H 0.0000392321 0.0001145944 0.0002441726
----------------------------------------------
cycle 16: E = -644.6516201 dE = 1.28889e-05 norm(grad) = 0.00479853
Step 15 : Displace = 1.600e-02/3.165e-02 (rms/max) Trust = 2.427e-02 (+) Grad = 1.047e-03/2.818e-03 (rms/max) E (change) = -644.6516200998 (+1.289e-05) Quality = -0.323
Hessian Eigenvalues: 8.78539e-03 1.93265e-02 2.10513e-02 ... 1.01025e+00 1.10456e+00 1.23060e+00
Geometry optimization cycle 17
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
O 13.727047 16.541640 0.872828 0.000327 -0.002760 -0.005314
C 13.333115 15.503599 1.650011 -0.000670 0.006426 0.005669
O 14.153714 14.867577 2.262669 0.002979 0.009834 0.004570
C 11.879435 15.192112 1.636311 0.000742 0.001911 0.004034
C 11.173819 15.214338 0.434548 0.001832 -0.000431 0.003781
C 9.831800 14.877864 0.393653 0.002176 -0.002516 0.001246
C 9.175510 14.532601 1.566903 0.001507 -0.001954 0.001242
C 9.861151 14.517176 2.770742 -0.000393 0.001750 0.002552
C 11.209226 14.829783 2.801142 -0.001088 0.004769 0.004718
O 11.836888 14.908602 4.028571 0.000702 0.001865 0.003991
C 12.544307 13.912461 4.685113 -0.002158 -0.001987 0.000690
O 12.991119 14.175450 5.765635 -0.002387 -0.000759 0.000651
C 12.659813 12.587884 3.999804 -0.001937 0.000056 -0.003514
H 13.048553 17.145188 0.590379 -0.001064 -0.008099 -0.014017
H 11.685238 15.468767 -0.474216 0.003588 -0.000028 0.004551
H 9.305041 14.886878 -0.539560 0.003635 -0.005008 0.000197
H 8.132672 14.284478 1.547334 0.001967 -0.004609 0.000202
H 9.363897 14.287048 3.691300 -0.001543 0.000934 0.001843
H 13.159423 11.904681 4.666784 -0.003950 -0.004582 -0.006327
H 11.685124 12.191960 3.744949 -0.002407 0.002842 -0.007214
H 13.241110 12.691916 3.095099 -0.001858 0.002346 -0.003551
converged SCF energy = -644.651655201799
--------------- RHF_Scanner gradients ---------------
x y z
0 O 0.0000274402 0.0000237588 -0.0002169120
1 C 0.0000731183 -0.0001494003 0.0002009016
2 O -0.0000164214 0.0000238936 0.0000071975
3 C 0.0003264074 0.0001326815 -0.0003802585
4 C -0.0001351157 -0.0000000046 0.0000169593
5 C 0.0000633588 0.0000127862 -0.0000349256
6 C 0.0000018508 0.0000143816 0.0000638349
7 C -0.0000810739 -0.0000386546 0.0000437381
8 C -0.0000705353 -0.0001034913 0.0001765494
9 O -0.0001736402 0.0000650812 0.0000343125
10 C 0.0001470201 0.0000067947 -0.0000573613
11 O -0.0001075737 -0.0000133094 0.0000653490
12 C 0.0000151424 0.0000207913 0.0000032891
13 H -0.0000067870 0.0000501986 0.0000668151
14 H 0.0000119224 0.0000187626 0.0000289592
15 H -0.0000183327 -0.0000072992 -0.0000118674
16 H -0.0000205862 -0.0000029389 0.0000096416
17 H -0.0000363026 -0.0000068164 0.0000072105
18 H 0.0000827607 0.0000067937 -0.0000326663
19 H -0.0000353461 -0.0000302824 0.0000540790
20 H -0.0000473066 -0.0000237267 -0.0000448457
----------------------------------------------
cycle 17: E = -644.651655202 dE = -3.5102e-05 norm(grad) = 0.000759606
Step 16 : Displace = 6.643e-03/1.622e-02 (rms/max) Trust = 8.000e-03 (-) Grad = 1.658e-04/5.184e-04 (rms/max) E (change) = -644.6516552018 (-3.510e-05) Quality = 1.020
Hessian Eigenvalues: 8.86013e-03 1.85188e-02 2.10356e-02 ... 1.01740e+00 1.10117e+00 1.23034e+00
Geometry optimization cycle 18
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
O 13.725478 16.545387 0.874769 -0.001569 0.003747 0.001941
C 13.332703 15.505518 1.649859 -0.000412 0.001919 -0.000153
O 14.154095 14.869528 2.261501 0.000381 0.001951 -0.001168
C 11.879508 15.192481 1.636348 0.000073 0.000370 0.000037
C 11.174569 15.213281 0.434234 0.000750 -0.001057 -0.000314
C 9.832705 14.875982 0.393723 0.000905 -0.001882 0.000070
C 9.176792 14.531565 1.567359 0.001282 -0.001036 0.000456
C 9.862685 14.517799 2.771148 0.001535 0.000623 0.000406
C 11.210519 14.830911 2.801185 0.001294 0.001127 0.000043
O 11.839767 14.909571 4.027867 0.002879 0.000968 -0.000704
C 12.545024 13.912234 4.684611 0.000717 -0.000227 -0.000501
O 12.993816 14.174953 5.764351 0.002698 -0.000497 -0.001284
C 12.657131 12.587280 3.999582 -0.002682 -0.000604 -0.000222
H 13.045919 17.147338 0.591481 -0.002633 0.002150 0.001102
H 11.686038 15.467020 -0.474730 0.000800 -0.001747 -0.000514
H 9.305976 14.883731 -0.539476 0.000935 -0.003146 0.000084
H 8.134151 14.282746 1.548151 0.001479 -0.001732 0.000817
H 9.365886 14.287976 3.691977 0.001989 0.000927 0.000677
H 13.152982 11.902269 4.667469 -0.006440 -0.002412 0.000685
H 11.681699 12.194775 3.742560 -0.003426 0.002815 -0.002389
H 13.240555 12.689657 3.096032 -0.000555 -0.002259 0.000933
converged SCF energy = -644.65165772155
--------------- RHF_Scanner gradients ---------------
x y z
0 O 0.0000752999 -0.0000179604 -0.0000923226
1 C -0.0001573732 -0.0000885642 0.0000289437
2 O -0.0000231139 0.0000838308 0.0000177148
3 C -0.0002156223 -0.0001329733 0.0001915098
4 C 0.0001019242 0.0000276861 -0.0000306565
5 C -0.0000435015 -0.0000126278 0.0000592147
6 C -0.0000284523 -0.0000128433 -0.0000660670
7 C 0.0001121550 0.0000606882 -0.0000401964
8 C 0.0001327947 0.0001107267 -0.0001521856
9 O 0.0000535196 -0.0000792081 0.0000562596
10 C 0.0000493964 -0.0000171898 0.0000181969
11 O -0.0000795141 0.0000167914 0.0000044039
12 C 0.0000271055 0.0000295835 -0.0000379233
13 H -0.0000181986 0.0000287632 0.0000545458
14 H 0.0000128433 0.0000037218 -0.0000116610
15 H 0.0000122577 0.0000040145 0.0000070218
16 H 0.0000040096 -0.0000003156 -0.0000055505
17 H 0.0000287814 0.0000041900 -0.0000118374
18 H 0.0000505339 0.0000196512 -0.0000240302
19 H -0.0000239679 -0.0000079823 0.0000605911
20 H -0.0000708773 -0.0000199826 -0.0000259716
----------------------------------------------
cycle 18: E = -644.651657722 dE = -2.51975e-06 norm(grad) = 0.000543396
Step 17 : Displace = 3.003e-03/6.993e-03 (rms/max) Trust = 1.131e-02 (+) Grad = 1.186e-04/3.176e-04 (rms/max) E (change) = -644.6516577215 (-2.520e-06) Quality = 1.148
Hessian Eigenvalues: 6.95363e-03 9.96236e-03 2.13319e-02 ... 1.01707e+00 1.10791e+00 1.23210e+00
Geometry optimization cycle 19
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
O 13.724756 16.548151 0.876900 -0.000722 0.002764 0.002131
C 13.333011 15.505676 1.648651 0.000308 0.000158 -0.001207
O 14.155115 14.867309 2.256918 0.001019 -0.002218 -0.004583
C 11.879753 15.192376 1.635696 0.000245 -0.000105 -0.000652
C 11.174278 15.212755 0.433935 -0.000290 -0.000527 -0.000299
C 9.832393 14.875327 0.394121 -0.000312 -0.000654 0.000399
C 9.176985 14.531303 1.568143 0.000193 -0.000262 0.000784
C 9.863370 14.518020 2.771667 0.000684 0.000220 0.000519
C 11.211244 14.831150 2.800875 0.000725 0.000239 -0.000311
O 11.841471 14.910317 4.027005 0.001704 0.000747 -0.000861
C 12.544119 13.912047 4.685084 -0.000905 -0.000186 0.000472
O 12.991063 14.174068 5.765761 -0.002753 -0.000885 0.001410
C 12.657244 12.587433 3.999601 0.000113 0.000153 0.000019
H 13.044232 17.148332 0.592248 -0.001687 0.000993 0.000768
H 11.685229 15.466169 -0.475430 -0.000809 -0.000851 -0.000700
H 9.305292 14.882698 -0.538875 -0.000684 -0.001033 0.000601
H 8.134344 14.282453 1.549463 0.000193 -0.000293 0.001312
H 9.366958 14.288556 3.692811 0.001071 0.000580 0.000834
H 13.145646 11.900073 4.670567 -0.007337 -0.002196 0.003098
H 11.682991 12.198036 3.733789 0.001292 0.003261 -0.008771
H 13.248506 12.689752 3.101069 0.007951 0.000095 0.005038
converged SCF energy = -644.651660927965
--------------- RHF_Scanner gradients ---------------
x y z
0 O 0.0000465755 -0.0000314100 0.0000018746
1 C -0.0001362734 0.0000893537 0.0000366300
2 O 0.0000013067 0.0000007140 -0.0000262729
3 C -0.0001769967 -0.0001530159 0.0001654638
4 C 0.0001033964 0.0000204723 0.0000098360
5 C -0.0000595217 -0.0000122533 0.0000527049
6 C -0.0000168399 -0.0000109413 -0.0000708847
7 C 0.0000759406 0.0000536838 -0.0000225275
8 C 0.0001230897 0.0000929537 -0.0001338378
9 O 0.0000512994 -0.0000739592 0.0000155823
10 C 0.0000893410 0.0000116688 0.0000140092
11 O -0.0000951695 -0.0000054411 -0.0000188116
12 C -0.0000049120 0.0000236424 -0.0000346012
13 H -0.0000079287 -0.0000042588 -0.0000006436
14 H 0.0000039655 -0.0000077191 -0.0000158157
15 H 0.0000117602 0.0000032158 0.0000028990
16 H 0.0000053948 -0.0000004738 -0.0000039984
17 H 0.0000232522 0.0000033293 -0.0000046509
18 H 0.0000361089 0.0000108170 -0.0000193336
19 H -0.0000223777 -0.0000143360 0.0000602760
20 H -0.0000514114 0.0000039577 -0.0000078979
----------------------------------------------
cycle 19: E = -644.651660928 dE = -3.20642e-06 norm(grad) = 0.000475133
Step 18 : Displace = 3.895e-03/9.366e-03 (rms/max) Trust = 1.600e-02 (+) Grad = 1.037e-04/2.866e-04 (rms/max) E (change) = -644.6516609280 (-3.206e-06) Quality = 1.572
Hessian Eigenvalues: 3.14224e-03 9.20482e-03 2.12231e-02 ... 1.01731e+00 1.10584e+00 1.23301e+00
Geometry optimization cycle 20
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
O 13.724135 16.550926 0.879416 -0.000621 0.002775 0.002516
C 13.333601 15.504727 1.646213 0.000590 -0.000949 -0.002439
O 14.156441 14.863813 2.250863 0.001326 -0.003496 -0.006055
C 11.879983 15.192029 1.634375 0.000230 -0.000348 -0.001322
C 11.173269 15.212109 0.433352 -0.001009 -0.000646 -0.000583
C 9.831299 14.874801 0.394790 -0.001094 -0.000526 0.000669
C 9.176757 14.531277 1.569484 -0.000229 -0.000026 0.001341
C 9.864021 14.518401 2.772487 0.000652 0.000381 0.000821
C 11.211985 14.831531 2.800408 0.000741 0.000382 -0.000467
O 11.843697 14.911446 4.025752 0.002227 0.001129 -0.001254
C 12.541850 13.911595 4.686328 -0.002269 -0.000452 0.001244
O 12.985347 14.172644 5.768738 -0.005716 -0.001424 0.002977
C 12.658737 12.587931 3.999556 0.001493 0.000498 -0.000046
H 13.042364 17.148918 0.593240 -0.001868 0.000586 0.000991
H 11.683283 15.465296 -0.476633 -0.001946 -0.000873 -0.001203
H 9.303389 14.881921 -0.537771 -0.001903 -0.000777 0.001104
H 8.134045 14.282583 1.551716 -0.000299 0.000131 0.002253
H 9.368163 14.289442 3.694088 0.001206 0.000886 0.001277
H 13.133575 11.896553 4.676141 -0.012071 -0.003520 0.005574
H 11.687420 12.203474 3.716782 0.004428 0.005438 -0.017007
H 13.264638 12.690585 3.110676 0.016132 0.000832 0.009606
converged SCF energy = -644.651663549845
--------------- RHF_Scanner gradients ---------------
x y z
0 O -0.0000066697 -0.0000317088 0.0002227762
1 C -0.0000109689 0.0000833172 -0.0002122782
2 O 0.0000528497 -0.0000083126 0.0000178560
3 C 0.0000289997 0.0000099245 -0.0000409873
4 C 0.0000098866 -0.0000173379 0.0000397521
5 C -0.0000105773 -0.0000070695 -0.0000068325
6 C -0.0000067793 -0.0000068445 0.0000081942
7 C -0.0000163271 -0.0000120431 -0.0000227691
8 C -0.0000554555 0.0000523417 0.0000667398
9 O 0.0000879953 0.0000241062 -0.0000393707
10 C -0.0000881290 -0.0000612965 0.0000509256
11 O -0.0000016046 0.0000204198 0.0000239944
12 C 0.0000425086 0.0000312508 -0.0000352580
13 H -0.0000006976 -0.0000493083 -0.0000563861
14 H -0.0000066110 0.0000019423 -0.0000098421
15 H -0.0000006948 -0.0000006797 -0.0000073250
16 H -0.0000076582 0.0000005513 0.0000017130
17 H -0.0000002960 -0.0000026058 0.0000028108
18 H 0.0000214585 -0.0000076744 -0.0000084609
19 H -0.0000113230 -0.0000058133 0.0000377648
20 H -0.0000199068 -0.0000131592 -0.0000330171
----------------------------------------------
cycle 20: E = -644.65166355 dE = -2.62188e-06 norm(grad) = 0.00040111
Step 19 : Displace = 7.064e-03/1.870e-02 (rms/max) Trust = 2.263e-02 (+) Grad = 8.753e-05/2.283e-04 (rms/max) E (change) = -644.6516635498 (-2.622e-06) Quality = 1.057
Hessian Eigenvalues: 2.58897e-03 9.20357e-03 2.12350e-02 ... 1.01743e+00 1.10509e+00 1.23920e+00
Geometry optimization cycle 21
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
O 13.723798 16.550527 0.878583 -0.000337 -0.000399 -0.000833
C 13.333422 15.504246 1.645474 -0.000179 -0.000480 -0.000738
O 14.156412 14.861956 2.248408 -0.000030 -0.001857 -0.002455
C 11.879691 15.191988 1.634117 -0.000292 -0.000041 -0.000257
C 11.172753 15.212430 0.433199 -0.000516 0.000321 -0.000153
C 9.830763 14.875295 0.394961 -0.000535 0.000494 0.000171
C 9.176547 14.531466 1.569739 -0.000209 0.000189 0.000254
C 9.864099 14.518145 2.772560 0.000078 -0.000256 0.000073
C 11.212100 14.831100 2.800084 0.000116 -0.000431 -0.000324
O 11.843903 14.911362 4.025355 0.000205 -0.000084 -0.000397
C 12.541438 13.911622 4.686652 -0.000412 0.000026 0.000324
O 12.983133 14.172386 5.769860 -0.002215 -0.000258 0.001121
C 12.659748 12.588046 3.999987 0.001010 0.000115 0.000431
H 13.042260 17.149502 0.593927 -0.000104 0.000584 0.000688
H 11.682570 15.465721 -0.476844 -0.000713 0.000425 -0.000211
H 9.302549 14.882755 -0.537403 -0.000840 0.000833 0.000368
H 8.133822 14.282908 1.552164 -0.000223 0.000325 0.000448
H 9.368458 14.289132 3.694252 0.000295 -0.000310 0.000164
H 13.129901 11.895772 4.678888 -0.003674 -0.000781 0.002748
H 11.689675 12.204990 3.711287 0.002255 0.001516 -0.005495
H 13.270957 12.690652 3.114750 0.006320 0.000067 0.004074
converged SCF energy = -644.651664286097
--------------- RHF_Scanner gradients ---------------
x y z
0 O -0.0000498001 -0.0000132366 0.0001122518
1 C 0.0000424905 0.0001637518 0.0000197680
2 O 0.0000051925 -0.0000868653 -0.0000590353
3 C -0.0000441776 -0.0000155240 0.0000258065
4 C 0.0000100738 -0.0000148484 0.0000080748
5 C -0.0000090908 0.0000016722 -0.0000019786
6 C 0.0000119354 0.0000078156 -0.0000109148
7 C -0.0000034124 -0.0000049662 0.0000199819
8 C 0.0000211955 -0.0000137788 -0.0000326991
9 O 0.0000058650 0.0000213208 -0.0000430306
10 C 0.0000894613 0.0000418522 0.0000055104
11 O -0.0000673547 -0.0000462825 0.0000052556
12 C -0.0000282452 -0.0000052916 -0.0000219094
13 H 0.0000168858 -0.0000399233 -0.0000599854
14 H -0.0000149735 -0.0000112222 -0.0000085955
15 H 0.0000050718 0.0000009479 0.0000071805
16 H 0.0000101036 0.0000019907 0.0000006893
17 H 0.0000022334 0.0000037220 -0.0000015209
18 H 0.0000148357 0.0000178125 -0.0000088927
19 H -0.0000007529 -0.0000214833 0.0000273420
20 H -0.0000175372 0.0000125367 0.0000167016
----------------------------------------------
cycle 21: E = -644.651664286 dE = -7.36252e-07 norm(grad) = 0.000299902
Step 20 : Displace = 2.584e-03/7.515e-03 (rms/max) Trust = 3.200e-02 (+) Grad = 6.544e-05/1.703e-04 (rms/max) E (change) = -644.6516642861 (-7.363e-07) Quality = 1.176
Hessian Eigenvalues: 2.24093e-03 8.90124e-03 1.30057e-02 ... 1.01849e+00 1.11290e+00 1.23052e+00
Geometry optimization cycle 22
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
O 13.723777 16.549229 0.876589 -0.000020 -0.001298 -0.001994
C 13.333309 15.504038 1.645155 -0.000113 -0.000208 -0.000319
O 14.156266 14.862677 2.249074 -0.000145 0.000721 0.000666
C 11.879540 15.192001 1.634181 -0.000151 0.000013 0.000064
C 11.172411 15.212529 0.433358 -0.000343 0.000099 0.000158
C 9.830425 14.875410 0.395218 -0.000338 0.000114 0.000257
C 9.176318 14.531474 1.570051 -0.000230 0.000008 0.000312
C 9.863971 14.518116 2.772809 -0.000128 -0.000029 0.000249
C 11.211990 14.831089 2.800212 -0.000111 -0.000011 0.000129
O 11.843925 14.911349 4.025414 0.000022 -0.000014 0.000059
C 12.541023 13.911491 4.686899 -0.000415 -0.000131 0.000247
O 12.982160 14.172077 5.770397 -0.000972 -0.000309 0.000538
C 12.660390 12.588188 3.999906 0.000643 0.000142 -0.000081
H 13.042589 17.149298 0.593354 0.000329 -0.000204 -0.000574
H 11.682206 15.465913 -0.476657 -0.000364 0.000192 0.000187
H 9.302083 14.882931 -0.537084 -0.000466 0.000177 0.000319
H 8.133593 14.282875 1.552539 -0.000229 -0.000034 0.000374
H 9.368382 14.289038 3.694523 -0.000076 -0.000094 0.000271
H 13.126282 11.894631 4.680448 -0.003619 -0.001141 0.001560
H 11.691286 12.206797 3.705897 0.001612 0.001808 -0.005390
H 13.276072 12.690849 3.117718 0.005115 0.000197 0.002968
converged SCF energy = -644.651665150126
--------------- RHF_Scanner gradients ---------------
x y z
0 O -0.0000362922 0.0000099979 0.0000434047
1 C 0.0000601566 0.0000765854 0.0000218574
2 O -0.0000093676 -0.0000569903 -0.0000330907
3 C -0.0000089350 0.0000115052 0.0000222898
4 C -0.0000061860 -0.0000155090 0.0000085048
5 C 0.0000071488 0.0000059085 -0.0000135526
6 C 0.0000073122 0.0000028800 0.0000079134
7 C -0.0000160519 -0.0000104574 0.0000177309
8 C -0.0000129535 -0.0000319465 -0.0000186872
9 O 0.0000360642 0.0000272487 -0.0000339262
10 C 0.0000519941 0.0000408125 -0.0000259820
11 O -0.0000535247 -0.0000407325 0.0000088050
12 C -0.0000165489 -0.0000073050 0.0000095943
13 H 0.0000119729 -0.0000167627 -0.0000326443
14 H -0.0000060223 -0.0000062862 0.0000010603
15 H -0.0000029201 -0.0000001324 0.0000026729
16 H 0.0000045005 -0.0000001957 -0.0000011156
17 H -0.0000067006 0.0000004584 0.0000011265
18 H 0.0000117699 0.0000090534 -0.0000029128
19 H -0.0000023856 -0.0000143147 0.0000099833
20 H -0.0000130310 0.0000161823 0.0000069682
----------------------------------------------
cycle 22: E = -644.65166515 dE = -8.64029e-07 norm(grad) = 0.000193121
Step 21 : Displace = 2.154e-03/5.938e-03 (rms/max) Trust = 4.526e-02 (+) Grad = 4.214e-05/9.981e-05 (rms/max) E (change) = -644.6516651501 (-8.640e-07) Quality = 1.528
Hessian Eigenvalues: 1.97963e-03 6.43532e-03 1.00996e-02 ... 1.01856e+00 1.11012e+00 1.23125e+00
Geometry optimization cycle 23
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
O 13.723704 16.547355 0.874230 -0.000074 -0.001874 -0.002359
C 13.332941 15.503906 1.645301 -0.000368 -0.000132 0.000146
O 14.155777 14.864179 2.251068 -0.000490 0.001502 0.001994
C 11.879238 15.191972 1.634398 -0.000302 -0.000029 0.000216
C 11.172127 15.212696 0.433526 -0.000283 0.000168 0.000168
C 9.830145 14.875642 0.395330 -0.000281 0.000233 0.000112
C 9.176002 14.531601 1.570113 -0.000316 0.000127 0.000063
C 9.863636 14.518078 2.772877 -0.000335 -0.000038 0.000068
C 11.211648 14.830992 2.800447 -0.000342 -0.000097 0.000235
O 11.843400 14.911022 4.025760 -0.000525 -0.000327 0.000346
C 12.540963 13.911351 4.687029 -0.000061 -0.000139 0.000130
O 12.982805 14.172291 5.770178 0.000644 0.000214 -0.000220
C 12.661035 12.588188 3.999849 0.000644 -0.000000 -0.000057
H 13.043020 17.148788 0.592610 0.000431 -0.000510 -0.000744
H 11.682025 15.466217 -0.476381 -0.000181 0.000304 0.000277
H 9.301824 14.883303 -0.536979 -0.000259 0.000371 0.000105
H 8.133267 14.283044 1.552564 -0.000326 0.000170 0.000025
H 9.368026 14.288890 3.694544 -0.000356 -0.000148 0.000021
H 13.123316 11.893604 4.681796 -0.002966 -0.001027 0.001348
H 11.692702 12.208267 3.701575 0.001416 0.001470 -0.004322
H 13.280402 12.690613 3.120165 0.004330 -0.000236 0.002446
converged SCF energy = -644.651665682446
--------------- RHF_Scanner gradients ---------------
x y z
0 O -0.0000078976 0.0000117890 -0.0000380706
1 C 0.0000198980 -0.0000274486 0.0000453364
2 O -0.0000134001 -0.0000035486 -0.0000072315
3 C -0.0000064635 0.0000248232 0.0000044195
4 C -0.0000133383 -0.0000036702 -0.0000293771
5 C 0.0000144532 0.0000017742 -0.0000028885
6 C -0.0000003969 0.0000013121 0.0000087705
7 C 0.0000057004 -0.0000073317 -0.0000030601
8 C -0.0000309806 -0.0000296315 0.0000096961
9 O 0.0000720829 0.0000331265 -0.0000158815
10 C -0.0000721053 -0.0000124000 0.0000034613
11 O 0.0000058474 -0.0000016365 0.0000186841
12 C 0.0000261988 -0.0000081924 0.0000001569
13 H -0.0000011262 0.0000094419 0.0000102000
14 H 0.0000008386 0.0000011382 0.0000021828
15 H 0.0000005136 0.0000002073 0.0000044865
16 H 0.0000038586 0.0000007100 -0.0000009633
17 H -0.0000000980 0.0000014999 -0.0000023045
18 H -0.0000005456 0.0000112257 -0.0000038458
19 H 0.0000048296 -0.0000014523 0.0000037277
20 H -0.0000078690 -0.0000017363 -0.0000074989
----------------------------------------------
cycle 23: E = -644.651665682 dE = -5.3232e-07 norm(grad) = 0.000150849
Step 22 : Displace = 1.939e-03/4.945e-03 (rms/max) Trust = 6.400e-02 (+) Grad = 3.292e-05/8.090e-05 (rms/max) E (change) = -644.6516656824 (-5.323e-07) Quality = 1.109
Hessian Eigenvalues: 1.89942e-03 5.72065e-03 9.85002e-03 ... 1.01879e+00 1.10827e+00 1.23472e+00
Geometry optimization cycle 24
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
O 13.723729 16.546987 0.874025 0.000025 -0.000368 -0.000205
C 13.332843 15.503965 1.645632 -0.000098 0.000059 0.000331
O 14.155599 14.864830 2.252141 -0.000177 0.000651 0.001074
C 11.879181 15.191917 1.634617 -0.000057 -0.000054 0.000220
C 11.172169 15.212593 0.433709 0.000042 -0.000103 0.000183
C 9.830165 14.875581 0.395339 0.000021 -0.000061 0.000009
C 9.175881 14.531609 1.570064 -0.000121 0.000008 -0.000050
C 9.863400 14.518146 2.772903 -0.000236 0.000068 0.000025
C 11.211421 14.831048 2.800616 -0.000227 0.000056 0.000169
O 11.843056 14.910917 4.025985 -0.000344 -0.000105 0.000225
C 12.541360 13.911441 4.686794 0.000397 0.000089 -0.000235
O 12.983698 14.172498 5.769705 0.000894 0.000207 -0.000472
C 12.661060 12.588225 3.999660 0.000025 0.000038 -0.000189
H 13.043097 17.148371 0.592165 0.000077 -0.000417 -0.000445
H 11.682192 15.466064 -0.476145 0.000167 -0.000153 0.000235
H 9.301972 14.883205 -0.537052 0.000148 -0.000097 -0.000074
H 8.133137 14.283058 1.552423 -0.000130 0.000013 -0.000140
H 9.367702 14.288961 3.694530 -0.000324 0.000071 -0.000014
H 13.122805 11.893356 4.681711 -0.000511 -0.000248 -0.000085
H 11.692688 12.208746 3.700935 -0.000014 0.000479 -0.000640
H 13.280845 12.690481 3.120242 0.000444 -0.000132 0.000078
converged SCF energy = -644.651665790963
--------------- RHF_Scanner gradients ---------------
x y z
0 O 0.0000058631 0.0000124035 -0.0000355507
1 C 0.0000052157 -0.0000450925 0.0000105108
2 O -0.0000074303 0.0000111000 0.0000090050
3 C 0.0000088809 0.0000173120 0.0000054173
4 C -0.0000017684 -0.0000046632 0.0000018035
5 C 0.0000012402 0.0000010965 -0.0000026433
6 C -0.0000009950 -0.0000040946 0.0000050569
7 C 0.0000024753 -0.0000084871 -0.0000082681
8 C -0.0000443945 -0.0000075787 0.0000086076
9 O 0.0000683080 0.0000238595 -0.0000122436
10 C -0.0000186470 -0.0000048156 -0.0000263788
11 O -0.0000111909 0.0000021391 0.0000230121
12 C 0.0000057723 -0.0000038401 0.0000097672
13 H -0.0000058339 0.0000110619 0.0000159058
14 H 0.0000066549 0.0000042335 0.0000037714
15 H -0.0000029933 -0.0000001810 -0.0000024032
16 H -0.0000031538 -0.0000004687 -0.0000006906
17 H -0.0000039248 -0.0000008215 0.0000014277
18 H 0.0000035699 -0.0000040611 0.0000010184
19 H -0.0000026371 -0.0000059227 -0.0000020110
20 H -0.0000050112 0.0000068211 -0.0000051145
----------------------------------------------
cycle 24: E = -644.651665791 dE = -1.08516e-07 norm(grad) = 0.000120743
Step 23 : Displace = 5.125e-04/1.259e-03 (rms/max) Trust = 9.051e-02 (+) Grad = 2.635e-05/7.338e-05 (rms/max) E (change) = -644.6516657910 (-1.085e-07) Quality = 1.484
Hessian Eigenvalues: 1.89942e-03 5.72065e-03 9.85002e-03 ... 1.01879e+00 1.10827e+00 1.23472e+00
Converged! =D
#==========================================================================#
#| If this code has benefited your research, please support us by citing: |#
#| |#
#| Wang, L.-P.; Song, C.C. (2016) "Geometry optimization made simple with |#
#| translation and rotation coordinates", J. Chem, Phys. 144, 214108. |#
#| http://dx.doi.org/10.1063/1.4952956 |#
#==========================================================================#Time elapsed since start of run_optimizer: 194.822 seconds
- The optimizer uses gradient information (forces) to move the nuclei toward the minimum energy structure.
- If the optimization requires many steps or appears slow, it might be due to the initial guess being far from the minimum or the chosen convergence criteria. In practice, one can adjust parameters (like step sizes) to improve convergence.
Final SCF Calculation
After obtaining the optimized geometry, we perform a final HF calculation to verify the energy and obtain the molecular orbitals.
# Use the optimized geometry for a final SCF calculation
mf_opt = scf.RHF(mol_eq)
print("\nRunning HF calculation on optimized geometry...")
mf_opt.kernel()
# Print results
print("\nInitial HF Energy:", mf.e_tot)
print("Optimized HF Energy:", mf_opt.e_tot)
print("\nOptimized Molecular Orbitals (first few):\n", mf_opt.mo_coeff[:5, :5])
print("\nMolecular Orbitals shape:\n", mf_opt.mo_coeff.shape)
Running HF calculation on optimized geometry...
converged SCF energy = -644.651665790917
Initial HF Energy: -644.5983588496609
Optimized HF Energy: -644.651665790917
Optimized Molecular Orbitals (first few):
[[ 9.95819501e-01 7.43335367e-04 5.95163720e-04 2.70259977e-06
-1.20871976e-04]
[ 2.32361493e-02 -1.08099884e-04 -4.12017754e-04 -5.25534616e-06
1.54079084e-04]
[-1.29675158e-02 3.73352535e-04 1.78680406e-03 -1.76761699e-05
2.16159720e-04]
[-1.92104349e-03 -2.20425640e-05 9.22746729e-05 -9.53404200e-06
2.26353961e-05]
[-5.14746716e-04 3.39824985e-05 1.15701177e-04 2.68735787e-06
-1.05479402e-04]]
Molecular Orbitals shape:
(133, 133)
Discussion
While the HF method provides a computationally efficient framework and the foundation for many post‑HF methods, it has important limitations:
- **Lack of Electron Correlation:** HF includes electron exchange exactly (for a given determinant) but neglects dynamic electron correlation. Methods such as MP2, CCSD, or configuration interaction (CI) are necessary for a more accurate description.
- **Basis Set Dependency:** The choice of basis set (e.g., 6‑31G) affects both the accuracy and computational cost. Larger basis sets generally yield better results at the expense of computational effort.
- **SCF Convergence Issues:** The iterative nature of the SCF procedure sometimes leads to convergence difficulties. Techniques like density mixing or DIIS (direct inversion in the iterative subspace) are often used to stabilize convergence.
In summary, we have:
- Derived the HF equations from the many‑electron Schrödinger equation using the variational principle with Lagrange multipliers.
- Shown how the Roothaan–Hall equations emerge when expressing molecular orbitals in a finite basis.
- Provided a pseudocode outline of the SCF procedure.
- Demonstrated an HF calculation for aspirin using PySCF, including geometry optimization.
- Discussed both the practical aspects and the limitations of the HF method.
This tutorial should serve as a comprehensive yet accessible guide for researchers with a strong mathematical background who wish to understand the logical progression from the fundamental quantum equations to practical computational chemistry methods.