Dimerización de NO_2
21. Dimerización de \(NO_2\)#
Warning
Si está utilizando Google Colab o la ejecución en línea, debe de ejecutar al inicio el siguiente código
!pip install pyscf
!pip install geomeTRIC
El \(N_2O_4\) es un compuesto que se encuentra en la atmósfera. Con los cambios de temperatura se descompone en el radical \(NO_2\) mediante la reacción:
\(N_2O_4\) ↔ \(2NO_2\)
Las geometrías de \(N_2O_4\) y \(NO_2\) se dan a continuación:
Molécula: \(N_2O_4\) Carga: 0 Multiplicidad: 1
Átomo |
x (Å) |
y (Å) |
z (Å) |
|---|---|---|---|
N |
0.0000 |
0.0000 |
0.0000 |
N |
-1.7820 |
0.0000 |
0.0000 |
O |
0.4516 |
1.1010 |
0.0000 |
O |
0.4516 |
-1.1010 |
0.0000 |
O |
-2.2336 |
1.1010 |
0.0000 |
O |
-2.2336 |
-1.1010 |
0.0000 |
Molécula: \(NO_2\) Carga: 0 Multiplicidad: 2
Átomo |
x (Å) |
y (Å) |
z (Å) |
|---|---|---|---|
N |
0.0000 |
0.0000 |
0.0000 |
O |
0.0000 |
1.0989 |
0.4653 |
O |
0.0000 |
-1.0989 |
0.4653 |
# Importe PySCF y su Optimizador
# Descomentar estas líneas si está en modo online
#!pip install pyscf
#!pip install geomeTRIC
import pyscf
from pyscf import scf
from pyscf import dft
from pyscf.geomopt.geometric_solver import optimize
Pregunta 1. Complete el siguiente código para calcular la energía de la molécula optimizada de \(N_2O_4\) con Hartree-Fock y la base 6-31G.
Ayuda. Reemplace XXXX por los valores apropiados.
N2O4 = pyscf.gto.Mole(atom="""
N XXXXXXX XXXXXXX XXXXXXX
N XXXXXXX XXXXXXX XXXXXXX
O XXXXXXX XXXXXXX XXXXXXX
O XXXXXXX XXXXXXX XXXXXXX
O XXXXXXX XXXXXXX XXXXXXX
O XXXXXXX XXXXXXX XXXXXXX
""",basis="XXXX")
N2O4.max_memory = XXXX
N2O4.build()
rhf = scf.RHF(N2O4)
N2O4_eq = optimize(rhf)
rhf = scf.RHF(N2O4_eq)
n2o4 = rhf.kernel()
# Optimice Geometría y obtenga la energia N2O4 HF/6-31G
N2O4 = pyscf.gto.Mole(atom="""
N -4.84638 1.76109 0.00000
N -3.46888 1.78415 0.00000
O -2.82385 2.93169 -0.00000
O -2.85055 0.76276 0.00000
O -5.46471 2.78248 0.00000
O -5.49141 0.61355 0.00000
""",basis="6-31G")
N2O4.max_memory = 2000
N2O4.build()
rhf = scf.RHF(N2O4)
N2O4_eq = optimize(rhf)
rhf = scf.RHF(N2O4_eq)
n2o4 = rhf.kernel()
geometric-optimize called with the following command line:
/home/jfhlewyee/anaconda3/envs/jb/lib/python3.10/site-packages/ipykernel_launcher.py -f /tmp/tmp20bm5290.json --HistoryManager.hist_file=:memory:
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-=# geomeTRIC started. Version: 1.0 #=-
Current date and time: 2022-12-13 13:53:02
Custom engine selected.
Bonds will be generated from interatomic distances less than 1.20 times sum of covalent radii
18 internal coordinates being used (instead of 18 Cartesians)
Internal coordinate system (atoms numbered from 1):
Distance 1-2
Distance 1-5
Distance 1-6
Distance 2-3
Distance 2-4
Angle 2-1-6
Angle 5-1-6
Angle 1-2-4
Angle 3-2-4
Out-of-Plane 1-2-5-6
Out-of-Plane 2-1-3-4
Dihedral 5-1-2-3
Dihedral 5-1-2-4
Dihedral 6-1-2-3
Dihedral 6-1-2-4
Translation-X 1-6
Translation-Y 1-6
Translation-Z 1-6
Rotation-A 1-6
Rotation-B 1-6
Rotation-C 1-6
<class 'geometric.internal.Distance'> : 5
<class 'geometric.internal.Angle'> : 4
<class 'geometric.internal.OutOfPlane'> : 2
<class 'geometric.internal.Dihedral'> : 4
<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 ===
Geometry optimization cycle 1
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
N -4.846380 1.761090 0.000000 0.000000 0.000000 0.000000
N -3.468880 1.784150 0.000000 0.000000 0.000000 0.000000
O -2.823850 2.931690 0.000000 0.000000 0.000000 0.000000
O -2.850550 0.762760 0.000000 0.000000 0.000000 0.000000
O -5.464710 2.782480 0.000000 0.000000 0.000000 0.000000
O -5.491410 0.613550 0.000000 0.000000 0.000000 0.000000
converged SCF energy = -407.731086258658
--------------- SCF_Scanner gradients ---------------
x y z
0 N 0.1364944014 0.0625759323 -0.0000000000
1 N -0.1364944014 -0.0625759323 0.0000000000
2 O 0.0609843523 0.0470933974 -0.0000000000
3 O 0.0289060280 0.0154588415 0.0000000000
4 O -0.0289060280 -0.0154588415 0.0000000000
5 O -0.0609843523 -0.0470933974 0.0000000000
----------------------------------------------
cycle 1: E = -407.731086259 dE = -407.731 norm(grad) = 0.243137
Step 0 : Gradient = 9.926e-02/1.502e-01 (rms/max) Energy = -407.7310862587
Hessian Eigenvalues: 2.30000e-02 2.81592e-02 2.85714e-02 ... 6.28366e-01 1.07911e+00 1.07911e+00
Geometry optimization cycle 2
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
N -4.859695 1.735825 0.000000 -0.013315 -0.025265 0.000000
N -3.450568 1.758850 0.000000 0.018312 -0.025300 0.000000
O -2.988665 2.947542 0.000000 -0.164815 0.015852 0.000000
O -2.831116 0.738932 -0.000000 0.019434 -0.023828 -0.000000
O -5.332764 2.831342 -0.000000 0.131946 0.048862 -0.000000
O -5.482972 0.623229 -0.000000 0.008438 0.009679 -0.000000
WARN: Large deviations found between the input molecule and the molecule from chkfile
Initial guess density matrix may have large error.
converged SCF energy = -407.750917665723
--------------- SCF_Scanner gradients ---------------
x y z
0 N 0.0943391425 0.0387264897 0.0000000000
1 N -0.0903687332 -0.0623329117 0.0000000000
2 O 0.0080957325 0.0618298086 -0.0000000000
3 O 0.0131065114 0.0033624877 -0.0000000000
4 O 0.0176448915 0.0069266968 -0.0000000000
5 O -0.0428175448 -0.0485125711 -0.0000000000
----------------------------------------------
cycle 2: E = -407.750917666 dE = -0.0198314 norm(grad) = 0.176265
Step 1 : Displace = 9.139e-02/1.656e-01 (rms/max) Trust = 1.000e-01 (=) Grad = 7.196e-02/1.098e-01 (rms/max) E (change) = -407.7509176657 (-1.983e-02) Quality = 0.794
Hessian Eigenvalues: 2.30000e-02 2.81592e-02 2.85714e-02 ... 1.07801e+00 1.07900e+00 1.33965e+00
Geometry optimization cycle 3
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
N -4.915822 1.782068 -0.000000 -0.056127 0.046243 -0.000000
N -3.390852 1.806572 -0.000000 0.059716 0.047723 -0.000000
O -2.913483 2.861478 0.000000 0.075182 -0.086064 0.000000
O -2.967615 0.693999 -0.000000 -0.136499 -0.044933 0.000000
O -5.508769 2.816442 0.000000 -0.176005 -0.014900 0.000000
O -5.249239 0.675160 -0.000000 0.233733 0.051931 -0.000000
WARN: Large deviations found between the input molecule and the molecule from chkfile
Initial guess density matrix may have large error.
converged SCF energy = -407.762539830669
--------------- SCF_Scanner gradients ---------------
x y z
0 N -0.0032089139 -0.0254232494 -0.0000000000
1 N 0.0120939071 0.0329851457 0.0000000000
2 O -0.0353281201 -0.0576892460 -0.0000000000
3 O -0.0350901526 0.0071808802 0.0000000000
4 O 0.0032286716 -0.0180561510 0.0000000000
5 O 0.0583046080 0.0610026204 0.0000000000
----------------------------------------------
cycle 3: E = -407.762539831 dE = -0.0116222 norm(grad) = 0.123317
Step 2 : Displace = 1.491e-01/2.385e-01 (rms/max) Trust = 1.414e-01 (+) Grad = 5.034e-02/8.438e-02 (rms/max) E (change) = -407.7625398307 (-1.162e-02) Quality = 0.290
Hessian Eigenvalues: 2.30000e-02 2.81592e-02 2.85714e-02 ... 1.07632e+00 1.08140e+00 1.38171e+00
Geometry optimization cycle 4
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
N -4.944516 1.731913 -0.000000 -0.028694 -0.050155 -0.000000
N -3.385457 1.811430 -0.000000 0.005394 0.004858 -0.000000
O -2.883788 2.897180 0.000000 0.029695 0.035702 0.000000
O -2.855817 0.739624 -0.000000 0.111798 0.045625 -0.000000
O -5.446839 2.818713 0.000000 0.061930 0.002271 0.000000
O -5.429362 0.636859 -0.000000 -0.180123 -0.038300 -0.000000
WARN: Large deviations found between the input molecule and the molecule from chkfile
Initial guess density matrix may have large error.
converged SCF energy = -407.775050492622
--------------- SCF_Scanner gradients ---------------
x y z
0 N 0.0167386493 -0.0163436526 -0.0000000000
1 N -0.0284120855 0.0160348932 0.0000000000
2 O 0.0145334538 -0.0073045289 -0.0000000000
3 O 0.0035574426 0.0073498720 0.0000000000
4 O 0.0031853919 0.0026720890 0.0000000000
5 O -0.0096028520 -0.0024086727 0.0000000000
----------------------------------------------
cycle 4: E = -407.775050493 dE = -0.0125107 norm(grad) = 0.0453676
Step 3 : Displace = 9.822e-02/1.845e-01 (rms/max) Trust = 1.414e-01 (=) Grad = 1.852e-02/3.262e-02 (rms/max) E (change) = -407.7750504926 (-1.251e-02) Quality = 0.715
Hessian Eigenvalues: 2.30000e-02 2.81592e-02 2.85714e-02 ... 1.07452e+00 1.08361e+00 1.32790e+00
Geometry optimization cycle 5
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
N -4.932195 1.772838 0.000000 0.012321 0.040925 0.000000
N -3.348101 1.757478 -0.000000 0.037356 -0.053952 0.000000
O -2.960658 2.897661 0.000000 -0.076870 0.000481 0.000000
O -2.791436 0.695477 -0.000000 0.064381 -0.044148 -0.000000
O -5.486881 2.835020 -0.000000 -0.040041 0.016306 -0.000000
O -5.426508 0.677247 -0.000000 0.002854 0.040387 -0.000000
WARN: Large deviations found between the input molecule and the molecule from chkfile
Initial guess density matrix may have large error.
converged SCF energy = -407.77279191531
--------------- SCF_Scanner gradients ---------------
x y z
0 N 0.0357477039 0.0285488303 0.0000000000
1 N -0.0045052705 -0.0323482972 -0.0000000000
2 O -0.0134293717 0.0182095003 0.0000000000
3 O 0.0126846343 -0.0110699765 0.0000000000
4 O -0.0194028901 -0.0038489686 -0.0000000000
5 O -0.0110948058 0.0005089119 -0.0000000000
----------------------------------------------
cycle 5: E = -407.772791915 dE = 0.00225858 norm(grad) = 0.0668555
Step 4 : Displace = 6.006e-02/7.812e-02 (rms/max) Trust = 1.414e-01 (=) Grad = 2.729e-02/4.575e-02 (rms/max) E (change) = -407.7727919153 (+2.259e-03) Quality = -0.627
Hessian Eigenvalues: 2.30000e-02 2.81592e-02 2.85714e-02 ... 1.08136e+00 1.14620e+00 1.33623e+00
Geometry optimization cycle 6
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
N -4.948260 1.753813 0.000000 -0.016064 -0.019025 -0.000000
N -3.360026 1.786434 -0.000000 -0.011924 0.028956 0.000000
O -2.918153 2.897632 0.000000 0.042505 -0.000030 -0.000000
O -2.831435 0.713653 -0.000000 -0.039999 0.018176 0.000000
O -5.471242 2.830404 -0.000000 0.015639 -0.004616 -0.000000
O -5.416664 0.653785 -0.000000 0.009844 -0.023462 0.000000
converged SCF energy = -407.777010757933
--------------- SCF_Scanner gradients ---------------
x y z
0 N 0.0154010104 0.0030923593 0.0000000000
1 N -0.0089625316 -0.0059584301 -0.0000000000
2 O -0.0007361967 0.0036441320 0.0000000000
3 O 0.0050445045 -0.0025678925 0.0000000000
4 O -0.0063731138 0.0016807551 -0.0000000000
5 O -0.0043736727 0.0001090761 -0.0000000000
----------------------------------------------
cycle 6: E = -407.777010758 dE = -0.00421884 norm(grad) = 0.0217032
Step 5 : Displace = 3.228e-02/4.400e-02 (rms/max) Trust = 3.003e-02 (-) Grad = 8.860e-03/1.571e-02 (rms/max) E (change) = -407.7770107579 (-4.219e-03) Quality = 1.014
Hessian Eigenvalues: 2.30000e-02 2.81592e-02 2.85714e-02 ... 1.07133e+00 1.11476e+00 1.33511e+00
Geometry optimization cycle 7
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
N -4.958218 1.749749 0.000000 -0.009958 -0.004064 -0.000000
N -3.356461 1.794699 0.000000 0.003564 0.008265 0.000000
O -2.908043 2.898367 -0.000000 0.010110 0.000735 -0.000000
O -2.844819 0.715404 -0.000000 -0.013384 0.001752 -0.000000
O -5.468233 2.830183 -0.000000 0.003010 -0.000220 -0.000000
O -5.410006 0.647317 -0.000000 0.006658 -0.006468 -0.000000
converged SCF energy = -407.777408714019
--------------- SCF_Scanner gradients ---------------
x y z
0 N 0.0043083815 -0.0034976279 -0.0000000000
1 N -0.0036180253 0.0030164519 0.0000000000
2 O -0.0010920174 -0.0017519136 -0.0000000000
3 O 0.0005217173 -0.0012770455 -0.0000000000
4 O -0.0006044468 0.0016804367 -0.0000000000
5 O 0.0004843907 0.0018296984 -0.0000000000
----------------------------------------------
cycle 7: E = -407.777408714 dE = -0.000397956 norm(grad) = 0.00811918
Step 6 : Displace = 9.806e-03/1.350e-02 (rms/max) Trust = 4.247e-02 (+) Grad = 3.315e-03/5.549e-03 (rms/max) E (change) = -407.7774087140 (-3.980e-04) Quality = 1.131
Hessian Eigenvalues: 2.30000e-02 2.81592e-02 2.85714e-02 ... 1.05076e+00 1.12800e+00 1.33199e+00
Geometry optimization cycle 8
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
N -4.963177 1.750279 -0.000000 -0.004959 0.000530 -0.000000
N -3.352683 1.795491 -0.000000 0.003778 0.000792 -0.000000
O -2.902689 2.899271 0.000000 0.005354 0.000904 0.000000
O -2.845295 0.715170 0.000000 -0.000475 -0.000235 0.000000
O -5.471582 2.830141 0.000000 -0.003350 -0.000042 0.000000
O -5.410354 0.645368 0.000000 -0.000348 -0.001949 0.000000
converged SCF energy = -407.77746632172
--------------- SCF_Scanner gradients ---------------
x y z
0 N 0.0016135500 -0.0018204235 0.0000000000
1 N -0.0021103603 0.0019798040 -0.0000000000
2 O -0.0001917970 -0.0005655466 0.0000000000
3 O 0.0000036980 -0.0011081985 0.0000000000
4 O -0.0000011732 0.0012770059 0.0000000000
5 O 0.0006860824 0.0002373587 0.0000000000
----------------------------------------------
cycle 8: E = -407.777466322 dE = -5.76077e-05 norm(grad) = 0.00424656
Step 7 : Displace = 3.757e-03/5.426e-03 (rms/max) Trust = 6.006e-02 (+) Grad = 1.734e-03/2.894e-03 (rms/max) E (change) = -407.7774663217 (-5.761e-05) Quality = 1.396
Hessian Eigenvalues: 2.30000e-02 2.81592e-02 2.85714e-02 ... 1.03997e+00 1.13528e+00 1.33164e+00
Geometry optimization cycle 9
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
N -4.967844 1.750370 0.000000 -0.004667 0.000091 0.000000
N -3.347870 1.794966 0.000000 0.004813 -0.000525 0.000000
O -2.900154 2.899180 -0.000000 0.002534 -0.000091 -0.000000
O -2.840854 0.715856 -0.000000 0.004440 0.000687 -0.000000
O -5.474477 2.829494 -0.000000 -0.002894 -0.000647 -0.000000
O -5.414580 0.645854 -0.000000 -0.004226 0.000486 -0.000000
converged SCF energy = -407.777487563799
--------------- SCF_Scanner gradients ---------------
x y z
0 N -0.0006769238 -0.0007927238 -0.0000000000
1 N 0.0001909845 0.0008840420 0.0000000000
2 O -0.0002124930 -0.0009779243 -0.0000000000
3 O -0.0000123071 0.0001856285 -0.0000000000
4 O 0.0002351671 -0.0002413196 -0.0000000000
5 O 0.0004755722 0.0009422972 -0.0000000000
----------------------------------------------
cycle 9: E = -407.777487564 dE = -2.12421e-05 norm(grad) = 0.00204166
Step 8 : Displace = 4.056e-03/4.845e-03 (rms/max) Trust = 8.493e-02 (+) Grad = 8.335e-04/1.056e-03 (rms/max) E (change) = -407.7774875638 (-2.124e-05) Quality = 0.950
Hessian Eigenvalues: 2.30000e-02 2.81592e-02 2.85714e-02 ... 1.06763e+00 1.13344e+00 1.34009e+00
Geometry optimization cycle 10
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
N -4.967545 1.750690 -0.000000 0.000300 0.000320 -0.000000
N -3.347710 1.794765 -0.000000 0.000160 -0.000201 -0.000000
O -2.899789 2.899865 0.000000 0.000365 0.000685 0.000000
O -2.841150 0.715474 0.000000 -0.000296 -0.000382 0.000000
O -5.474792 2.829592 0.000000 -0.000315 0.000098 0.000000
O -5.414794 0.645335 0.000000 -0.000214 -0.000519 0.000000
converged SCF energy = -407.777488977639
--------------- SCF_Scanner gradients ---------------
x y z
0 N 0.0000385726 0.0002400961 0.0000000000
1 N -0.0000661667 -0.0001143478 -0.0000000000
2 O 0.0001470824 0.0003034762 0.0000000000
3 O -0.0000136078 -0.0001655059 0.0000000000
4 O -0.0000414104 0.0000320455 0.0000000000
5 O -0.0000644701 -0.0002957641 0.0000000000
----------------------------------------------
cycle 10: E = -407.777488978 dE = -1.41384e-06 norm(grad) = 0.000558812
Step 9 : Displace = 5.027e-04/7.841e-04 (rms/max) Trust = 1.201e-01 (+) Grad = 2.281e-04/3.372e-04 (rms/max) E (change) = -407.7774889776 (-1.414e-06) Quality = 0.710
Hessian Eigenvalues: 2.30000e-02 2.81592e-02 2.85714e-02 ... 1.12912e+00 1.15995e+00 1.31317e+00
Geometry optimization cycle 11
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
N -4.967460 1.750594 0.000000 0.000085 -0.000096 0.000000
N -3.347821 1.794687 0.000000 -0.000111 -0.000078 0.000000
O -2.900219 2.899680 -0.000000 -0.000429 -0.000184 -0.000000
O -2.840848 0.715608 -0.000000 0.000302 0.000134 -0.000000
O -5.474510 2.829621 -0.000000 0.000282 0.000029 -0.000000
O -5.414922 0.645530 -0.000000 -0.000128 0.000195 -0.000000
converged SCF energy = -407.777489182369
--------------- SCF_Scanner gradients ---------------
x y z
0 N -0.0000024820 0.0000040969 -0.0000000000
1 N -0.0000158577 0.0000369278 0.0000000000
2 O 0.0000063276 -0.0000166462 -0.0000000000
3 O 0.0000143615 -0.0000255472 -0.0000000000
4 O -0.0000113681 0.0000129975 -0.0000000000
5 O 0.0000090187 -0.0000118288 -0.0000000000
----------------------------------------------
cycle 11: E = -407.777489182 dE = -2.0473e-07 norm(grad) = 5.77368e-05
Step 10 : Displace = 2.876e-04/4.654e-04 (rms/max) Trust = 1.201e-01 (=) Grad = 2.357e-05/4.019e-05 (rms/max) E (change) = -407.7774891824 (-2.047e-07) Quality = 1.036
Hessian Eigenvalues: 2.30000e-02 2.81592e-02 2.85714e-02 ... 1.12912e+00 1.15995e+00 1.31317e+00
Converged! =D
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#| 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: 17.373 seconds
converged SCF energy = -407.777489182482
Pregunta 2. Complete el siguiente código para calcular la energía de la molécula optimizada de \(NO_2\) con Hartree-Fock y la base 6-31G.
Ayuda. Reemplace XXXX por los valores apropiados.
Nota. El \(NO_2\) es un doblete (\(2S+1 = 2\), capa abierta) mientras que el \(N_2O_4\) es un singulete (\(2S+1 = 1\), capa cerrada). ¿Que diferencias tiene el código de esta celda respecto al de la anterior?
NO2 = pyscf.gto.Mole(atom="""
N XXXXXXX XXXXXXX XXXXXXX
O XXXXXXX XXXXXXX XXXXXXX
O XXXXXXX XXXXXXX XXXXXXX
""",spin=1,basis="6-31G")
NO2.max_memory = XXXX
NO2.build()
uhf = scf.UHF(NO2)
NO2_eq = optimize(uhf)
uhf = scf.UHF(NO2_eq)
no2 = uhf.kernel()
# Optimice Geometría y obtenga la energia NO2 HF/6-31G
NO2 = pyscf.gto.Mole(atom="""
N -4.39539 1.87380 0.00000
O -3.90978 3.09520 -0.00000
O -3.65594 0.93810 0.00000
""",spin=1,basis="6-31G")
NO2.max_memory = 2000
NO2.build()
uhf = scf.UHF(NO2)
NO2_eq = optimize(uhf)
uhf = scf.UHF(NO2_eq)
no2 = uhf.kernel()
geometric-optimize called with the following command line:
/home/jfhlewyee/anaconda3/envs/jb/lib/python3.10/site-packages/ipykernel_launcher.py -f /tmp/tmp20bm5290.json --HistoryManager.hist_file=:memory:
())))))))))))))))/
())))))))))))))))))))))))),
*)))))))))))))))))))))))))))))))))
#, ()))))))))/ .)))))))))),
#%%%%, ()))))) .))))))))*
*%%%%%%, )) .. ,))))))).
*%%%%%%, ***************/. .)))))))
#%%/ (%%%%%%, /*********************. )))))))
.%%%%%%# *%%%%%%, *******/, **********, .))))))
.%%%%%%/ *%%%%%%, ** ******** .))))))
## .%%%%%%/ (%%%%%%, ,****** /)))))
%%%%%% .%%%%%%# *%%%%%%, ,/////. ****** ))))))
#% %% .%%%%%%/ *%%%%%%, ////////, *****/ ,)))))
#%% %%% %%%# .%%%%%%/ (%%%%%%, ///////. /***** ))))).
#%%%%. %%%%%# /%%%%%%* #%%%%%% /////) ****** ))))),
#%%%%##% %%%# .%%%%%%/ (%%%%%%, ///////. /***** ))))).
## %%% .%%%%%%/ *%%%%%%, ////////. *****/ ,)))))
#%%%%# /%%%%%%/ (%%%%%% /)/)// ****** ))))))
## .%%%%%%/ (%%%%%%, ******* ))))))
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#%%/ (%%%%%%, *********************/ )))))))
*%%%%%%, ,**************/ ,))))))/
(%%%%%% () ))))))))
#%%%%, ()))))) ,)))))))),
#, ()))))))))) ,)))))))))).
()))))))))))))))))))))))))))))))/
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())))))))))))))),
-=# geomeTRIC started. Version: 1.0 #=-
Current date and time: 2022-12-13 13:53:20
Custom engine selected.
Bonds will be generated from interatomic distances less than 1.20 times sum of covalent radii
9 internal coordinates being used (instead of 9 Cartesians)
Internal coordinate system (atoms numbered from 1):
Distance 1-2
Distance 1-3
Angle 2-1-3
Translation-X 1-3
Translation-Y 1-3
Translation-Z 1-3
Rotation-A 1-3
Rotation-B 1-3
Rotation-C 1-3
<class 'geometric.internal.Distance'> : 2
<class 'geometric.internal.Angle'> : 1
<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 ===
Geometry optimization cycle 1
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
N -4.395390 1.873800 0.000000 0.000000 0.000000 0.000000
O -3.909780 3.095200 0.000000 0.000000 0.000000 0.000000
O -3.655940 0.938100 0.000000 0.000000 0.000000 0.000000
converged SCF energy = -203.882695374303 <S^2> = 0.80452483 2S+1 = 2.0538012
--------------- SCF_Scanner gradients ---------------
x y z
0 N -0.1062928148 -0.0412675055 -0.0000000000
1 O 0.0553697683 0.0414978706 -0.0000000000
2 O 0.0509230464 -0.0002303650 0.0000000000
----------------------------------------------
cycle 1: E = -203.882695374 dE = -203.883 norm(grad) = 0.142766
Step 0 : Gradient = 8.243e-02/1.140e-01 (rms/max) Energy = -203.8826953743
Hessian Eigenvalues: 5.00000e-02 5.00000e-02 5.00000e-02 ... 2.50000e-01 6.33488e-01 1.08625e+00
Geometry optimization cycle 2
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
N -4.273186 1.902920 0.000000 0.122204 0.029120 0.000000
O -3.977526 3.135717 0.000000 -0.067746 0.040517 0.000000
O -3.710397 0.868462 -0.000000 -0.054457 -0.069638 -0.000000
WARN: Large deviations found between the input molecule and the molecule from chkfile
Initial guess density matrix may have large error.
converged SCF energy = -203.901354509923 <S^2> = 0.77734474 2S+1 = 2.0271603
--------------- SCF_Scanner gradients ---------------
x y z
0 N -0.0109124496 -0.0504452233 -0.0000000000
1 O 0.0096178119 0.0669108747 0.0000000000
2 O 0.0012946378 -0.0164656514 0.0000000000
----------------------------------------------
cycle 2: E = -203.90135451 dE = -0.0186591 norm(grad) = 0.0866381
Step 1 : Displace = 9.971e-02/1.256e-01 (rms/max) Trust = 1.000e-01 (=) Grad = 5.002e-02/6.760e-02 (rms/max) E (change) = -203.9013545099 (-1.866e-02) Quality = 0.980
Hessian Eigenvalues: 5.00000e-02 5.00000e-02 5.00000e-02 ... 2.68542e-01 6.41709e-01 1.07062e+00
Geometry optimization cycle 3
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
N -4.257463 1.925148 0.000000 0.015723 0.022228 0.000000
O -3.986571 3.089708 0.000000 -0.009044 -0.046009 -0.000000
O -3.717076 0.892243 -0.000000 -0.006679 0.023781 0.000000
WARN: Large deviations found between the input molecule and the molecule from chkfile
Initial guess density matrix may have large error.
converged SCF energy = -203.906059614238 <S^2> = 0.76765288 2S+1 = 2.0175757
--------------- SCF_Scanner gradients ---------------
x y z
0 N 0.0286709510 -0.0281400904 0.0000000000
1 O -0.0067255623 0.0013751407 0.0000000000
2 O -0.0219453888 0.0267649497 -0.0000000000
----------------------------------------------
cycle 3: E = -203.906059614 dE = -0.0047051 norm(grad) = 0.0534694
Step 2 : Displace = 3.437e-02/4.659e-02 (rms/max) Trust = 1.414e-01 (+) Grad = 3.087e-02/4.017e-02 (rms/max) E (change) = -203.9060596142 (-4.705e-03) Quality = 1.027
Hessian Eigenvalues: 5.00000e-02 5.00000e-02 5.00000e-02 ... 3.33010e-01 4.79949e-01 1.29868e+00
Geometry optimization cycle 4
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
N -4.275164 1.928065 0.000000 -0.017701 0.002917 0.000000
O -3.979321 3.084953 -0.000000 0.007249 -0.004755 -0.000000
O -3.706624 0.894082 0.000000 0.010452 0.001838 0.000000
WARN: Large deviations found between the input molecule and the molecule from chkfile
Initial guess density matrix may have large error.
converged SCF energy = -203.907030721303 <S^2> = 0.76811904 2S+1 = 2.0180377
--------------- SCF_Scanner gradients ---------------
x y z
0 N 0.0064333903 -0.0126381801 0.0000000000
1 O 0.0000265982 0.0017440774 -0.0000000000
2 O -0.0064599885 0.0108941027 -0.0000000000
----------------------------------------------
cycle 4: E = -203.907030721 dE = -0.000971107 norm(grad) = 0.0190937
Step 3 : Displace = 1.301e-02/1.801e-02 (rms/max) Trust = 2.000e-01 (+) Grad = 1.102e-02/1.418e-02 (rms/max) E (change) = -203.9070307213 (-9.711e-04) Quality = 1.236
Hessian Eigenvalues: 5.00000e-02 5.00000e-02 5.00000e-02 ... 3.73607e-01 4.21668e-01 9.94827e-01
Geometry optimization cycle 5
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
N -4.277793 1.932140 -0.000000 -0.002629 0.004075 -0.000000
O -3.979411 3.083437 -0.000000 -0.000089 -0.001516 -0.000000
O -3.703906 0.891523 0.000000 0.002718 -0.002559 0.000000
WARN: Large deviations found between the input molecule and the molecule from chkfile
Initial guess density matrix may have large error.
converged SCF energy = -203.907151331469 <S^2> = 0.76820709 2S+1 = 2.018125
--------------- SCF_Scanner gradients ---------------
x y z
0 N 0.0012212717 -0.0007327856 0.0000000000
1 O -0.0001961482 -0.0015289036 0.0000000000
2 O -0.0010251235 0.0022616893 -0.0000000000
----------------------------------------------
cycle 5: E = -203.907151331 dE = -0.00012061 norm(grad) = 0.00325125
Step 4 : Displace = 3.622e-03/4.954e-03 (rms/max) Trust = 2.828e-01 (+) Grad = 1.877e-03/2.483e-03 (rms/max) E (change) = -203.9071513315 (-1.206e-04) Quality = 1.096
Hessian Eigenvalues: 5.00000e-02 5.00000e-02 5.00000e-02 ... 3.73054e-01 4.80258e-01 7.81474e-01
Geometry optimization cycle 6
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
N -4.278012 1.932263 -0.000000 -0.000219 0.000123 -0.000000
O -3.979501 3.084753 -0.000000 -0.000090 0.001316 -0.000000
O -3.703597 0.890083 0.000000 0.000309 -0.001440 0.000000
converged SCF energy = -203.907155413675 <S^2> = 0.76833946 2S+1 = 2.0182561
--------------- SCF_Scanner gradients ---------------
x y z
0 N -0.0003892613 -0.0005234345 -0.0000000000
1 O 0.0002174125 0.0008308163 0.0000000000
2 O 0.0001718488 -0.0003073818 -0.0000000000
----------------------------------------------
cycle 6: E = -203.907155414 dE = -4.08221e-06 norm(grad) = 0.00113448
Step 5 : Displace = 1.151e-03/1.472e-03 (rms/max) Trust = 3.000e-01 (+) Grad = 6.550e-04/8.588e-04 (rms/max) E (change) = -203.9071554137 (-4.082e-06) Quality = 0.729
Hessian Eigenvalues: 5.00000e-02 5.00000e-02 5.00000e-02 ... 3.75615e-01 4.81307e-01 9.82314e-01
Geometry optimization cycle 7
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
N -4.277873 1.932476 -0.000000 0.000139 0.000213 0.000000
O -3.979589 3.084376 -0.000000 -0.000088 -0.000377 -0.000000
O -3.703648 0.890248 0.000000 -0.000051 0.000165 0.000000
converged SCF energy = -203.907155932957 <S^2> = 0.76830571 2S+1 = 2.0182227
--------------- SCF_Scanner gradients ---------------
x y z
0 N 0.0000049473 0.0000391722 -0.0000000000
1 O -0.0000106355 -0.0000212663 0.0000000000
2 O 0.0000056882 -0.0000179059 -0.0000000000
----------------------------------------------
cycle 7: E = -203.907155933 dE = -5.19283e-07 norm(grad) = 4.97723e-05
Step 6 : Displace = 2.852e-04/3.849e-04 (rms/max) Trust = 3.000e-01 (=) Grad = 2.874e-05/3.948e-05 (rms/max) E (change) = -203.9071559330 (-5.193e-07) Quality = 0.986
Hessian Eigenvalues: 5.00000e-02 5.00000e-02 5.00000e-02 ... 3.75615e-01 4.81307e-01 9.82314e-01
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: 2.511 seconds
converged SCF energy = -203.907155922822 <S^2> = 0.76830428 2S+1 = 2.0182213
Pregunta a. Calcule el \(\Delta U\) de la reacción \(N_2O_4\) ↔ \(2NO_2\) según HF.
# Obtenga la energía de reacción (2E_{NO2} - E_{N2O4}). Recuerde convertur Hartree->kcal/mol.
(2*no2-n2o4)*2625.5
-96.67790213111948
Pregunta 3. Calcule la energía de la molécula optimizada de \(N_2O_4\) con DFT B3LYP y la base 6-31G.
Ayuda. Reutilice el código de la pregunta 1, pero recuerde que va a usar DFT y requiere especificar un funcional.
# Optimice Geometría y obtenga la energia N2O4 B3LYP/6-31G
N2O4 = pyscf.gto.Mole(atom="""
N -4.84638 1.76109 0.00000
N -3.46888 1.78415 0.00000
O -2.82385 2.93169 -0.00000
O -2.85055 0.76276 0.00000
O -5.46471 2.78248 0.00000
O -5.49141 0.61355 0.00000
""",basis="6-31G")
N2O4.max_memory = 2000
N2O4.build()
rks = dft.RKS(N2O4)
rks.xc = "B3LYP"
N2O4_eq = optimize(rks)
rks = dft.RKS(N2O4_eq)
rks.xc = "B3LYP"
n2o4 = rks.kernel()
geometric-optimize called with the following command line:
/home/jfhlewyee/anaconda3/envs/jb/lib/python3.10/site-packages/ipykernel_launcher.py -f /tmp/tmp20bm5290.json --HistoryManager.hist_file=:memory:
())))))))))))))))/
())))))))))))))))))))))))),
*)))))))))))))))))))))))))))))))))
#, ()))))))))/ .)))))))))),
#%%%%, ()))))) .))))))))*
*%%%%%%, )) .. ,))))))).
*%%%%%%, ***************/. .)))))))
#%%/ (%%%%%%, /*********************. )))))))
.%%%%%%# *%%%%%%, *******/, **********, .))))))
.%%%%%%/ *%%%%%%, ** ******** .))))))
## .%%%%%%/ (%%%%%%, ,****** /)))))
%%%%%% .%%%%%%# *%%%%%%, ,/////. ****** ))))))
#% %% .%%%%%%/ *%%%%%%, ////////, *****/ ,)))))
#%% %%% %%%# .%%%%%%/ (%%%%%%, ///////. /***** ))))).
#%%%%. %%%%%# /%%%%%%* #%%%%%% /////) ****** ))))),
#%%%%##% %%%# .%%%%%%/ (%%%%%%, ///////. /***** ))))).
## %%% .%%%%%%/ *%%%%%%, ////////. *****/ ,)))))
#%%%%# /%%%%%%/ (%%%%%% /)/)// ****** ))))))
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.%%%%%%/ *%%%%%%, **. /******* .))))))
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*%%%%%%, ,**************/ ,))))))/
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-=# geomeTRIC started. Version: 1.0 #=-
Current date and time: 2022-12-13 13:53:22
Custom engine selected.
Bonds will be generated from interatomic distances less than 1.20 times sum of covalent radii
18 internal coordinates being used (instead of 18 Cartesians)
Internal coordinate system (atoms numbered from 1):
Distance 1-2
Distance 1-5
Distance 1-6
Distance 2-3
Distance 2-4
Angle 2-1-6
Angle 5-1-6
Angle 1-2-4
Angle 3-2-4
Out-of-Plane 1-2-5-6
Out-of-Plane 2-1-3-4
Dihedral 5-1-2-3
Dihedral 5-1-2-4
Dihedral 6-1-2-3
Dihedral 6-1-2-4
Translation-X 1-6
Translation-Y 1-6
Translation-Z 1-6
Rotation-A 1-6
Rotation-B 1-6
Rotation-C 1-6
<class 'geometric.internal.Distance'> : 5
<class 'geometric.internal.Angle'> : 4
<class 'geometric.internal.OutOfPlane'> : 2
<class 'geometric.internal.Dihedral'> : 4
<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 ===
Geometry optimization cycle 1
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
N -4.846380 1.761090 0.000000 0.000000 0.000000 0.000000
N -3.468880 1.784150 0.000000 0.000000 0.000000 0.000000
O -2.823850 2.931690 0.000000 0.000000 0.000000 0.000000
O -2.850550 0.762760 0.000000 0.000000 0.000000 0.000000
O -5.464710 2.782480 0.000000 0.000000 0.000000 0.000000
O -5.491410 0.613550 0.000000 0.000000 0.000000 0.000000
converged SCF energy = -409.756385238947
--------------- SCF_Scanner gradients ---------------
x y z
0 N 0.1341253624 0.0842921006 0.0000000000
1 N -0.1341253629 -0.0842920968 0.0000000000
2 O 0.0496368527 0.0186572750 -0.0000000000
3 O -0.0108256294 0.0765464853 -0.0000000000
4 O 0.0108256301 -0.0765464877 0.0000000000
5 O -0.0496368529 -0.0186572764 0.0000000000
----------------------------------------------
cycle 1: E = -409.756385239 dE = -409.756 norm(grad) = 0.26032
Step 0 : Gradient = 1.063e-01/1.584e-01 (rms/max) Energy = -409.7563852389
Hessian Eigenvalues: 2.30000e-02 2.81592e-02 2.85714e-02 ... 6.28366e-01 1.07911e+00 1.07911e+00
Geometry optimization cycle 2
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
N -4.871262 1.749145 -0.000000 -0.024882 -0.011945 -0.000000
N -3.426965 1.741374 -0.000000 0.041915 -0.042776 -0.000000
O -3.001013 2.961382 0.000000 -0.177163 0.029692 0.000000
O -2.783837 0.702231 0.000000 0.066713 -0.060529 0.000000
O -5.369365 2.865086 -0.000000 0.095345 0.082606 -0.000000
O -5.493338 0.616502 -0.000000 -0.001928 0.002952 -0.000000
WARN: Large deviations found between the input molecule and the molecule from chkfile
Initial guess density matrix may have large error.
converged SCF energy = -409.78329074404
--------------- SCF_Scanner gradients ---------------
x y z
0 N 0.1102494294 0.0516268946 0.0000000000
1 N -0.0917653930 -0.0645874793 -0.0000000000
2 O -0.0055182626 0.0419895584 0.0000000000
3 O 0.0054255790 0.0143390792 -0.0000000000
4 O 0.0141163791 -0.0113971693 0.0000000000
5 O -0.0324643265 -0.0320147729 -0.0000000000
----------------------------------------------
cycle 2: E = -409.783290744 dE = -0.0269055 norm(grad) = 0.178464
Step 1 : Displace = 1.005e-01/1.796e-01 (rms/max) Trust = 1.000e-01 (=) Grad = 7.286e-02/1.217e-01 (rms/max) E (change) = -409.7832907440 (-2.691e-02) Quality = 0.807
Hessian Eigenvalues: 2.30000e-02 2.81592e-02 2.85714e-02 ... 7.78060e-01 1.07803e+00 1.29127e+00
Geometry optimization cycle 3
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
N -4.957379 1.783357 -0.000000 -0.086117 0.034212 -0.000000
N -3.363882 1.806757 0.000000 0.063083 0.065384 0.000000
O -2.816321 2.918297 0.000000 0.184692 -0.043086 0.000000
O -2.870150 0.648331 0.000000 -0.086312 -0.053899 0.000000
O -5.598452 2.870605 -0.000000 -0.229086 0.005519 -0.000000
O -5.340442 0.609227 -0.000000 0.152896 -0.007276 -0.000000
WARN: Large deviations found between the input molecule and the molecule from chkfile
Initial guess density matrix may have large error.
converged SCF energy = -409.806973112744
--------------- SCF_Scanner gradients ---------------
x y z
0 N 0.0626381325 -0.0044809072 0.0000000000
1 N -0.0673613948 0.0094590597 -0.0000000000
2 O 0.0120372450 0.0095800103 -0.0000000000
3 O 0.0103439790 -0.0306342733 0.0000000000
4 O -0.0276270127 0.0267624820 -0.0000000000
5 O 0.0099364897 -0.0106857380 0.0000000000
----------------------------------------------
cycle 3: E = -409.806973113 dE = -0.0236824 norm(grad) = 0.107448
Step 2 : Displace = 1.523e-01/2.276e-01 (rms/max) Trust = 1.414e-01 (+) Grad = 4.387e-02/6.802e-02 (rms/max) E (change) = -409.8069731127 (-2.368e-02) Quality = 0.644
Hessian Eigenvalues: 2.30000e-02 2.81592e-02 2.85714e-02 ... 1.04661e+00 1.08809e+00 1.24286e+00
Geometry optimization cycle 4
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
N -5.023104 1.708541 -0.000000 -0.065725 -0.074816 0.000000
N -3.325983 1.839231 0.000000 0.037899 0.032473 0.000000
O -2.818150 2.933124 0.000000 -0.001829 0.014827 0.000000
O -2.805907 0.697082 0.000000 0.064242 0.048751 -0.000000
O -5.502899 2.870556 0.000000 0.095553 -0.000049 0.000000
O -5.469354 0.588827 -0.000000 -0.128912 -0.020400 -0.000000
WARN: Large deviations found between the input molecule and the molecule from chkfile
Initial guess density matrix may have large error.
converged SCF energy = -409.81402743392
--------------- SCF_Scanner gradients ---------------
x y z
0 N 0.0164778802 -0.0602690022 -0.0000000000
1 N -0.0374042921 0.0594036500 0.0000000000
2 O 0.0045765596 -0.0250472986 -0.0000000000
3 O 0.0095958000 -0.0176345202 -0.0000000000
4 O 0.0011226215 0.0304528581 0.0000000000
5 O 0.0056088662 0.0130917806 0.0000000000
----------------------------------------------
cycle 4: E = -409.814027434 dE = -0.00705432 norm(grad) = 0.10495
Step 3 : Displace = 8.688e-02/1.316e-01 (rms/max) Trust = 1.414e-01 (=) Grad = 4.285e-02/7.020e-02 (rms/max) E (change) = -409.8140274339 (-7.054e-03) Quality = 0.742
Hessian Eigenvalues: 2.30000e-02 2.81592e-02 2.85714e-02 ... 8.79754e-01 1.07735e+00 1.25069e+00
Geometry optimization cycle 5
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
N -5.030364 1.743040 -0.000000 -0.007260 0.034499 -0.000000
N -3.260110 1.791623 0.000000 0.065873 -0.047607 0.000000
O -2.862663 2.929961 0.000000 -0.044513 -0.003163 0.000000
O -2.724719 0.672623 0.000000 0.081189 -0.024459 0.000000
O -5.561214 2.862758 0.000000 -0.058316 -0.007798 -0.000000
O -5.504625 0.638058 -0.000000 -0.035272 0.049231 -0.000000
WARN: Large deviations found between the input molecule and the molecule from chkfile
Initial guess density matrix may have large error.
converged SCF energy = -409.819010653918
--------------- SCF_Scanner gradients ---------------
x y z
0 N 0.0168211431 -0.0317565804 -0.0000000000
1 N -0.0049936490 0.0282677790 -0.0000000000
2 O -0.0117340331 -0.0179909805 -0.0000000000
3 O 0.0082758866 -0.0153442335 0.0000000000
4 O -0.0127076495 0.0051644656 0.0000000000
5 O 0.0043654529 0.0316766646 0.0000000000
----------------------------------------------
cycle 5: E = -409.819010654 dE = -0.00498322 norm(grad) = 0.0639637
Step 4 : Displace = 6.345e-02/8.476e-02 (rms/max) Trust = 1.414e-01 (=) Grad = 2.611e-02/3.594e-02 (rms/max) E (change) = -409.8190106539 (-4.983e-03) Quality = 0.832
Hessian Eigenvalues: 2.30000e-02 2.81592e-02 2.85714e-02 ... 9.04650e-01 1.08958e+00 1.24987e+00
Geometry optimization cycle 6
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
N -5.046589 1.744259 -0.000000 -0.016225 0.001219 -0.000000
N -3.257673 1.792388 0.000000 0.002436 0.000765 0.000000
O -2.842440 2.945963 0.000000 0.020223 0.016002 0.000000
O -2.737933 0.680189 0.000000 -0.013215 0.007566 0.000000
O -5.545762 2.866327 -0.000000 0.015453 0.003569 -0.000000
O -5.514239 0.608119 -0.000000 -0.009614 -0.029939 -0.000000
WARN: Large deviations found between the input molecule and the molecule from chkfile
Initial guess density matrix may have large error.
converged SCF energy = -409.821185296234
--------------- SCF_Scanner gradients ---------------
x y z
0 N 0.0130528207 0.0009188019 -0.0000000000
1 N -0.0058515686 -0.0000682204 0.0000000000
2 O -0.0017621084 0.0048577168 0.0000000000
3 O 0.0019477382 -0.0058110893 -0.0000000000
4 O -0.0030522910 0.0040040132 0.0000000000
5 O -0.0043176354 -0.0038908955 -0.0000000000
----------------------------------------------
cycle 6: E = -409.821185296 dE = -0.00217464 norm(grad) = 0.0181345
Step 5 : Displace = 2.003e-02/3.125e-02 (rms/max) Trust = 2.000e-01 (+) Grad = 7.403e-03/1.309e-02 (rms/max) E (change) = -409.8211852962 (-2.175e-03) Quality = 1.037
Hessian Eigenvalues: 2.30000e-02 2.81592e-02 2.85714e-02 ... 8.76114e-01 1.09084e+00 1.25276e+00
Geometry optimization cycle 7
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
N -5.063170 1.743193 -0.000000 -0.016581 -0.001066 0.000000
N -3.250713 1.795663 0.000000 0.006960 0.003275 -0.000000
O -2.828522 2.943152 0.000000 0.013918 -0.002811 -0.000000
O -2.738220 0.684663 0.000000 -0.000287 0.004474 -0.000000
O -5.551989 2.865660 -0.000000 -0.006228 -0.000667 0.000000
O -5.512880 0.604053 -0.000000 0.001359 -0.004066 0.000000
converged SCF energy = -409.821515173617
--------------- SCF_Scanner gradients ---------------
x y z
0 N 0.0014819560 -0.0000384272 0.0000000000
1 N 0.0000384215 0.0004354839 -0.0000000000
2 O -0.0019864342 -0.0002348005 0.0000000000
3 O -0.0005119280 -0.0001943968 0.0000000000
4 O 0.0012040947 0.0015663906 -0.0000000000
5 O -0.0002181271 -0.0015280380 -0.0000000000
----------------------------------------------
cycle 7: E = -409.821515174 dE = -0.000329877 norm(grad) = 0.00360217
Step 6 : Displace = 1.011e-02/1.646e-02 (rms/max) Trust = 2.828e-01 (+) Grad = 1.471e-03/2.000e-03 (rms/max) E (change) = -409.8215151736 (-3.299e-04) Quality = 1.180
Hessian Eigenvalues: 2.30000e-02 2.81592e-02 2.85714e-02 ... 9.86634e-01 1.07921e+00 1.10760e+00
Geometry optimization cycle 8
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
N -5.069162 1.743938 0.000000 -0.005992 0.000745 0.000000
N -3.246852 1.797242 0.000000 0.003860 0.001579 0.000000
O -2.816732 2.942327 0.000000 0.011790 -0.000824 -0.000000
O -2.737297 0.685387 -0.000000 0.000923 0.000723 -0.000000
O -5.563359 2.862908 0.000000 -0.011369 -0.002752 0.000000
O -5.512683 0.603834 -0.000000 0.000198 -0.000219 0.000000
converged SCF energy = -409.821577746442
--------------- SCF_Scanner gradients ---------------
x y z
0 N -0.0005584784 -0.0002692440 -0.0000000000
1 N 0.0002369049 -0.0002890492 0.0000000000
2 O -0.0007190763 -0.0002566646 -0.0000000000
3 O -0.0002690242 0.0006400977 0.0000000000
4 O 0.0010601166 0.0001375104 0.0000000000
5 O 0.0002532686 0.0000404158 0.0000000000
----------------------------------------------
cycle 8: E = -409.821577746 dE = -6.25728e-05 norm(grad) = 0.00167262
Step 7 : Displace = 7.420e-03/1.230e-02 (rms/max) Trust = 3.000e-01 (+) Grad = 6.828e-04/1.069e-03 (rms/max) E (change) = -409.8215777464 (-6.257e-05) Quality = 1.335
Hessian Eigenvalues: 2.30000e-02 2.81592e-02 2.85714e-02 ... 8.25487e-01 1.04977e+00 1.10295e+00
Geometry optimization cycle 9
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
N -5.071283 1.744981 0.000000 -0.002121 0.001043 0.000000
N -3.244748 1.798765 0.000000 0.002105 0.001523 -0.000000
O -2.809041 2.942042 0.000000 0.007691 -0.000285 0.000000
O -2.738357 0.685030 -0.000000 -0.001060 -0.000357 -0.000000
O -5.572392 2.860938 0.000000 -0.009033 -0.001970 0.000000
O -5.510688 0.603343 -0.000000 0.001994 -0.000490 0.000000
converged SCF energy = -409.821592777858
--------------- SCF_Scanner gradients ---------------
x y z
0 N -0.0003702796 -0.0001276713 0.0000000000
1 N -0.0000671893 -0.0000968196 -0.0000000000
2 O -0.0000078020 -0.0000740443 -0.0000000000
3 O 0.0001208752 0.0002053730 0.0000000000
4 O 0.0002870430 -0.0001413401 -0.0000000000
5 O 0.0000383360 0.0002353635 -0.0000000000
----------------------------------------------
cycle 9: E = -409.821592778 dE = -1.50314e-05 norm(grad) = 0.00062359
Step 8 : Displace = 5.176e-03/8.706e-03 (rms/max) Trust = 3.000e-01 (=) Grad = 2.546e-04/3.917e-04 (rms/max) E (change) = -409.8215927779 (-1.503e-05) Quality = 1.151
Hessian Eigenvalues: 2.30000e-02 2.81592e-02 2.85714e-02 ... 8.05513e-01 1.05388e+00 1.10306e+00
Geometry optimization cycle 10
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
N -5.071195 1.745262 -0.000000 0.000088 0.000280 -0.000000
N -3.244475 1.799392 0.000000 0.000273 0.000627 0.000000
O -2.807661 2.942267 0.000000 0.001380 0.000225 0.000000
O -2.739556 0.684849 -0.000000 -0.001199 -0.000181 -0.000000
O -5.574663 2.860334 0.000000 -0.002271 -0.000605 0.000000
O -5.509073 0.602860 -0.000000 0.001615 -0.000484 -0.000000
converged SCF energy = -409.821593872364
--------------- SCF_Scanner gradients ---------------
x y z
0 N -0.0000967791 -0.0000401706 -0.0000000000
1 N -0.0000441705 0.0000487271 0.0000000000
2 O 0.0000377759 0.0000048933 0.0000000000
3 O 0.0000976515 -0.0000423263 -0.0000000000
4 O 0.0000418445 -0.0000358526 0.0000000000
5 O -0.0000360253 0.0000649746 0.0000000000
----------------------------------------------
cycle 10: E = -409.821593872 dE = -1.09451e-06 norm(grad) = 0.000191414
Step 9 : Displace = 1.389e-03/2.019e-03 (rms/max) Trust = 3.000e-01 (=) Grad = 7.814e-05/1.064e-04 (rms/max) E (change) = -409.8215938724 (-1.095e-06) Quality = 1.186
Hessian Eigenvalues: 2.30000e-02 2.81592e-02 2.85714e-02 ... 7.97881e-01 1.05556e+00 1.11443e+00
Geometry optimization cycle 11
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
N -5.070963 1.745221 0.000000 0.000232 -0.000041 0.000000
N -3.244576 1.799734 0.000000 -0.000101 0.000342 -0.000000
O -2.807681 2.942564 0.000000 -0.000020 0.000297 -0.000000
O -2.740055 0.685036 -0.000000 -0.000498 0.000186 0.000000
O -5.575364 2.859936 0.000000 -0.000701 -0.000398 -0.000000
O -5.508021 0.602434 -0.000000 0.001051 -0.000426 -0.000000
converged SCF energy = -409.821594013783
--------------- SCF_Scanner gradients ---------------
x y z
0 N 0.0000043644 0.0000056734 0.0000000000
1 N -0.0000045504 0.0000441808 -0.0000000000
2 O 0.0000112355 0.0000073351 -0.0000000000
3 O 0.0000322918 -0.0000582980 0.0000000000
4 O -0.0000146363 0.0000170920 -0.0000000000
5 O -0.0000286509 -0.0000159516 -0.0000000000
----------------------------------------------
cycle 11: E = -409.821594014 dE = -1.41418e-07 norm(grad) = 9.0703e-05
Step 10 : Displace = 5.122e-04/7.834e-04 (rms/max) Trust = 3.000e-01 (=) Grad = 3.703e-05/6.664e-05 (rms/max) E (change) = -409.8215940138 (-1.414e-07) Quality = 1.100
Hessian Eigenvalues: 2.30000e-02 2.81592e-02 2.85714e-02 ... 7.97881e-01 1.05556e+00 1.11443e+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: 34.959 seconds
converged SCF energy = -409.821594013813
Pregunta 4. Calcule la energía de la molécula optimizada de \(NO_2\) con DFT B3LYP y la base 6-31G.
# Optimice Geometría y obtenga la energia NO2 B3LYP/6-31G
NO2 = pyscf.gto.Mole(atom="""
N -4.39539 1.87380 0.00000
O -3.90978 3.09520 -0.00000
O -3.65594 0.93810 0.00000
""",spin=1,basis="6-31G")
NO2.max_memory = 2000
NO2.build()
uks = dft.UKS(NO2)
uks.xc = "B3LYP"
NO2_eq = optimize(uks)
uks = dft.UKS(NO2_eq)
uks.xc = "B3LYP"
no2 = uks.kernel()
geometric-optimize called with the following command line:
/home/jfhlewyee/anaconda3/envs/jb/lib/python3.10/site-packages/ipykernel_launcher.py -f /tmp/tmp20bm5290.json --HistoryManager.hist_file=:memory:
())))))))))))))))/
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*)))))))))))))))))))))))))))))))))
#, ()))))))))/ .)))))))))),
#%%%%, ()))))) .))))))))*
*%%%%%%, )) .. ,))))))).
*%%%%%%, ***************/. .)))))))
#%%/ (%%%%%%, /*********************. )))))))
.%%%%%%# *%%%%%%, *******/, **********, .))))))
.%%%%%%/ *%%%%%%, ** ******** .))))))
## .%%%%%%/ (%%%%%%, ,****** /)))))
%%%%%% .%%%%%%# *%%%%%%, ,/////. ****** ))))))
#% %% .%%%%%%/ *%%%%%%, ////////, *****/ ,)))))
#%% %%% %%%# .%%%%%%/ (%%%%%%, ///////. /***** ))))).
#%%%%. %%%%%# /%%%%%%* #%%%%%% /////) ****** ))))),
#%%%%##% %%%# .%%%%%%/ (%%%%%%, ///////. /***** ))))).
## %%% .%%%%%%/ *%%%%%%, ////////. *****/ ,)))))
#%%%%# /%%%%%%/ (%%%%%% /)/)// ****** ))))))
## .%%%%%%/ (%%%%%%, ******* ))))))
.%%%%%%/ *%%%%%%, **. /******* .))))))
*%%%%%%/ (%%%%%% ********/*..,*/********* *))))))
#%%/ (%%%%%%, *********************/ )))))))
*%%%%%%, ,**************/ ,))))))/
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-=# geomeTRIC started. Version: 1.0 #=-
Current date and time: 2022-12-13 13:53:59
Custom engine selected.
Bonds will be generated from interatomic distances less than 1.20 times sum of covalent radii
9 internal coordinates being used (instead of 9 Cartesians)
Internal coordinate system (atoms numbered from 1):
Distance 1-2
Distance 1-3
Angle 2-1-3
Translation-X 1-3
Translation-Y 1-3
Translation-Z 1-3
Rotation-A 1-3
Rotation-B 1-3
Rotation-C 1-3
<class 'geometric.internal.Distance'> : 2
<class 'geometric.internal.Angle'> : 1
<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 ===
Geometry optimization cycle 1
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
N -4.395390 1.873800 0.000000 0.000000 0.000000 0.000000
O -3.909780 3.095200 0.000000 0.000000 0.000000 0.000000
O -3.655940 0.938100 0.000000 0.000000 0.000000 0.000000
converged SCF energy = -204.884655674854 <S^2> = 0.75536923 2S+1 = 2.005362
--------------- SCF_Scanner gradients ---------------
x y z
0 N -0.0475126816 -0.0829330014 -0.0000000000
1 O 0.0470121470 0.0170939883 0.0000000000
2 O 0.0005220145 0.0658258507 -0.0000000000
----------------------------------------------
cycle 1: E = -204.884655675 dE = -204.885 norm(grad) = 0.126376
Step 0 : Gradient = 7.296e-02/9.558e-02 (rms/max) Energy = -204.8846556749
Hessian Eigenvalues: 5.00000e-02 5.00000e-02 5.00000e-02 ... 2.50000e-01 6.33488e-01 1.08625e+00
Geometry optimization cycle 2
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
N -4.290089 1.906467 -0.000000 0.105301 0.032667 -0.000000
O -3.973639 3.156396 -0.000000 -0.063859 0.061196 -0.000000
O -3.697666 0.844411 0.000000 -0.041726 -0.093689 0.000000
WARN: Large deviations found between the input molecule and the molecule from chkfile
Initial guess density matrix may have large error.
converged SCF energy = -204.897651313982 <S^2> = 0.75406334 2S+1 = 2.0040592
--------------- SCF_Scanner gradients ---------------
x y z
0 N 0.0025851465 -0.0505465178 0.0000000000
1 O 0.0056965349 0.0508862012 -0.0000000000
2 O -0.0082997865 -0.0003048790 -0.0000000000
----------------------------------------------
cycle 2: E = -204.897651314 dE = -0.0129956 norm(grad) = 0.0724739
Step 1 : Displace = 1.008e-01/1.103e-01 (rms/max) Trust = 1.000e-01 (=) Grad = 4.184e-02/5.120e-02 (rms/max) E (change) = -204.8976513140 (-1.300e-02) Quality = 0.703
Hessian Eigenvalues: 5.00000e-02 5.00000e-02 5.00000e-02 ... 3.23187e-01 6.65132e-01 1.07758e+00
Geometry optimization cycle 3
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
N -4.292313 1.922101 0.000000 -0.002224 0.015634 0.000000
O -3.974766 3.126956 -0.000000 -0.001126 -0.029440 0.000000
O -3.693854 0.857235 0.000000 0.003812 0.012824 0.000000
WARN: Large deviations found between the input molecule and the molecule from chkfile
Initial guess density matrix may have large error.
converged SCF energy = -204.900667068534 <S^2> = 0.75351996 2S+1 = 2.0035169
--------------- SCF_Scanner gradients ---------------
x y z
0 N 0.0072295109 -0.0196276593 0.0000000000
1 O -0.0001212039 0.0154998766 0.0000000000
2 O -0.0071208683 0.0041660042 -0.0000000000
----------------------------------------------
cycle 3: E = -204.900667069 dE = -0.00301575 norm(grad) = 0.02731
Step 2 : Displace = 2.074e-02/2.913e-02 (rms/max) Trust = 1.000e-01 (=) Grad = 1.577e-02/2.092e-02 (rms/max) E (change) = -204.9006670685 (-3.016e-03) Quality = 1.366
Hessian Eigenvalues: 4.99989e-02 5.00000e-02 5.00000e-02 ... 3.38091e-01 4.19989e-01 1.10614e+00
Geometry optimization cycle 4
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
N -4.300972 1.928900 0.000000 -0.008659 0.006799 -0.000000
O -3.972155 3.111034 -0.000000 0.002610 -0.015922 -0.000000
O -3.687294 0.864644 0.000000 0.006561 0.007409 0.000000
WARN: Large deviations found between the input molecule and the molecule from chkfile
Initial guess density matrix may have large error.
converged SCF energy = -204.901038316177 <S^2> = 0.75343602 2S+1 = 2.0034331
--------------- SCF_Scanner gradients ---------------
x y z
0 N 0.0037620998 0.0018012223 0.0000000000
1 O -0.0015644120 -0.0054096622 -0.0000000000
2 O -0.0022010828 0.0036368325 -0.0000000000
----------------------------------------------
cycle 4: E = -204.901038316 dE = -0.000371248 norm(grad) = 0.0081964
Step 3 : Displace = 1.256e-02/1.589e-02 (rms/max) Trust = 1.414e-01 (+) Grad = 4.732e-03/5.631e-03 (rms/max) E (change) = -204.9010383162 (-3.712e-04) Quality = 0.857
Hessian Eigenvalues: 4.99897e-02 5.00000e-02 5.00000e-02 ... 3.16734e-01 5.10246e-01 1.13144e+00
Geometry optimization cycle 5
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
N -4.302618 1.927193 0.000000 -0.001646 -0.001707 0.000000
O -3.971830 3.113485 -0.000000 0.000325 0.002451 0.000000
O -3.685891 0.863175 0.000000 0.001402 -0.001468 -0.000000
WARN: Large deviations found between the input molecule and the molecule from chkfile
Initial guess density matrix may have large error.
converged SCF energy = -204.901070705864 <S^2> = 0.75348786 2S+1 = 2.0034848
--------------- SCF_Scanner gradients ---------------
x y z
0 N 0.0007569673 -0.0013713950 0.0000000000
1 O 0.0000657927 -0.0001796256 0.0000000000
2 O -0.0008253780 0.0015780802 0.0000000000
----------------------------------------------
cycle 5: E = -204.901070706 dE = -3.23897e-05 norm(grad) = 0.00237948
Step 4 : Displace = 2.244e-03/2.808e-03 (rms/max) Trust = 2.000e-01 (+) Grad = 1.374e-03/1.781e-03 (rms/max) E (change) = -204.9010707059 (-3.239e-05) Quality = 1.089
Hessian Eigenvalues: 4.98734e-02 4.99997e-02 5.00000e-02 ... 3.19490e-01 6.03581e-01 8.66122e-01
Geometry optimization cycle 6
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
N -4.302708 1.926989 0.000000 -0.000090 -0.000204 -0.000000
O -3.972722 3.113505 -0.000000 -0.000892 0.000021 -0.000000
O -3.684803 0.862340 0.000000 0.001088 -0.000835 -0.000000
converged SCF energy = -204.901073122787 <S^2> = 0.75349676 2S+1 = 2.0034937
--------------- SCF_Scanner gradients ---------------
x y z
0 N 0.0001388812 -0.0004813607 -0.0000000000
1 O 0.0000763453 0.0001071453 0.0000000000
2 O -0.0002180883 0.0004010930 0.0000000000
----------------------------------------------
cycle 6: E = -204.901073123 dE = -2.41692e-06 norm(grad) = 0.000690466
Step 5 : Displace = 5.355e-04/7.558e-04 (rms/max) Trust = 2.828e-01 (+) Grad = 3.986e-04/5.010e-04 (rms/max) E (change) = -204.9010731228 (-2.417e-06) Quality = 1.237
Hessian Eigenvalues: 4.73284e-02 4.99999e-02 5.00000e-02 ... 3.20269e-01 5.11689e-01 7.86984e-01
Geometry optimization cycle 7
Cartesian coordinates (Angstrom)
Atom New coordinates dX dY dZ
N -4.302647 1.926517 0.000000 0.000062 -0.000472 0.000000
O -3.973712 3.113143 -0.000000 -0.000991 -0.000362 -0.000000
O -3.683739 0.861935 0.000000 0.001064 -0.000405 0.000000
converged SCF energy = -204.901073327061 <S^2> = 0.75349872 2S+1 = 2.0034957
--------------- SCF_Scanner gradients ---------------
x y z
0 N -0.0000242121 0.0000258814 0.0000000000
1 O 0.0000236040 0.0000285469 0.0000000000
2 O -0.0000026627 -0.0000278871 -0.0000000000
----------------------------------------------
cycle 7: E = -204.901073327 dE = -2.04274e-07 norm(grad) = 5.84203e-05
Step 6 : Displace = 1.983e-04/2.613e-04 (rms/max) Trust = 3.000e-01 (+) Grad = 3.373e-05/3.704e-05 (rms/max) E (change) = -204.9010733271 (-2.043e-07) Quality = 0.791
Hessian Eigenvalues: 4.73284e-02 4.99999e-02 5.00000e-02 ... 3.20269e-01 5.11689e-01 7.86984e-01
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: 7.351 seconds
converged SCF energy = -204.90107332717 <S^2> = 0.75349869 2S+1 = 2.0034956
Pregunta b. Calcule el \(\Delta U\) de la reacción \(N_2O_4\) ↔ \(2NO_2\) según DFT B3LYP.
# Obtenga la energía de reacción (2E_{NO2} - E_{N2O4}). Recuerde convertur Hartree->kcal/mol.
(2*no2-n2o4)*2625.5
51.05904229581648