A basic quantum chemical program written in Python 3 using the numpy and scipy libraries.
Currently this program fully supports RHF, UHF, CIS, TDHF, DFT, CCSD and CCSD(T). My next plans are to implementing more CI based methods and work on speeding up the CCSD iterations.
I used Attlia Szabo and Neil S. Ostlunds Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory and David B. Cooks Handbook of Computational Quantum Chemistry as my main references for the theories and methods behind the electronic structure calculations. The developers resources at http://www.psicode.org/developers.php were also invaluable to the success of project and had a number of excellent tutorials and programming examples.
- To run this program add the desired .mol and .gbs files to the
molfiles
andbasisset
directories. - Next edit the
src/main/main.py
menu()
function so that the desired calculations are made for example,
def menu():
start('H2O.mol', 'STO-3G.gbs', 'CCSD', 4)
for DFT calculation the functional are given inputted using a tuple for SVWN3,
def menu():
start('He.mol', 'STO-3G.gbs', ('DFT', 'S', 'VWN3'), 4)
the start function contains more options such as the number of processes used during the multiprocessing sections of the code and whether symmetry is turned on for faster integral calculations. See start()
for more details,
def start(mol, basis, method, processes, symmetry=False)
- Now run the main.py, for example on a Windows machine,
C:\Anaconda3\python.exe C:\Users\username\PycharmProjects\Quantum_Chemistry\src\main.py
- Restricted Hartree-Fock
- Unrestricted Hartree-Fock
- Density Functional Theory - SVWN and S_X
- Møller–Plesset Second Order
- Coupled Cluster Singles and Doubles
- Coupled Cluster Singles and Doubles with Perturbation Triples
- Configuration Interaction Singles
- Time-Dependent Hartree-Fock
- DIIS for SCF Calculations
- Multiprocessing during ERI evaluations
- Reduced ERI evaluations with Symmetry
- Obara-Saika recursion relation for ERI
- Nelder-Mead method for geometry optimization
Completed my first calculation of HeH+ with a bond-length of 1.4632 a0 using the STO-3G basis set. Comparison with Spartan Student Edition v5,
SCF model:
A restricted Hartree-Fock SCF calculation will be
performed using Pulay DIIS + Geometric Direct Minimization
SCF total energy: -2.8418365 hartrees
Reason for exit: Successful completion
Quantum Calculation CPU Time : .39
Quantum Calculation Wall Time: 2.85
ORBITAL COEFFICIENTS
[[-0.87660574 0.79774813]
[-0.20247895 -1.16783645]]
TOTAL ENERGY: -2.841836483 a.u.
Time Taken: 0.10287352007652968s
SPARTAN STUDENT Quantum Mechanics Program: (PC/x86) Release 5.0.0v4
Job type: Single point.
Method: RHF
Basis set: 6-311+G**
Number of shells: 8
Number of basis functions: 12
Charge : +1
Multiplicity: 1
SCF model:
A restricted Hartree-Fock SCF calculation will be
performed using Pulay DIIS + Geometric Direct Minimization
SCF total energy: -2.9292278 hartrees
TOTAL NUCLEAR REPULSION ENERGY: 1.36687066232 a.u.
TOTAL ENERGY: -2.92922773418 a.u.
*********************************************************************************************************
Time Taken: 10.986138812057659s
Job type: Single point.
Method: RHF
Basis set: 3-21G(*)
Number of shells: 14
Number of basis functions: 26
Multiplicity: 1
SCF model:
A restricted Hartree-Fock SCF calculation will be
performed using Pulay DIIS + Geometric Direct Minimization
SCF total energy: -77.6009882 hartrees
TOTAL NUCLEAR REPULSION ENERGY: 33.4424184132 a.u.
TOTAL ENERGY: -77.6004608443 a.u.
*********************************************************************************************************
Time Taken: 72.70841306778921s
Completed UHF calculation of O2 with a bond-length of 2.28541 a0 using the STO-3G basis set. Comparison with Psi4,
Alpha Virtual:
3B1u 0.687444
Beta Occupied:
1B1u -20.409351 1Ag -20.409200 2Ag -1.488240
2B1u -0.897684 3Ag -0.554936 1B2u -0.443771
1B3u -0.443771
Beta Virtual:
1B2g 0.270958 1B3g 0.270958 3B1u 0.777260
Final Occupation by Irrep:
Ag B1g B2g B3g Au B1u B2u B3u
DOCC [ 3, 0, 0, 0, 0, 2, 1, 1 ]
SOCC [ 0, 0, 1, 1, 0, 0, 0, 0 ]
Energy converged.
@UHF Final Energy: -147.63402658708560
ORBITAL ENERGY EIGENVALUES
[-20.44092476 -20.43982562 -1.61895614 -1.0904038 -0.71572756 -0.71572756 -0.60782104 -0.41366455 -0.41366455 0.68744582]
[-20.40935163 -20.40920055 -1.48824156 -0.89768363 -0.55493306 -0.44377123 -0.44377123 0.27095791 0.27095791 0.7772591 ]
ORBITAL COEFFICIENTS
[[ -7.02723743e-01 -7.03498943e-01 1.71186239e-01 -1.88587548e-01 -4.38136920e-16 1.19802374e-17 -6.20530364e-02 -8.32248930e-16 2.84706141e-18 8.93225221e-02]
[ -2.07586114e-02 -1.33148014e-02 -5.81674920e-01 7.92133414e-01 1.29734380e-15 3.71511481e-17 3.16982472e-01 3.08736402e-15 -3.65588944e-16 -5.57900536e-01]
[ 1.59916666e-17 -2.52119849e-16 1.27385408e-15 -7.42459545e-16 -4.33303675e-01 -4.96366048e-01 -2.08215235e-15 7.60305796e-01 -1.06614927e-01 1.76041920e-16]
[ -1.37080901e-16 3.00960019e-16 -1.03883038e-15 1.24001296e-16 -4.96366048e-01 4.33303675e-01 -1.09619443e-15 1.06614927e-01 7.60305796e-01 -5.66762209e-17]
[ 5.90696987e-03 3.16583297e-05 1.57503690e-01 1.31270800e-01 -2.26167345e-15 5.19105390e-16 6.18859802e-01 4.64771775e-16 -6.38429068e-16 9.47820940e-01]
[ 7.02723743e-01 -7.03498944e-01 1.71186239e-01 1.88587548e-01 -2.58412115e-16 -9.27419675e-17 -6.20530364e-02 -3.28901489e-16 9.31297183e-17 -8.93225221e-02]
[ 2.07586114e-02 -1.33148014e-02 -5.81674920e-01 -7.92133414e-01 3.84888710e-16 4.50797609e-16 3.16982472e-01 1.42655930e-15 -5.81164887e-16 5.57900536e-01]
[ 3.44654784e-18 1.38685853e-16 -3.47376755e-15 7.39837664e-16 -4.33303675e-01 -4.96366048e-01 7.58971316e-16 -7.60305796e-01 1.06614927e-01 -3.10964058e-16]
[ 5.02204089e-17 -2.41135394e-16 -1.66280656e-15 5.28441640e-16 -4.96366048e-01 4.33303675e-01 -2.13054056e-15 -1.06614927e-01 -7.60305796e-01 -1.82929277e-16]
[ 5.90696987e-03 -3.16583298e-05 -1.57503690e-01 1.31270800e-01 1.62284816e-15 -6.40098778e-16 -6.18859802e-01 -5.62572989e-16 7.22391062e-16 9.47820940e-01]]
[[ 7.03199293e-01 7.03825068e-01 1.66962912e-01 1.81606050e-01 -6.94242840e-02 1.26199526e-16 2.37550839e-16 1.77535693e-16 -2.92964372e-16 -9.94707578e-02]
[ 1.85908180e-02 1.21320747e-02 -5.66324587e-01 -7.58247086e-01 3.43700682e-01 -6.01633883e-16 -1.20255279e-15 -9.26041850e-16 1.11962646e-15 6.03220533e-01]
[ -2.30303447e-17 3.74738486e-17 1.00456372e-16 3.85334205e-16 2.57053817e-16 -6.56094837e-01 6.05879007e-02 3.82223195e-01 6.65835622e-01 -1.14402786e-15]
[ 1.36810067e-16 -6.76093540e-17 -6.51507432e-16 2.75583445e-16 -4.07776121e-15 -6.05879007e-02 -6.56094837e-01 -6.65835622e-01 3.82223195e-01 -9.99012108e-16]
[ -5.34087079e-03 -1.80846940e-04 1.86114521e-01 -1.86377670e-01 6.10865141e-01 5.78752902e-16 1.76602239e-17 -2.60046091e-15 6.16760811e-16 -9.38544772e-01]
[ -7.03199293e-01 7.03825068e-01 1.66962912e-01 -1.81606050e-01 -6.94242840e-02 -1.09924417e-16 -8.22394905e-17 1.92915095e-16 -2.94288502e-17 9.94707578e-02]
[ -1.85908180e-02 1.21320747e-02 -5.66324587e-01 7.58247086e-01 3.43700682e-01 6.32390267e-16 4.46164071e-16 -9.94462356e-16 1.50639288e-16 -6.03220533e-01]
[ -4.73773095e-18 6.29499495e-17 7.34517638e-18 -4.13141002e-17 -1.13153197e-16 -6.56094837e-01 6.05879007e-02 -3.82223195e-01 -6.65835622e-01 2.06338813e-16]
[ -4.63093672e-17 -1.75133756e-17 6.65940253e-16 1.48690066e-16 2.63853965e-15 -6.05879007e-02 -6.56094837e-01 6.65835622e-01 -3.82223195e-01 -3.54232274e-16]
[ -5.34087079e-03 1.80846940e-04 -1.86114521e-01 -1.86377670e-01 -6.10865141e-01 4.88140539e-16 1.51136604e-15 2.46856157e-15 -2.14894630e-15 -9.38544772e-01]]
TOTAL NUCLEAR REPULSION ENERGY: 28.0036243561 a.u.
TOTAL ENERGY: -147.634028138 a.u.
*****************************************************************************************************
TIME TAKEN: 7.575840318746571
Completed DFT/SVWN calculation of He using the STO-3G basis set. Fairly close agreement to Psi4, differences are probably due to the different numerical integration techniques used.
@RKS Final Energy: -2.80959859524104
=> Energetics <=
Nuclear Repulsion Energy = 0.0000000000000000
One-Electron Energy = -3.8634969002750466
Two-Electron Energy = 2.1114258854701449
DFT Exchange-Correlation Energy = -1.0575275804361373
Empirical Dispersion Energy = 0.0000000000000000
PCM Polarization Energy = 0.0000000000000000
EFP Energy = 0.0000000000000000
Total Energy = -2.8095985952410389
NUCLEAR REPULSION ENERGY: 0.0 a.u.
SCF ENERGY: -2.809831281891216 a.u.
CORRELATION ENERGY: 0.0 a.u.
TOTAL ENERGY: -2.80983128189 a.u.
*************************************************************************************************
TIME TAKEN: 48.94459470800236s
@RKS Final Energy: -1.15582107524090
=> Energetics <=
Nuclear Repulsion Energy = 0.7559674408428576
One-Electron Energy = -2.5557060084773302
Two-Electron Energy = 1.3647790651283140
DFT Exchange-Correlation Energy = -0.7208615727347415
Empirical Dispersion Energy = 0.0000000000000000
PCM Polarization Energy = 0.0000000000000000
EFP Energy = 0.0000000000000000
Total Energy = -1.1558210752409002
NUCLEAR REPULSION ENERGY: 0.755967561438 a.u.
SCF ENERGY: -1.9118948955020598 a.u.
CORRELATION ENERGY: 0.0 a.u.
TOTAL ENERGY: -1.15592733406 a.u.
*************************************************************************************************
TIME TAKEN: 46.66810950479239s
MP2 calculation of CO with a bond-length of 2.14005 a0 using the STO-3G basis set. Comparison with Psi4,
Computing MP2 energy using SCF MOs (Canonical MP2)...
==============================================================================
Nuclear Repulsion Energy (a.u.) : 22.42938094724525
SCF Energy (a.u.) : -111.22496033969136
REF Energy (a.u.) : -111.22496033969136
Alpha-Alpha Contribution (a.u.) : -0.01678813489592
Alpha-Beta Contribution (a.u.) : -0.09597521248030
Beta-Beta Contribution (a.u.) : -0.01678813489592
Scaled_SS Correlation Energy (a.u.): -0.01119208993061
Scaled_OS Correlation Energy (a.u.): -0.11517025497636
SCS-MP2 Total Energy (a.u.) : -111.35132268459833
SOS-MP2 Total Energy (a.u.) : -111.22496033969136
SCSN-MP2 Total Energy (a.u.) : -111.28405457452502
SCS-MP2-VDW Total Energy (a.u.) : -111.36459674656207
SOS-PI-MP2 Total Energy (a.u.) : -111.35932563716378
MP2 Correlation Energy (a.u.) : -0.12955148227214
MP2 Total Energy (a.u.) : -111.35451182196350
==============================================================================
NUCLEAR REPULSION ENERGY: 22.4293809472 a.u.
SCF ENERGY: -133.65434203636403 a.u.
CORRELATION ENERGY: -0.129556206728 a.u.
TOTAL ENERGY: -111.354517296 a.u.
*****************************************************************************************************
TIME TAKEN: 36.23057195376635s
CCSD calculation of CH4 in the STO-3G basis set. comparison with Psi4,
SCF energy (wfn) = -39.726835850063679
Reference energy (file100) = -39.726835850063708
Opposite-spin MP2 correlation energy = -0.053165399377273
Same-spin MP2 correlation energy = -0.002972275669006
MP2 correlation energy = -0.056137675046280
* MP2 total energy = -39.782973525109988
Opposite-spin CCSD correlation energy = -0.076647951103079
Same-spin CCSD correlation energy = -0.001821943731474
CCSD correlation energy = -0.078469894846414
* CCSD total energy = -39.805305744910122
NUCLEAR REPULSION ENERGY: 13.486321423 a.u.
SCF ENERGY: -53.21315722943018 a.u.
CORRELATION ENERGY: -0.0784698838517 a.u.
TOTAL ENERGY: -39.8053056903 a.u.
*************************************************************************************************
TIME TAKEN: 354.9196610947245s
Spartan Student Wavefunction, Inc. Irvine, CA Except for molecular mechanics and semi-empirical models, the calculation methods used in Spartan Student have been documented in: Y. Shao, L.F. Molnar, Y. Jung, J. Kussmann, C. Ochsenfeld, S.T. Brown, A.T.B. Gilbert, L.V. Slipchenko, S.V. Levchenko, D.P. O’Neill, R.A. DiStasio Jr., R.C. Lochan, T. Wang, G.J.O. Beran, N.A. Besley, J.M. Herbert, C.Y. Lin, T. Van Voorhis, S.H. Chien, A. Sodt, R.P. Steele, V.A. Rassolov, P.E. Maslen, P.P. Korambath, R.D. Adamson, B. Austin, J. Baker, E.F.C. Byrd, H. Dachsel, R.J. Doerksen, A. Dreuw, B.D. Dunietz, A.D. Dutoi, T.R. Furlani, S.R. Gwaltney, A. Heyden, S. Hirata, C-P. Hsu, G. Kedziora, R.Z. Khalliulin, P. Klunzinger, A.M. Lee, M.S. Lee, W.Z. Liang, I. Lotan, N. Nair, B. Peters, E.I. Proynov, P.A. Pieniazek, Y.M. Rhee, J. Ritchie, E. Rosta, C.D. Sherrill, A.C. Simmonett, J.E. Subotnik, H.L. Woodcock III, W. Zhang, A.T. Bell, A.K. Chakraborty, D.M. Chipman, F.J. Keil, A.Warshel, W.J. Hehre, H.F. Schaefer, J. Kong, A.I. Krylov, P.M.W. Gill and M. Head-Gordon, Phys. Chem. Chem. Phys., 8, 3172 (2006).
“Psi4: An open-source ab initio electronic structure program,” J. M. Turney, A. C. Simmonett, R. M. Parrish, E. G. Hohenstein, F. Evangelista, J. T. Fermann, B. J. Mintz, L. A. Burns, J. J. Wilke, M. L. Abrams, N. J. Russ, M. L. Leininger, C. L. Janssen, E. T. Seidl, W. D. Allen, H. F. Schaefer, R. A. King, E. F. Valeev, C. D. Sherrill, and T. D. Crawford, WIREs Comput. Mol. Sci. 2, 556 (2012).