The quantum_chemistry from hokru

Introduction

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.

Instructions

To run this program add the desired .mol and .gbs files to the molfiles and basisset 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

Supported Features and Methods

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

Example Calculations and Energy Comparisons

Restricted Hartree-Fock

HeH⁺ STO-3G

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

HeH⁺ 6-311+G**

    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

C₂H₄ 3-21G

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

Unrestricted Hartree-Fock

O₂ STO-3G

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

Density Functional Theory

SVWN He STO-3G

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

SVWN H₂ STO-3G

  @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

Møller–Plesset Second Order

CO STO-3G

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

Coupled Cluster Singles and Doubles

CH₄ STO-3G

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

Citations

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).

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quantum_chemistry's Introduction

Introduction

Instructions

Supported Features and Methods

Example Calculations and Energy Comparisons

Restricted Hartree-Fock

HeH+ STO-3G

HeH+ 6-311+G**

C2H4 3-21G

Unrestricted Hartree-Fock

O2 STO-3G

Density Functional Theory

SVWN He STO-3G

SVWN H2 STO-3G

Møller–Plesset Second Order

CO STO-3G

Coupled Cluster Singles and Doubles

CH4 STO-3G

Citations

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