Quantum Chemistry Tools in Wolfram Language

Jason Biggs, Wolfram Research
(RowDefault[, (Spacer1), , (Spacer1), ])  #WolframTechConf

ABSTRACT

The release of Version 12.0 of the Wolfram Language introduced the Molecule, a symbolic object for representing molecular systems. This talk will present new functionality designed to compute electronic energies using various methods, including Hartree-Fock, density functional theory, and complete active space methods. Applications such as geometry optimization and excited-state calculations will also be discussed, showcasing the new capabilities in quantum chemistry research.

What does Electronic Structure Software Do?

Solves Schrödinger’s Equation Iteratively: Electronic structure software numerically solves the Schrödinger equation for molecular systems by employing iterative methods to approximate wavefunctions and energy levels.

One- and Two-Electron Integrals: It computes complex integrals over atomic and molecular orbitals to account for interactions between electrons, including both one-electron (e.g., kinetic and potential energy) and two-electron (electron-electron repulsion) integrals.

Gaussian-Type Orbitals (GTOs): These software packages often use Gaussian-type orbitals (GTOs) as basis functions because their mathematical form simplifies the computation of integrals, making calculations more efficient.

Basis Set Approximations: By expanding molecular wavefunctions in terms of basis sets like GTOs, electronic structure methods balance computational cost and accuracy.

Self-Consistent Field (SCF) Method: SCF iterations adjust the electron distribution until a stable, self-consistent solution is reached, providing an optimized electronic structure for the system.

Quantum Chemistry Methods: Various quantum chemical methods (e.g., Hartree-Fock, Density Functional Theory) are implemented to model electron correlation and system energies more accurately.

Molecular Properties & Spectra: These software tools predict molecular properties like bond lengths, dipole moments, vibrational frequencies, and optical spectra by analyzing electronic structure.

Applications in Chemistry & Materials Science: Widely used in computational chemistry and materials science to model chemical reactions, molecular interactions, and the behavior of materials at the quantum level.

How Is Electronic Structure Traditionally run?

From the command line:

Prepare an input text file containing the molecular geometry along with a set of keywords describing the job type and parameters.

Results are piped to a plain text output file containing the input data along and the calculation results, along with a plethora of intermediate data

Requires knowledge of the input keywords/syntax

Requires parsing the output files to get the information you need

Example NWChem input file

start h2o 
 title "Water in 6-31g basis set" 

 geometry units au  
   O      0.00000000    0.00000000    0.00000000  
   H      0.00000000    1.43042809   -1.10715266  
   H      0.00000000   -1.43042809   -1.10715266 
 end  
 basis  
   H library 6-31g  
   O library 6-31g  
 end
 task scf

Example NWChem output file

argument  1 = dvb_gopt_hf.nw
                                         
                                         


              Northwest Computational Chemistry Package (NWChem) 6.5
              ------------------------------------------------------


                    Environmental Molecular Sciences Laboratory
                       Pacific Northwest National Laboratory
                                Richland, WA 99352

                              Copyright (c) 1994-2014
                       Pacific Northwest National Laboratory
                            Battelle Memorial Institute

             NWChem is an open-source computational chemistry package
                        distributed under the terms of the
                      Educational Community License (ECL) 2.0
             A copy of the license is included with this distribution
                              in the LICENSE.TXT file

                                  ACKNOWLEDGMENT
                                  --------------

            This software and its documentation were developed at the
            EMSL at Pacific Northwest National Laboratory, a multiprogram
            national laboratory, operated for the U.S. Department of Energy
            by Battelle under Contract Number DE-AC05-76RL01830. Support
            for this work was provided by the Department of Energy Office
            of Biological and Environmental Research, Office of Basic
            Energy Sciences, and the Office of Advanced Scientific Computing.


           Job information
           ---------------

    hostname        = boman
    program         = /usr/lib64/mpich/bin/nwchem_mpich
    date            = Sat Jan 17 16:28:30 2015

    compiled        = Sat_Dec_06_13:02:58_2014
    source          = /builddir/build/BUILD/Nwchem-6.5.revision26243-src.2014-09-10
    nwchem branch   = 6.5
    nwchem revision = 26243
    ga revision     = 10506
    input           = dvb_gopt_hf.nw
    prefix          = dvb.
    data base       = ./dvb.db
    status          = startup
    nproc           =        1
    time left       =     -1s



           Memory information
           ------------------

    heap     =   13107194 doubles =    100.0 Mbytes
    stack    =   13107199 doubles =    100.0 Mbytes
    global   =   26214400 doubles =    200.0 Mbytes (distinct from heap & stack)
    total    =   52428793 doubles =    400.0 Mbytes
    verify   = yes
    hardfail = no 


           Directory information
           ---------------------

  0 permanent = .
  0 scratch   = .




                                NWChem Input Module
                                -------------------


                        Divinylbenzene in STO-3G basis set
                        ----------------------------------

 Scaling coordinates for geometry "geometry" by  1.889725989
 (inverse scale =  0.529177249)

 C2H symmetry detected

          ------
          auto-z
          ------


                             Geometry "geometry" -> ""
                             -------------------------

 Output coordinates in angstroms (scale by  1.889725989 to convert to a.u.)

  No.       Tag          Charge          X              Y              Z
 ---- ---------------- ---------- -------------- -------------- --------------
    1 C                    6.0000     0.23680554     1.41416660     0.00000000
    2 C                    6.0000    -0.23680554    -1.41416660     0.00000000
    3 C                    6.0000     1.31675086     0.48901061     0.00000000
    4 C                    6.0000    -1.31675086    -0.48901061     0.00000000
    5 C                    6.0000     1.08679847    -0.89447642     0.00000000
    6 C                    6.0000    -1.08679847     0.89447642     0.00000000
    7 H                    1.0000     2.34780221     0.86863451     0.00000000
    8 H                    1.0000    -2.34780221    -0.86863451     0.00000000
    9 H                    1.0000     1.93764188    -1.58693865     0.00000000
   10 H                    1.0000    -1.93764188     1.58693865     0.00000000
   11 C                    6.0000    -0.53450789    -2.88212824     0.00000000
   12 C                    6.0000     0.53450789     2.88212824     0.00000000
   13 H                    1.0000    -1.60655769    -3.13289308     0.00000000
   14 H                    1.0000     1.60655769     3.13289308     0.00000000
   15 C                    6.0000     0.36419263    -3.88177971     0.00000000
   16 C                    6.0000    -0.36419263     3.88177971     0.00000000
   17 H                    1.0000     1.44522900    -3.70144241     0.00000000
   18 H                    1.0000    -1.44522900     3.70144241     0.00000000
   19 H                    1.0000     0.04815351    -4.93192286     0.00000000
   20 H                    1.0000    -0.04815351     4.93192286     0.00000000

      Atomic Mass 
      ----------- 

      C                 12.000000
      H                  1.007825


 Effective nuclear repulsion energy (a.u.)     445.9370121674

            Nuclear Dipole moment (a.u.) 
            ----------------------------
        X                 Y               Z
 ---------------- ---------------- ----------------
     0.0000000000     0.0000000000     0.0000000000

      Symmetry information
      --------------------

 Group name             C2h       
 Group number             21
 Group order               4
 No. of unique centers    10

      Symmetry unique atoms

     1    3    5    7    9   11   13   15   17   19


......

                       ROHF Final Molecular Orbital Analysis
                       -------------------------------------

 Vector   11  Occ=2.000000D+00  E=-1.112882D+00  Symmetry=ag
              MO Center= -1.4D-16, -6.9D-16, -1.9D-17, r^2= 2.8D+00
   Bfn.  Coefficient  Atom+Function         Bfn.  Coefficient  Atom+Function  
  ----- ------------  ---------------      ----- ------------  ---------------
     2      0.269208   1 C  s                 7      0.269208   2 C  s         
    12      0.244670   3 C  s                17      0.244670   4 C  s         
    22      0.244603   5 C  s                27      0.244603   6 C  s         

 Vector   12  Occ=2.000000D+00  E=-1.037372D+00  Symmetry=bu
              MO Center=  1.9D-16,  4.4D-16,  4.0D-34, r^2= 8.0D+00
   Bfn.  Coefficient  Atom+Function         Bfn.  Coefficient  Atom+Function  
  ----- ------------  ---------------      ----- ------------  ---------------
    36      0.295138  11 C  s                41     -0.295138  12 C  s         
     2     -0.259768   1 C  s                 7      0.259768   2 C  s         
    48      0.218845  15 C  s                53     -0.218845  16 C  s         

 Vector   13  Occ=2.000000D+00  E=-9.952245D-01  Symmetry=ag
              MO Center= -5.2D-16, -1.2D-14, -9.4D-18, r^2= 1.1D+01
   Bfn.  Coefficient  Atom+Function         Bfn.  Coefficient  Atom+Function  
  ----- ------------  ---------------      ----- ------------  ---------------
    36      0.311306  11 C  s                41      0.311306  12 C  s         
    48      0.307950  15 C  s                53      0.307950  16 C  s         

 Vector   14  Occ=2.000000D+00  E=-9.651398D-01  Symmetry=bu
              MO Center=  1.6D-15,  6.3D-16,  8.5D-20, r^2= 3.0D+00
   Bfn.  Coefficient  Atom+Function         Bfn.  Coefficient  Atom+Function  
  ----- ------------  ---------------      ----- ------------  ---------------
    12      0.353451   3 C  s                17     -0.353451   4 C  s         
    22      0.318884   5 C  s                27     -0.318884   6 C  s         

 Vector   15  Occ=2.000000D+00  E=-9.279313D-01  Symmetry=bu
              MO Center= -4.3D-17,  1.2D-14, -2.7D-19, r^2= 8.2D+00
   Bfn.  Coefficient  Atom+Function         Bfn.  Coefficient  Atom+Function  
  ----- ------------  ---------------      ----- ------------  ---------------
     2      0.282481   1 C  s                 7     -0.282481   2 C  s         
    48      0.276987  15 C  s                53     -0.276987  16 C  s         
    22     -0.202273   5 C  s                27      0.202273   6 C  s         

......

 ==============================================================================
                                internuclear distances
 ------------------------------------------------------------------------------
       center one      |      center two      | atomic units |  angstroms
 ------------------------------------------------------------------------------
    3 C                |   1 C                |     2.63816  |     1.39606
    4 C                |   2 C                |     2.63816  |     1.39606
    5 C                |   2 C                |     2.63668  |     1.39527
    5 C                |   3 C                |     2.61146  |     1.38193
    6 C                |   1 C                |     2.63668  |     1.39527
    6 C                |   4 C                |     2.61146  |     1.38193
    7 H                |   3 C                |     2.04581  |     1.08259
    8 H                |   4 C                |     2.04581  |     1.08259
    9 H                |   5 C                |     2.04340  |     1.08132
   10 H                |   6 C                |     2.04340  |     1.08132
   11 C                |   2 C                |     2.82732  |     1.49615
   12 C                |   1 C                |     2.82732  |     1.49615
   13 H                |  11 C                |     2.04922  |     1.08440
   14 H                |  12 C                |     2.04922  |     1.08440
   15 C                |  11 C                |     2.48239  |     1.31362
   16 C                |  12 C                |     2.48239  |     1.31362
   17 H                |  15 C                |     2.04165  |     1.08040
   18 H                |  16 C                |     2.04165  |     1.08040
   19 H                |  15 C                |     2.04307  |     1.08115
   20 H                |  16 C                |     2.04307  |     1.08115
 ------------------------------------------------------------------------------
                         number of included internuclear distances:         20
 ==============================================================================



 ==============================================================================
                                 internuclear angles
 ------------------------------------------------------------------------------
        center 1       |       center 2       |       center 3       |  degrees
 ------------------------------------------------------------------------------
    3 C                |   1 C                |   6 C                |   117.84
    3 C                |   1 C                |  12 C                |   119.16
    6 C                |   1 C                |  12 C                |   122.99
    4 C                |   2 C                |   5 C                |   117.84
    4 C                |   2 C                |  11 C                |   119.16
    5 C                |   2 C                |  11 C                |   122.99
    1 C                |   3 C                |   5 C                |   121.35
    1 C                |   3 C                |   7 H                |   119.23
    5 C                |   3 C                |   7 H                |   119.42
    2 C                |   4 C                |   6 C                |   121.35
    2 C                |   4 C                |   8 H                |   119.23
    6 C                |   4 C                |   8 H                |   119.42
    2 C                |   5 C                |   3 C                |   120.81
    2 C                |   5 C                |   9 H                |   120.07
    3 C                |   5 C                |   9 H                |   119.13
    1 C                |   6 C                |   4 C                |   120.81
    1 C                |   6 C                |  10 H                |   120.07
    4 C                |   6 C                |  10 H                |   119.13
    2 C                |  11 C                |  13 H                |   114.17
    2 C                |  11 C                |  15 C                |   126.87
   13 H                |  11 C                |  15 C                |   118.96
    1 C                |  12 C                |  14 H                |   114.17
    1 C                |  12 C                |  16 C                |   126.87
   14 H                |  12 C                |  16 C                |   118.96
   11 C                |  15 C                |  17 H                |   123.13
   11 C                |  15 C                |  19 H                |   121.27
   17 H                |  15 C                |  19 H                |   115.60
   12 C                |  16 C                |  18 H                |   123.13
   12 C                |  16 C                |  20 H                |   121.27
   18 H                |  16 C                |  20 H                |   115.60
 ------------------------------------------------------------------------------
                            number of included internuclear angles:         30
 ==============================================================================




 Task  times  cpu:       28.3s     wall:       30.9s
 Summary of allocated global arrays
-----------------------------------
  No active global arrays



                         GA Statistics for process    0
                         ------------------------------

       create   destroy   get      put      acc     scatter   gather  read&inc
calls: 1558     1558     1.30e+05 3.21e+04 1.43e+05    0        0     3.80e+04 
number of processes/call 1.00e+00 1.00e+00 1.00e+00 0.00e+00 0.00e+00
bytes total:             5.87e+07 3.17e+07 1.91e+07 0.00e+00 0.00e+00 3.04e+05
bytes remote:            0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00
Max memory consumed for GA by this process: 427200 bytes
MA_summarize_allocated_blocks: starting scan ...
MA_summarize_allocated_blocks: scan completed: 0 heap blocks, 0 stack blocks
MA usage statistics:

	allocation statistics:
					      heap	     stack
					      ----	     -----
	current number of blocks	         0	         0
	maximum number of blocks	        20	        29
	current total bytes		         0	         0
	maximum total bytes		   9987096	  22510808
	maximum total K-bytes		      9988	     22511
	maximum total M-bytes		        10	        23

Example Gaussian input file

%mem=32MB
% chk=water.chk
# opt freq geom b3lyp/6-31+g(d,p) geom=connectivity integral=ultrafine scf=maxcyc=1024

water

0 1
O 1.80172602 0.06746038 0.00000000
H 2.76172599 0.06770148 0.00000000
H 1.48149872 0.97247667 0.00000000

Example Gaussian output file

Entering Gaussian System, Link 0=g03
 Initial command:
 /usr/local/lib/g03_revC.02_amd/g03/l1.exe /scratch/jls/Gau-7570.inp -scrdir=/scratch/jls/
 Entering Link 1 = /usr/local/lib/g03_revC.02_amd/g03/l1.exe PID=      7571.
  
 Copyright (c) 1988,1990,1992,1993,1995,1998,2003,2004, Gaussian, Inc.
                  All Rights Reserved.
  
 ......
 
 ******************************************
 Gaussian 03:  IA32L-G03RevC.02 12-Jun-2004
                25-Aug-2004 
 ******************************************
 %chk=/n/srv2/jls/gauss/check/bisCWdhpe2Cl_13benz_c1.chk
 %mem=925mb
 %nproc=2
 Will use up to    2 processors via shared memory.
 -------------------------------------------------------------------
 #p TPSSTPSS genecp 5d 7f pop=nbo freq geom=check guess=check nosymm
 -------------------------------------------------------------------
 1/10=4,29=2,30=1,38=1/1,3;
 2/15=1,40=1/2;
 3/5=7,8=11,11=2,16=1,17=8,25=1,30=1,74=2523/1,2,3;
 4/5=1/1;
 5/5=2,38=6/2;
 8/6=4,10=90,11=11/1;
 11/6=1,8=1,9=11,15=111,16=1,31=1/1,2,10;
 10/6=1,31=1/2;
 6/7=2,8=2,9=2,10=2,18=1,28=1/1,7;
 7/8=1,10=1,25=1,30=1/1,2,3,16;
 1/10=4,30=1/3;
 99//99;
 Leave Link    1 at Wed Aug 25 12:03:53 2004, MaxMem=  121241600 cpu:       0.3
 (Enter /usr/local/lib/g03_revC.02_amd/g03/l101.exe)
 -------------------------------------------------
 [CW(dhpe)2Cl]2C5H4 C1 opt freq nbo (geom=C2v opt)
 -------------------------------------------------
 Redundant internal coordinates taken from checkpoint file:
 /n/srv2/jls/gauss/check/bisCWdhpe2Cl_13benz_c1.chk
 Charge =  0 Multiplicity = 1
 C,0,-0.4444098091,-1.2157434833,-3.0132781802
 C,0,-0.2655090489,-1.2371764399,-1.6030386753
 C,0,-0.187937062,0.0000503015,-0.9178055672
 C,0,-0.2655297836,1.237333687,-1.6029332227
 C,0,-0.444411452,1.2160167707,-3.0131768839
 C,0,-0.5361913248,0.0001651635,-3.69959807
 H,0,-0.5056887582,-2.1612671763,-3.5502125499
 H,0,-0.0604239447,0.0000050524,0.1633873992
 H,0,-0.5057039146,2.1615849064,-3.5500317674
 H,0,-0.6744746778,0.0002102415,-4.7809433913
 C,0,-0.1514593669,-2.480756966,-0.8820572983
 W,0,0.031331894,-4.052223344,0.0657439894
 Cl,0,0.3074654887,-6.2308517182,1.4417449847
 P,0,-1.6660127489,-5.2915557126,-1.2058177717
 P,0,2.0326355491,-4.7826692283,-1.1550739136
 P,0,1.7868751843,-3.2443155587,1.5958455601
 P,0,-1.9269267053,-3.7299068509,1.5304004735
 C,0,-3.4027450017,-4.9819798205,-0.5210145382
 H,0,-1.9230164306,-5.1343959272,-2.5901374087
 H,0,-1.6338817594,-6.7075809152,-1.1704704907
 C,0,3.6064756184,-4.0451295254,-0.4053735852
 H,0,2.277377586,-4.5312560648,-2.5274575404
 H,0,2.3744405379,-6.1578197629,-1.1414025268
 C,0,3.4641022952,-3.9805403338,1.1263020186
 H,0,2.1068011173,-1.8653927345,1.6479105391
 H,0,1.8067248043,-3.5001271579,2.9894086341
 C,0,-3.3396540334,-4.8759963464,1.0136042794
 H,0,-2.5915820155,-2.4800041891,1.5558322261
 H,0,-1.9286725577,-3.9799194345,2.9253115576
 H,0,-4.0958171229,-5.773092891,-0.8365478746
 H,0,-3.7473008645,-4.0322540495,-0.9558640799
 H,0,4.4896142237,-4.6286113574,-0.6976156391
 H,0,3.712325894,-3.0337793243,-0.8245225089
 H,0,3.4697203246,-4.995068208,1.5493812225
 H,0,4.2852842654,-3.4117041002,1.582145841
 H,0,-3.103787667,-5.8559390724,1.4524296656
 H,0,-4.2956901354,-4.5331805545,1.4309244738
 C,0,-0.1514988562,2.4808561933,-0.8818499843
 W,0,0.0313672311,4.052214885,0.0661174782
 Cl,0,0.3078267003,6.230642649,1.4423768309
 P,0,2.0325958993,4.7827825728,-1.154753356
 P,0,-1.6660225951,5.291713631,-1.2052160947
 P,0,-1.926832738,3.7297052396,1.5307945468
 P,0,1.7870018994,3.2441486725,1.5960313206
 C,0,3.6064909277,4.0452506561,-0.4051619228
 H,0,2.2772640876,4.5314333949,-2.5271612946
 H,0,2.3743637142,6.1579406962,-1.1410407691
 C,0,-3.4027461877,4.9819095387,-0.5204952705
 H,0,-1.9230075467,5.1348228342,-2.5895706236
 H,0,-1.6339632421,6.7077342719,-1.1695860462
 C,0,-3.3396719236,4.8757188029,1.0141088599
 H,0,-2.5913897087,2.4797503368,1.5561791542
 H,0,-1.9285791645,3.9796466121,2.9257201118
 C,0,3.4641653501,3.9805257518,1.1265129476
 H,0,2.1070135492,1.8652361477,1.6478896589
 H,0,1.8068812953,3.4997698358,2.9896269919
 H,0,4.4895938736,4.6287983567,-0.6973797096
 H,0,3.7123754147,3.0339399303,-0.8243979645
 H,0,-4.0958734257,5.7730134001,-0.8359315184
 H,0,-3.7472197197,4.0322179528,-0.9554841662
 H,0,-3.1039219621,5.855627939,1.4530727823
 H,0,-4.2956813144,4.5327500657,1.4313647395
 H,0,3.4697238367,4.9950190335,1.5496747166
 H,0,4.2853960071,3.4117027244,1.5822853836
 Recover connectivity data from disk.
                    Isotopes and Nuclear Properties:

  Atom         1           2           3           4           5           6           7           8           9          10
 IAtWgt=          12          12          12          12          12          12           1           1           1           1
 AtmWgt=  12.0000000  12.0000000  12.0000000  12.0000000  12.0000000  12.0000000   1.0078250   1.0078250   1.0078250   1.0078250
 IAtSpn=           0           0           0           0           0           0           1           1           1           1
 AtZEff=  -3.6000000  -3.6000000  -3.6000000  -3.6000000  -3.6000000  -3.6000000  -1.0000000  -1.0000000  -1.0000000  -1.0000000
 AtQMom=   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
 AtGFac=   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   2.7928460   2.7928460   2.7928460   2.7928460

  Atom        11          12          13          14          15          16          17          18          19          20
 IAtWgt=          12         184          35          31          31          31          31          12           1           1
 AtmWgt=  12.0000000 183.9510000  34.9688527  30.9737634  30.9737634  30.9737634  30.9737634  12.0000000   1.0078250   1.0078250
 IAtSpn=           0           0           3           1           1           1           1           0           1           1
 AtZEff=  -3.6000000************ -14.2400000 -12.9400000 -12.9400000 -12.9400000 -12.9400000  -3.6000000  -1.0000000  -1.0000000
 AtQMom=   0.0000000   0.0000000  -8.2490000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
 AtGFac=   0.0000000   0.0000000   0.8218740   1.1316000   1.1316000   1.1316000   1.1316000   0.0000000   2.7928460   2.7928460

  Atom        21          22          23          24          25          26          27          28          29          30
 IAtWgt=          12           1           1          12           1           1          12           1           1           1
 AtmWgt=  12.0000000   1.0078250   1.0078250  12.0000000   1.0078250   1.0078250  12.0000000   1.0078250   1.0078250   1.0078250
 IAtSpn=           0           1           1           0           1           1           0           1           1           1
 AtZEff=  -3.6000000  -1.0000000  -1.0000000  -3.6000000  -1.0000000  -1.0000000  -3.6000000  -1.0000000  -1.0000000  -1.0000000
 AtQMom=   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
 AtGFac=   0.0000000   2.7928460   2.7928460   0.0000000   2.7928460   2.7928460   0.0000000   2.7928460   2.7928460   2.7928460

 ..........

  Atom        61          62          63          64
 IAtWgt=           1           1           1           1
 AtmWgt=   1.0078250   1.0078250   1.0078250   1.0078250
 IAtSpn=           1           1           1           1
 AtZEff=  -1.0000000  -1.0000000  -1.0000000  -1.0000000
 AtQMom=   0.0000000   0.0000000   0.0000000   0.0000000
 AtGFac=   2.7928460   2.7928460   2.7928460   2.7928460
 Leave Link  101 at Wed Aug 25 12:04:00 2004, MaxMem=  121241600 cpu:       0.1
 (Enter /usr/local/lib/g03_revC.02_amd/g03/l103.exe)

 GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
 Berny optimization.
 Initialization pass.
                           ----------------------------
                           !    Initial Parameters    !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  1.4217         calculate D2E/DX2 analytically  !
 ! R2    R(1,6)                  1.3992         calculate D2E/DX2 analytically  !
 ! R3    R(1,7)                  1.0891         calculate D2E/DX2 analytically  !
 ! R4    R(2,3)                  1.4164         calculate D2E/DX2 analytically  !
 ! R5    R(2,11)                 1.442          calculate D2E/DX2 analytically  !
 ! R6    R(3,4)                  1.4164         calculate D2E/DX2 analytically  !
 ! R7    R(3,8)                  1.0887         calculate D2E/DX2 analytically  !
 ! R8    R(4,5)                  1.4217         calculate D2E/DX2 analytically  !
 ! R9    R(4,38)                 1.442          calculate D2E/DX2 analytically  !
 ! R10   R(5,6)                  1.3992         calculate D2E/DX2 analytically  !
 .........
 ! D106  D(16,12,17,29)        -38.5513         calculate D2E/DX2 analytically  !
 ! D107  D(12,14,18,27)        -37.0102         calculate D2E/DX2 analytically  !
 ! D108  D(12,14,18,30)       -160.1664         calculate D2E/DX2 analytically  !
 ! D109  D(12,14,18,31)         82.3631         calculate D2E/DX2 analytically  !
 ! D110  D(19,14,18,27)       -170.9352         calculate D2E/DX2 analytically  !
 ! D111  D(19,14,18,30)         65.9087         calculate D2E/DX2 analytically  !
 ! D112  D(19,14,18,31)        -51.5619         calculate D2E/DX2 analytically  !
 ! D113  D(20,14,18,27)         89.0363         calculate D2E/DX2 analytically  !
 ! D114  D(20,14,18,30)        -34.1199         calculate D2E/DX2 analytically  !
 ! D115  D(20,14,18,31)       -151.5904         calculate D2E/DX2 analytically  !
 ! D116  D(12,15,21,24)         36.6606         calculate D2E/DX2 analytically  !
 ! D117  D(12,15,21,32)        159.6956         calculate D2E/DX2 analytically  !
 ! D118  D(12,15,21,33)        -82.8844         calculate D2E/DX2 analytically  !
 ! D119  D(22,15,21,24)        170.2123         calculate D2E/DX2 analytically  !
 ! D120  D(22,15,21,32)        -66.7527         calculate D2E/DX2 analytically  !
 ! D121  D(22,15,21,33)         50.6674         calculate D2E/DX2 analytically  !
 ! D122  D(23,15,21,24)        -89.721          calculate D2E/DX2 analytically  !
 ! D123  D(23,15,21,32)         33.314          calculate D2E/DX2 analytically  !
 ! D124  D(23,15,21,33)        150.7341         calculate D2E/DX2 analytically  !
 ! D125  D(12,16,24,21)         38.6773         calculate D2E/DX2 analytically  !
 ! D126  D(12,16,24,34)        -80.1841         calculate D2E/DX2 analytically  !
 ! D127  D(12,16,24,35)        162.6398         calculate D2E/DX2 analytically  !
 ! D128  D(25,16,24,21)        -89.481          calculate D2E/DX2 analytically  !
 ! D129  D(25,16,24,34)        151.6576         calculate D2E/DX2 analytically  !
 ! D130  D(25,16,24,35)         34.4815         calculate D2E/DX2 analytically  !
 ! D131  D(26,16,24,21)        170.6125         calculate D2E/DX2 analytically  !
 ! D132  D(26,16,24,34)         51.7512         calculate D2E/DX2 analytically  !
 ! D133  D(26,16,24,35)        -65.425          calculate D2E/DX2 analytically  !
 ! D134  D(12,17,27,18)        -38.3063         calculate D2E/DX2 analytically  !
 ! D135  D(12,17,27,36)         80.7386         calculate D2E/DX2 analytically  !
 ! D136  D(12,17,27,37)       -162.116          calculate D2E/DX2 analytically  !
 ! D137  D(28,17,27,18)         89.6399         calculate D2E/DX2 analytically  !
 ! D138  D(28,17,27,36)       -151.3153         calculate D2E/DX2 analytically  !
 ! D139  D(28,17,27,37)        -34.1698         calculate D2E/DX2 analytically  !
 ! D140  D(29,17,27,18)       -170.3785         calculate D2E/DX2 analytically  !
 ! D141  D(29,17,27,36)        -51.3337         calculate D2E/DX2 analytically  !
 ! D142  D(29,17,27,37)         65.8118         calculate D2E/DX2 analytically  !


 ................

 GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
 Berny optimization.
 Internal  Forces:  Max     0.000003786 RMS     0.000000394
 Search for a local minimum.
 Step number   1 out of a maximum of   2
 All quantities printed in internal units (Hartrees-Bohrs-Radians)
 Second derivative matrix not updated -- analytic derivatives used.
     Eigenvalues ---    0.00054   0.00055   0.00090   0.00106   0.00113
     Eigenvalues ---    0.00182   0.00183   0.00243   0.00244   0.00414
     Eigenvalues ---    0.00416   0.00547   0.00684   0.00688   0.00803
     Eigenvalues ---    0.00811   0.01220   0.01221   0.01253   0.01261
     Eigenvalues ---    0.01338   0.01339   0.01396   0.01497   0.01504
     Eigenvalues ---    0.01524   0.01654   0.01706   0.01770   0.01770
     Eigenvalues ---    0.01864   0.01867   0.01873   0.01874   0.01917
     Eigenvalues ---    0.02038   0.02040   0.02162   0.02351   0.02434
     Eigenvalues ---    0.02463   0.02553   0.02657   0.02705   0.02817
     Eigenvalues ---    0.03169   0.03174   0.03199   0.03217   0.03257
     Eigenvalues ---    0.03319   0.03417   0.03439   0.03491   0.03832
     Eigenvalues ---    0.03868   0.03877   0.03879   0.04068   0.04071
     Eigenvalues ---    0.04158   0.04242   0.04459   0.04518   0.04636
     Eigenvalues ---    0.04662   0.04681   0.04709   0.05013   0.05092
     Eigenvalues ---    0.05196   0.05511   0.05531   0.05554   0.05597
     Eigenvalues ---    0.05632   0.05656   0.05676   0.05730   0.05982
     Eigenvalues ---    0.05991   0.06103   0.06141   0.06188   0.06195
     Eigenvalues ---    0.06311   0.06343   0.06380   0.06383   0.06440
     Eigenvalues ---    0.06766   0.07388   0.07399   0.07494   0.07496
     Eigenvalues ---    0.07832   0.07849   0.08063   0.08170   0.08178
     Eigenvalues ---    0.08194   0.08215   0.08219   0.08279   0.08311
     Eigenvalues ---    0.09809   0.10537   0.10555   0.10758   0.10919
     Eigenvalues ---    0.11164   0.11234   0.11264   0.11732   0.12408
     Eigenvalues ---    0.14134   0.14287   0.14332   0.14409   0.14419
     Eigenvalues ---    0.14555   0.14563   0.14585   0.14610   0.15643
     Eigenvalues ---    0.15692   0.15869   0.15876   0.16269   0.18030
     Eigenvalues ---    0.18105   0.18595   0.19171   0.19175   0.19444
     Eigenvalues ---    0.19456   0.21617   0.21620   0.21665   0.21669
     Eigenvalues ---    0.21697   0.21707   0.21821   0.21823   0.21824
     Eigenvalues ---    0.21837   0.21868   0.21878   0.21911   0.21939
     Eigenvalues ---    0.22004   0.22013   0.25174   0.25176   0.25234
     Eigenvalues ---    0.25240   0.28443   0.30595   0.31471   0.32731
     Eigenvalues ---    0.32732   0.32760   0.32761   0.32961   0.32964
     Eigenvalues ---    0.32970   0.32971   0.33362   0.33362   0.33401
     Eigenvalues ---    0.33402   0.33546   0.33547   0.33555   0.33559
     Eigenvalues ---    0.35012   0.35391   0.35400   0.35698   0.38199
     Eigenvalues ---    0.38495   0.39711   0.40129   0.42656   0.43820
     Eigenvalues ---    0.479201000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.000001000.000001000.000001000.000001000.00000
     Eigenvalues --- 1000.00000
 Angle between quadratic step and forces=  69.95 degrees.
 Linear search not attempted -- first point.
 Iteration  1 RMS(Cart)=  0.00012330 RMS(Int)=  0.00000000
 Iteration  2 RMS(Cart)=  0.00000001 RMS(Int)=  0.00000000
 Variable       Old X    -DE/DX   Delta X   Delta X   Delta X     New X
                                 (Linear)    (Quad)   (Total)
    R1        2.68663   0.00000   0.00000   0.00000   0.00000   2.68663
    R2        2.64419   0.00000   0.00000   0.00000   0.00000   2.64419
    R3        2.05804   0.00000   0.00000   0.00000   0.00000   2.05804
    R4        2.67668   0.00000   0.00000   0.00000   0.00000   2.67668
    R5        2.72495   0.00000   0.00000   0.00000   0.00000   2.72495
    R6        2.67668   0.00000   0.00000   0.00000   0.00000   2.67668
    R7        2.05732   0.00000   0.00000   0.00000   0.00000   2.05732
    R8        2.68663   0.00000   0.00000   0.00000   0.00000   2.68663
    R9        2.72495   0.00000   0.00000   0.00000   0.00000   2.72495
   R10        2.64419   0.00000   0.00000   0.00000   0.00000   2.64419
   R11        2.05804   0.00000   0.00000   0.00000   0.00000   2.05804
   R12        2.06009   0.00000   0.00000   0.00000   0.00000   2.06009
   R13        3.48512   0.00000   0.00000   0.00000   0.00000   3.48512
   R14        4.89729   0.00000   0.00000   0.00000   0.00000   4.89730
   R15        4.64188   0.00000   0.00000   0.00000   0.00000   4.64188
   R16        4.64010   0.00000   0.00000  -0.00001  -0.00001   4.64009
   R17        4.65803   0.00000   0.00000   0.00000   0.00000   4.65803
   R18        4.66111   0.00000   0.00000   0.00000   0.00000   4.66111
   R19        3.57604   0.00000   0.00000   0.00000   0.00000   3.57604
   R20        2.67721   0.00000   0.00000   0.00000   0.00000   2.67721
   R21        2.67742   0.00000   0.00000   0.00000   0.00000   2.67742
   R22        3.57702   0.00000   0.00000   0.00000   0.00000   3.57702
   R23        2.67684   0.00000   0.00000   0.00000   0.00000   2.67684
   R24        2.67785   0.00000   0.00000   0.00000   0.00000   2.67785
   R25        3.57333   0.00000   0.00000   0.00000   0.00000   3.57332
   R26        2.67681   0.00000   0.00000   0.00000   0.00000   2.67681
   R27        2.67772   0.00000   0.00000   0.00000   0.00000   2.67771
   R28        3.57373   0.00000   0.00000   0.00000   0.00000   3.57373
   R29        2.67559   0.00000   0.00000   0.00000   0.00000   2.67559
   R30        2.67801   0.00000   0.00000   0.00000   0.00000   2.67801
   R31        2.90936   0.00000   0.00000   0.00000   0.00000   2.90936
   R32        2.07506   0.00000   0.00000   0.00000   0.00000   2.07506
   R33        2.07852   0.00000   0.00000   0.00000   0.00000   2.07852
   R34        2.90949   0.00000   0.00000   0.00000   0.00000   2.90949
   R35        2.07508   0.00000   0.00000   0.00000   0.00000   2.07508
   R36        2.07846   0.00000   0.00000   0.00000   0.00000   2.07846
   R37        2.07723   0.00000   0.00000   0.00000   0.00000   2.07723
   R38        2.07501   0.00000   0.00000   0.00000   0.00000   2.07501
   R39        2.07740   0.00000   0.00000   0.00000   0.00000   2.07740
   R40        2.07499   0.00000   0.00000   0.00000   0.00000   2.07499
   R41        3.48512   0.00000   0.00000   0.00000   0.00000   3.48512
   R42        4.89730   0.00000   0.00000   0.00000   0.00000   4.89729
   R43        4.64010   0.00000   0.00000  -0.00001  -0.00001   4.64009
   R44        4.64188   0.00000   0.00000   0.00001   0.00001   4.64188
   R45        4.66109   0.00000   0.00000   0.00002   0.00002   4.66111
   R46        4.65804   0.00000   0.00000   0.00000   0.00000   4.65803
   R47        3.57702   0.00000   0.00000   0.00000   0.00000   3.57702
   R48        2.67684   0.00000   0.00000   0.00000   0.00000   2.67684
   R49        2.67785   0.00000   0.00000   0.00000   0.00000   2.67785
   R50        3.57604   0.00000   0.00000   0.00000   0.00000   3.57604
   R51        2.67721   0.00000   0.00000   0.00000   0.00000   2.67721
   R52        2.67742   0.00000   0.00000   0.00000   0.00000   2.67742
   R53        3.57374   0.00000   0.00000  -0.00001  -0.00001   3.57373
   R54        2.67559   0.00000   0.00000   0.00000   0.00000   2.67559
   R55        2.67801   0.00000   0.00000   0.00000   0.00000   2.67801
   R56        3.57332   0.00000   0.00000   0.00000   0.00000   3.57332
   R57        2.67681   0.00000   0.00000   0.00000   0.00000   2.67681
   R58        2.67771   0.00000   0.00000   0.00000   0.00000   2.67771
   R59        2.90949   0.00000   0.00000   0.00000   0.00000   2.90949
   R60        2.07508   0.00000   0.00000   0.00000   0.00000   2.07508
   R61        2.07846   0.00000   0.00000   0.00000   0.00000   2.07846
   R62        2.90936   0.00000   0.00000   0.00000   0.00000   2.90936
   R63        2.07506   0.00000   0.00000   0.00000   0.00000   2.07506
   R64        2.07852   0.00000   0.00000   0.00000   0.00000   2.07852
   R65        2.07740   0.00000   0.00000   0.00000   0.00000   2.07740
   R66        2.07499   0.00000   0.00000   0.00000   0.00000   2.07499
   R67        2.07723   0.00000   0.00000   0.00000   0.00000   2.07723
   R68        2.07501   0.00000   0.00000   0.00000   0.00000   2.07501
    A1        2.10353   0.00000   0.00000   0.00000   0.00000   2.10353
    A2        2.07492   0.00000   0.00000   0.00000   0.00000   2.07492
    A3        2.10473   0.00000   0.00000   0.00000   0.00000   2.10473
    A4        2.06416   0.00000   0.00000   0.00000   0.00000   2.06416
    A5        2.11638   0.00000   0.00000   0.00001   0.00001   2.11639
    A6        2.10259   0.00000   0.00000  -0.00001  -0.00001   2.10259
    A7        2.12469   0.00000   0.00000   0.00000   0.00000   2.12469
    A8        2.07924   0.00000   0.00000   0.00000   0.00000   2.07924
    A9        2.07924   0.00000   0.00000   0.00000   0.00000   2.07924
   A10        2.06416   0.00000   0.00000   0.00000   0.00000   2.06416
   A11        2.10260   0.00000   0.00000   0.00000   0.00000   2.10259
   A12        2.11638   0.00000   0.00000   0.00000   0.00000   2.11638
   A13        2.10353   0.00000   0.00000   0.00000   0.00000   2.10353
   A14        2.07492   0.00000   0.00000   0.00000   0.00000   2.07492
   A15        2.10473   0.00000   0.00000   0.00000   0.00000   2.10473
   A16        2.10617   0.00000   0.00000   0.00000   0.00000   2.10617
   A17        2.08850   0.00000   0.00000   0.00000   0.00000   2.08850
   A18        2.08850   0.00000   0.00000   0.00000   0.00000   2.08850
   A19        1.66633   0.00000   0.00000   0.00002   0.00002   1.66635
   A20        1.64962   0.00000   0.00000  -0.00001  -0.00001   1.64961
   A21        1.68135   0.00000   0.00000  -0.00001  -0.00001   1.68134
   A22        1.68619   0.00000   0.00000   0.00000   0.00000   1.68619
   A23        1.49506   0.00000   0.00000   0.00004   0.00004   1.49509
   A24        1.49779   0.00000   0.00000  -0.00003  -0.00003   1.49776
   A25        1.44049   0.00000   0.00000  -0.00005  -0.00005   1.44044
   A26        1.44966   0.00000   0.00000   0.00005   0.00005   1.44971
   A27        1.72716   0.00000   0.00000  -0.00002  -0.00002   1.72714
   A28        1.39461   0.00000   0.00000   0.00000   0.00000   1.39460
   A29        1.39555   0.00000   0.00000   0.00000   0.00000   1.39555
   A30        1.72542   0.00000   0.00000   0.00002   0.00002   1.72544
   A31        1.94368   0.00000   0.00000   0.00000   0.00000   1.94368
   A32        2.18365   0.00000   0.00000   0.00001   0.00001   2.18366
   A33        2.06652   0.00000   0.00000  -0.00001  -0.00001   2.06651
   A34        1.74058   0.00000   0.00000   0.00000   0.00000   1.74058
   A35        1.74699   0.00000   0.00000   0.00000   0.00000   1.74699
   A36        1.71061   0.00000   0.00000   0.00000   0.00000   1.71061
   A37        1.94426   0.00000   0.00000   0.00000   0.00000   1.94426
   A38        2.17696   0.00000   0.00000  -0.00002  -0.00002   2.17694
   A39        2.07200   0.00000   0.00000   0.00001   0.00001   2.07201
   A40        1.74255   0.00000   0.00000   0.00001   0.00001   1.74256
   A41        1.74542   0.00000   0.00000   0.00001   0.00001   1.74543
   A42        1.71117   0.00000   0.00000   0.00000   0.00000   1.71117
   A43        1.92833   0.00000   0.00000  -0.00001  -0.00001   1.92832
   A44        2.09756   0.00000   0.00000   0.00001   0.00001   2.09757
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   D138      -2.64095   0.00000   0.00000   0.00001   0.00001  -2.64094
   D139      -0.59638   0.00000   0.00000   0.00001   0.00001  -0.59637
   D140      -2.97367   0.00000   0.00000   0.00001   0.00001  -2.97366
   D141      -0.89594   0.00000   0.00000   0.00000   0.00000  -0.89594
   D142       1.14863   0.00000   0.00000   0.00000   0.00000   1.14863
   D143       0.82112   0.00000   0.00000   0.00000   0.00000   0.82111
   D144      -1.20816   0.00000   0.00000   0.00000   0.00000  -1.20817
   D145       2.97746   0.00000   0.00000   0.00000   0.00000   2.97746
   D146       2.96776   0.00000   0.00000  -0.00001  -0.00001   2.96775
   D147       0.93848   0.00000   0.00000   0.00000   0.00000   0.93847
   D148      -1.15909   0.00000   0.00000   0.00000   0.00000  -1.15909
   D149      -1.22177   0.00000   0.00000  -0.00001  -0.00001  -1.22178
   D150       3.03214   0.00000   0.00000   0.00000   0.00000   3.03213
   D151       0.93457   0.00000   0.00000   0.00000   0.00000   0.93457
   D152      -0.82151   0.00000   0.00000  -0.00001  -0.00001  -0.82151
   D153       1.20395   0.00000   0.00000  -0.00001  -0.00001   1.20393
   D154      -2.98070   0.00000   0.00000  -0.00001  -0.00001  -2.98071
   D155      -2.96558   0.00000   0.00000  -0.00001  -0.00001  -2.96559
   D156      -0.94013   0.00000   0.00000  -0.00001  -0.00001  -0.94015
   D157       1.15841   0.00000   0.00000  -0.00001  -0.00001   1.15840
   D158       1.22418   0.00000   0.00000  -0.00001  -0.00001   1.22417
   D159      -3.03355   0.00000   0.00000  -0.00002  -0.00002  -3.03357
   D160      -0.93501   0.00000   0.00000  -0.00001  -0.00001  -0.93503
   D161      -1.49021   0.00000   0.00000   0.00005   0.00005  -1.49016
   D162       0.59842   0.00000   0.00000   0.00005   0.00005   0.59847
   D163       2.78048   0.00000   0.00000   0.00005   0.00005   2.78053
   D164       1.63023   0.00000   0.00000   0.00008   0.00008   1.63030
   D165      -2.56432   0.00000   0.00000   0.00007   0.00007  -2.56425
   D166      -0.38226   0.00000   0.00000   0.00007   0.00007  -0.38219
   D167       3.11264   0.00000   0.00000   0.00004   0.00004   3.11268
   D168      -1.08191   0.00000   0.00000   0.00004   0.00004  -1.08188
   D169       1.10015   0.00000   0.00000   0.00004   0.00004   1.10019
   D170       0.17916   0.00000   0.00000   0.00004   0.00004   0.17920
   D171       2.26779   0.00000   0.00000   0.00003   0.00003   2.26783
   D172      -1.83333   0.00000   0.00000   0.00003   0.00003  -1.83330
   D173       2.86569   0.00000   0.00000  -0.00004  -0.00004   2.86564
   D174      -1.33657   0.00000   0.00000  -0.00006  -0.00006  -1.33663
   D175       0.88773   0.00000   0.00000  -0.00003  -0.00003   0.88770
   D176      -1.24726   0.00000   0.00000  -0.00004  -0.00004  -1.24730
   D177       0.83366   0.00000   0.00000  -0.00005  -0.00005   0.83361
   D178       3.05796   0.00000   0.00000  -0.00002  -0.00002   3.05794
   D179       0.90776   0.00000   0.00000  -0.00005  -0.00005   0.90771
   D180       2.98869   0.00000   0.00000  -0.00006  -0.00006   2.98862
   D181      -1.07021   0.00000   0.00000  -0.00003  -0.00003  -1.07024
   D182       1.48520   0.00000   0.00000   0.00011   0.00011   1.48531
   D183      -0.60557   0.00000   0.00000   0.00010   0.00010  -0.60548
   D184      -2.78766   0.00000   0.00000   0.00010   0.00010  -2.78756
   D185      -1.64722   0.00000   0.00000   0.00011   0.00011  -1.64712
   D186       2.54518   0.00000   0.00000   0.00010   0.00010   2.54528
   D187       0.36310   0.00000   0.00000   0.00010   0.00010   0.36320
   D188      -3.13185   0.00000   0.00000   0.00009   0.00009  -3.13176
   D189       1.06056   0.00000   0.00000   0.00008   0.00008   1.06063
   D190      -1.12153   0.00000   0.00000   0.00008   0.00008  -1.12145
   D191      -0.18615   0.00000   0.00000   0.00007   0.00007  -0.18608
   D192      -2.27693   0.00000   0.00000   0.00006   0.00006  -2.27687
   D193       1.82417   0.00000   0.00000   0.00007   0.00007   1.82424
   D194      -2.87567   0.00000   0.00000   0.00005   0.00005  -2.87563
   D195       1.32371   0.00000   0.00000   0.00003   0.00003   1.32374
   D196      -0.90364   0.00000   0.00000   0.00004   0.00004  -0.90360
   D197       1.22846   0.00000   0.00000   0.00004   0.00004   1.22850
   D198      -0.85535   0.00000   0.00000   0.00003   0.00003  -0.85532
   D199      -3.08270   0.00000   0.00000   0.00004   0.00004  -3.08266
   D200      -0.92230   0.00000   0.00000   0.00004   0.00004  -0.92226
   D201      -3.00610   0.00000   0.00000   0.00002   0.00002  -3.00607
   D202       1.04974   0.00000   0.00000   0.00003   0.00003   1.04977
   D203      -1.85567   0.00000   0.00000  -0.00009  -0.00009  -1.85576
   D204       0.18114   0.00000   0.00000  -0.00010  -0.00010   0.18104
   D205       2.37459   0.00000   0.00000  -0.00008  -0.00008   2.37451
   D206       1.30719   0.00000   0.00000  -0.00012  -0.00012   1.30707
   D207      -2.93919   0.00000   0.00000  -0.00013  -0.00013  -2.93932
   D208      -0.74574   0.00000   0.00000  -0.00011  -0.00011  -0.74585
   D209      -0.20789   0.00000   0.00000  -0.00008  -0.00008  -0.20797
   D210       1.82892   0.00000   0.00000  -0.00009  -0.00009   1.82883
   D211      -2.26082   0.00000   0.00000  -0.00008  -0.00008  -2.26089
   D212       2.72587   0.00000   0.00000  -0.00008  -0.00008   2.72579
   D213      -1.52051   0.00000   0.00000  -0.00009  -0.00009  -1.52060
   D214       0.67294   0.00000   0.00000  -0.00007  -0.00007   0.67286
   D215       1.84656   0.00000   0.00000  -0.00006  -0.00006   1.84650
   D216      -0.19010   0.00000   0.00000  -0.00007  -0.00007  -0.19017
   D217      -2.38595   0.00000   0.00000  -0.00007  -0.00007  -2.38602
   D218      -1.30430   0.00000   0.00000  -0.00006  -0.00006  -1.30437
   D219       2.94222   0.00000   0.00000  -0.00007  -0.00007   2.94215
   D220       0.74637   0.00000   0.00000  -0.00007  -0.00007   0.74630
   D221       0.21492   0.00000   0.00000  -0.00005  -0.00005   0.21488
   D222      -1.82174   0.00000   0.00000  -0.00005  -0.00005  -1.82179
   D223       2.26560   0.00000   0.00000  -0.00005  -0.00005   2.26555
   D224      -2.73090   0.00000   0.00000  -0.00003  -0.00003  -2.73093
   D225       1.51562   0.00000   0.00000  -0.00004  -0.00004   1.51558
   D226      -0.68023   0.00000   0.00000  -0.00003  -0.00003  -0.68026
   D227      -0.63981   0.00000   0.00000  -0.00002  -0.00002  -0.63983
   D228      -2.78717   0.00000   0.00000  -0.00003  -0.00003  -2.78720
   D229       1.44664   0.00000   0.00000  -0.00003  -0.00003   1.44662
   D230      -2.97071   0.00000   0.00000  -0.00002  -0.00002  -2.97073
   D231       1.16511   0.00000   0.00000  -0.00002  -0.00002   1.16509
   D232      -0.88426   0.00000   0.00000  -0.00002  -0.00002  -0.88428
   D233       1.56598   0.00000   0.00000  -0.00002  -0.00002   1.56596
   D234      -0.58139   0.00000   0.00000  -0.00002  -0.00002  -0.58141
   D235      -2.63076   0.00000   0.00000  -0.00002  -0.00002  -2.63078
   D236       0.64602   0.00000   0.00000  -0.00005  -0.00005   0.64597
   D237       2.79550   0.00000   0.00000  -0.00005  -0.00005   2.79545
   D238      -1.43744   0.00000   0.00000  -0.00005  -0.00005  -1.43749
   D239       2.98345   0.00000   0.00000  -0.00004  -0.00004   2.98341
   D240      -1.15025   0.00000   0.00000  -0.00004  -0.00004  -1.15029
   D241       0.90000   0.00000   0.00000  -0.00004  -0.00004   0.89996
   D242      -1.55391   0.00000   0.00000  -0.00004  -0.00004  -1.55395
   D243       0.59557   0.00000   0.00000  -0.00004  -0.00004   0.59553
   D244       2.64582   0.00000   0.00000  -0.00004  -0.00004   2.64578
   D245       0.66847   0.00000   0.00000   0.00009   0.00009   0.66855
   D246      -1.40926   0.00000   0.00000   0.00009   0.00009  -1.40917
   D247       2.82936   0.00000   0.00000   0.00009   0.00009   2.82945
   D248      -1.56461   0.00000   0.00000   0.00009   0.00009  -1.56453
   D249       2.64085   0.00000   0.00000   0.00009   0.00009   2.64094
   D250       0.59628   0.00000   0.00000   0.00008   0.00008   0.59637
   D251       2.97357   0.00000   0.00000   0.00008   0.00008   2.97366
   D252       0.89585   0.00000   0.00000   0.00009   0.00009   0.89593
   D253      -1.14872   0.00000   0.00000   0.00008   0.00008  -1.14864
   D254      -0.67512   0.00000   0.00000   0.00005   0.00005  -0.67507
   D255       1.39940   0.00000   0.00000   0.00005   0.00005   1.39946
   D256      -2.83866   0.00000   0.00000   0.00004   0.00004  -2.83862
   D257       1.56168   0.00000   0.00000   0.00004   0.00004   1.56172
   D258      -2.64699   0.00000   0.00000   0.00005   0.00005  -2.64694
   D259      -0.60187   0.00000   0.00000   0.00004   0.00004  -0.60183
   D260      -2.97780   0.00000   0.00000   0.00004   0.00004  -2.97776
   D261      -0.90328   0.00000   0.00000   0.00005   0.00005  -0.90324
   D262       1.14183   0.00000   0.00000   0.00004   0.00004   1.14187
   D263       0.82153   0.00000   0.00000  -0.00002  -0.00002   0.82151
   D264      -1.20392   0.00000   0.00000  -0.00002  -0.00002  -1.20394
   D265       2.98072   0.00000   0.00000  -0.00001  -0.00001   2.98071
   D266       2.96561   0.00000   0.00000  -0.00001  -0.00001   2.96559
   D267       0.94016   0.00000   0.00000  -0.00001  -0.00001   0.94015
   D268      -1.15839   0.00000   0.00000   0.00000   0.00000  -1.15840
   D269      -1.22416   0.00000   0.00000  -0.00001  -0.00001  -1.22417
   D270       3.03358   0.00000   0.00000  -0.00001  -0.00001   3.03357
   D271       0.93503   0.00000   0.00000   0.00000   0.00000   0.93503
   D272      -0.82109   0.00000   0.00000  -0.00003  -0.00003  -0.82112
   D273       1.20820   0.00000   0.00000  -0.00004  -0.00004   1.20816
   D274      -2.97743   0.00000   0.00000  -0.00003  -0.00003  -2.97746
   D275      -2.96773   0.00000   0.00000  -0.00003  -0.00003  -2.96776
   D276      -0.93844   0.00000   0.00000  -0.00004  -0.00004  -0.93848
   D277       1.15911   0.00000   0.00000  -0.00003  -0.00003   1.15908
   D278       1.22180   0.00000   0.00000  -0.00003  -0.00003   1.22177
   D279      -3.03210   0.00000   0.00000  -0.00003  -0.00003  -3.03214
   D280      -0.93455   0.00000   0.00000  -0.00003  -0.00003  -0.93458
         Item               Value     Threshold  Converged?
 Maximum Force            0.000004     0.000450     YES
 RMS     Force            0.000000     0.000300     YES
 Maximum Displacement     0.000768     0.001800     YES
 RMS     Displacement     0.000123     0.001200     YES
 Predicted change in Energy=-1.184681D-09
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
 .......


 IT IS BETTER TO THINK YOU ARE HALF DRY THAN TO KNOW YOU
 ARE ALL WET.  -- SNOOPY
 Job cpu time:  2 days 12 hours 52 minutes  1.9 seconds.
 File lengths (MBytes):  RWF=   1802 Int=      0 D2E=      0 Chk=     27 Scr=      1
 Normal termination of Gaussian 03 at Sat Aug 28 01:02:25 2004.

Example Molpro input file

***,methylene in 631g* basis
memory,4,m

print,orbitals,civector

basis=6-31g**

geomtyp=xyz
geometry={
3
ch2
c,0.0,0.0,0.0
h,0.0,0.966748,0.463168
h,0.0,-0.966748,0.463168
}

int,
pri,0;

rhf
wf,8,2,2;
occ,3,1,1,0;
closed,2,0,1,0;
optg;
freqscf;
pop;
individual;

ImportComputationalChemistryData

ChemistryFunctions paclet 1.1

Reads computational chemistry result files from ADF, DALTON, GAMESS (US), GAMESS-UK, Gaussian, Jaguar, Molcas, Molpro, MOPAC, NBO, NWChem, ORCA, Psi4, Q-Chem, and Turbomole.

Uses the cclib python library to read in the data

Available through the Import format “ComputationalChemistryOutput”

Import["https://raw.githubusercontent.com/cclib/cclib/master/data/NWChem/basicNWChem6.5/dvb_gopt_hf.out",{"ComputationalChemistry","Elements"}]

Import["https://raw.githubusercontent.com/cclib/cclib/master/data/NWChem/basicNWChem6.8/dvb_dispersion_bp86_d3zero.out",{"ComputationalChemistry","Elements"}]

Import["https://raw.githubusercontent.com/cclib/cclib/master/data/QChem/basicQChem5.4/dvb_sp_un.out",{"ComputationalChemistry","Elements"}]

Import["https://raw.githubusercontent.com/cclib/cclib/master/data/NWChem/basicNWChem6.8/dvb_dispersion_bp86_d3zero.out","ComputationalChemistry"]

ListPlot[Import["ExampleData/bisCWdhpe2Cl_13benz_c1_freq.log",{"ComputationalChemistry",{"VibrationalFrequencies","IRIntensities"}}]//Transpose//QuantityMagnitude,Filling->0,]

Running Computational Chemistry Jobs From the Wolfram Language

Built on the open source quantum chemistry package PySCF using the ExternalEvaluate functionality

from pyscf import gto, scf

mol = gto.Mole()
mol.verbose = 4
mol.atom = '''
O        0.000000    0.066777    0.000000
H       -0.763468   -0.529945    0.000000
H        0.763468   -0.529945    0.000000'''
mol.basis = '6-31g'
mol.symmetry = 1
mol.build()

mf = scf.RHF(mol)
mf.kernel()

ElectronicStructure[Molecule["water"],"GroundStateEnergy",<|"BasisSet"->"6-31g"|>]["Energy"]

Goals of this project

Provide a consistent for setting up and running electronic structure calculations from the Wolfram Language

Descriptive job titles and parameter names, rather than shortened keywords that confuse new users.

The shortened keywords should still work as aliases

Computing ground-state electronic wave functions, excited state transition dipoles, visualizing molecular orbitals

Molecular Geometry Optimization

Molecular Vibrational Analysis

Work with other backends in addition to PySCF, e.g. Gaussian, NWChem, Psi4

Provide additional functions for analyzing electronic structure results

Simulating optical and infrared spectroscopy

Animating vibrational modes

Computing multidimensional potential energy surfaces

ElectronicStructure & ElectronicStructureResult

ElectronicStructure[molecule_,jobType_,parameters_]

molecule - a Molecule object

extensions to BioMolecule and crystal structures forthcoming

jobyType: currently supports “GroundStateEnergy”, “ExcitedStateEnergy”, and “GeometryOptimization”

parameters: an Association specifying the model chemistry and calculation parameters

Return value: ElectronicStructureResult

subvalues to return molecular orbitals, orbital occupations, dipole moments, etc

can be used for further computation, e.g. plotting orbitals, using as initial guess for a higher-level computation

res=ElectronicStructure[Molecule["water"],"GroundStateEnergy",<|"BasisSet"->"6-31g"|>]

res["Properties"]

res["MetaInformation"]//Dataset

res["MolecularOrbitalEnergies"]//ListPlot

res["GaussianBasis"]

Computing Ground State Potential Energy Curves

Since version 12 the Wolfram Language has had built-in molecular force fields - MMFF and UFF

Force fields are empirical, and provide a classical approximation of molecular interactions.

Great for large systems out of the range of wave-function based methods

Very fast

But they fail when outside the parameter range

uffH2StretchEnergy=AssociationMap[Function[d,Molecule[{"H","H"},{Bond[{1,2},"Single"]},AtomCoordinates->{{0,0,0},{0,0,d}}]["UFFEnergy"]],Range[0.01,3,0.1]];
ListLinePlot[uffH2StretchEnergy,Frame->True,]

hfH2StretchEnergy=AssociationMap[Function[d,ElectronicStructure[Molecule[{"H","H"},{Bond[{1,2},"Single"]},AtomCoordinates->{{0,0,0},{0,0,d}}],"GroundStateEnergy",<|"BasisSet"->"6-31G","Method"->"UnrestrictedHartreeFock"|>]["Energy"]],Range[0.2,5,.1]];

ListLinePlot[hfH2StretchEnergy,Frame->True,]

dftH2StretchEnergy=AssociationMap[Function[d,ElectronicStructure[Molecule[{"H","H"},{Bond[{1,2},"Single"]},AtomCoordinates->{{0,0,0},{0,0,d}}],"GroundStateEnergy",<|"Method"->"DensityFunctionalTheory"|>]["Energy"]],Range[0.2,5,.1]];

ListLinePlot[{hfH2StretchEnergy,dftH2StretchEnergy},Frame->True,]

We can even watch the electron density as the hydrogen atoms are brought closer together

frames=monitorMap[Function[d,ElectronicStructurePlot3D[Molecule[{"H","H"},{Bond[{1,2},"Single"]},AtomCoordinates->{{0,0,0},{0,0,d}}],"Density",Contours->{-.05,0.06}]],Range[5,.5,-.1]]

ListAnimate[]

Visualizing Molecular Orbitals

Plot the highest occupied and lowest unoccupied molecular orbitals of water:

Row[{ElectronicStructurePlot3D[Molecule["water"],"HOMO",ImageSize->300],ElectronicStructurePlot3D[Molecule["water"],"LUMO",ImageSize->300]}]

Compute the orbitals using a larger basis set:

Row[{ElectronicStructurePlot3D[Molecule["water"],"HOMO",<|"BasisSet"->"6-311G*"|>,ImageSize->300,Contours->{-.06,0.06}],ElectronicStructurePlot3D[Molecule["water"],"LUMO",<|"BasisSet"->"6-311G*"|>,ImageSize->300,Contours->{-.06,0.06}]}]

ElectronicStructurePlot3D[Molecule["water"],"Density"]

Visualizing Molecular Orbitals (2)

Now let’s look at a more complicated molecule, a metacyclophane

m=Molecule[];

MoleculePlot3D[m]

For a larger molecule it is useful to run the electronic structure job once and use the results in subsequent calls to ElectronicStructurePlot3D.

We can also use a correlation consistent basis set with polarization and double zeta split valence functions

This took ~75 seconds on my machine so not doing it live :-)

res=ElectronicStructure[m,"GroundStateEnergy",<|"BasisSet"->"ccpvdz"|>]

Here are the two highest-energy occupied orbitals:

ElectronicStructurePlot3D[res,"HOMO"]

ElectronicStructurePlot3D[res,"HOMO"-1]

And the two lowest-energy unoccupied orbitals

ElectronicStructurePlot3D[res,"LUMO"]

ElectronicStructurePlot3D[res,"LUMO"+1]

ElectronicStructurePlot3D[res,"LUMO"+2]

Or we can choose an arbitrary orbital:

ElectronicStructurePlot3D[res,{"Orbital",300}]

ElectronicStructurePlot3D[res,{"Orbital",30}]

Final Slide

Look for these functions in the “WolframChemistry/ChemistryFunctions” paclet when Wolfram version 14.2 is released