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Total Energy of Benzene Within Hartree-Fock Approximation

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Total Energy of Benzene Within Hartree-Fock Approximation Example I: Total energy of Benzene within Hartree-Fock approximation In this example we will calculate the total energy of the benzene using the Hartree-Fock (HF) approximation. Let us look at the input file The first directive “echo” is optional but highly recommended. Its purpose is to write out the contents of your input file into the output echo file. The “title” is also optional. You might want to put a short sentence identifying the nature of your calculation . title "total energy of benzene, HF/3-21G" The “start” directive is required. It indicates that this is a new calculation and sets up the name of the database to store your results. start c6h6-scf The name of the database file that you would like to associate with this calculation scratch_dir ./scratch The location of permanent and scratch permanent_dir ./perm directories. The scratch directory contains temporary files. The permanent directory contains essential files which will be required should you wish to restart your calculation The geometry block specifies the name of the elements that comprise your system as well as their coordinates in the following format: Name1 x1 y1 z1 Name2 x2 y2 z2 …… Unless indicated otherwise the default units are angstroms, and the system will be centered around the origin. geometry C 0.99261000 0.99261000 0.00000000 C -1.35593048 0.36332048 0.00000000 C 0.36332048 -1.35593048 0.00000000 C -0.99261000 -0.99261000 0.00000000 C 1.35593048 -0.36332048 0.00000000 C -0.36332048 1.35593048 0.00000000 H 1.75792000 1.75792000 0.00000000 H -2.40136338 0.64344338 0.00000000 H 0.64344338 -2.40136338 0.00000000 H -1.75792000 -1.75792000 0.00000000 H 2.40136338 -0.64344338 0.00000000 H -0.64344338 2.40136338 0.00000000 end The basis block defines which Gaussian basis sets are to be used with the HF calculation. basis * library 3-21G * denotes that all atoms use 3-21G basis. Other end basis for atoms can explicitly be defined: basis H library 3-21G C library 3-21G end scf end The scf block contains parameters that define the HF calculation. task scf energy Task directive requests the actual calculation. In this case we are using self-consistent field Hartree- Fock method (scf) and requesting total energy calculation. Much of the content of the output file is self-explanatory. There is a section in the output file that summarizes the setup of the calculation …. Summary of "ao basis" -> "" (cartesian) ------------------------------------------------------------------------------ Tag Description Shells Functions and Types ---------------- ------------------------------ ------ --------------------- * 3-21G on all atoms Basis "ao basis" -> "ao basis" (cartesian) ----- C (Carbon) ---------- Exponent Coefficients -------------- --------------------------------------------------------- 1 S 1.72256000E+02 0.061767 1 S 2.59109000E+01 0.358794 1 S 5.53335000E+00 0.700713 2 S 3.66498000E+00 -0.395897 2 S 7.70545000E-01 1.215840 Gaussian 3 P 3.66498000E+00 0.236460 3 P 7.70545000E-01 0.860619 basis sets parameters 4 S 1.95857000E-01 1.000000 5 P 1.95857000E-01 1.000000 H (Hydrogen) ------------ Exponent Coefficients -------------- --------------------------------------------------------- 1 S 5.44717800E+00 0.156285 1 S 8.24547000E-01 0.904691 2 S 1.83192000E-01 1.000000 Summary of "ao basis" -> "ao basis" (cartesian) ------------------------------------------------------------------------------ Tag Description Shells Functions and Types ---------------- ------------------------------ ------ --------------------- C 3-21G 5 9 3s2p H 3-21G 2 2 2s NWChem SCF Module ----------------- total energy of benzene, HF/3-21G ao basis = "ao basis" functions = 66 atoms = 12 closed shells = 21 open shells = 0 charge = 0.00 wavefunction = RHF input vectors = atomic output vectors = ./perm/c6h6-scf.movecs use symmetry = T symmetry adapt = T Summary of "ao basis" -> "ao basis" (cartesian) ------------------------------------------------------------------------------ Tag Description Shells Functions and Types ---------------- ------------------------------ ------ --------------------- C 3-21G 5 9 3s2p H 3-21G 2 2 2s Symmetry analysis of basis -------------------------- a1g 7 a1u 0 a2g 2 a2u 2 b1g 0 b1u 7 b2g 2 b2u 2 e1g 4 e1u 18 e2g 18 e2u 4 Forming initial guess at 0.6s Superposition of Atomic Density Guess ------------------------------------- Sum of atomic energies: -227.75976746 Non-variational initial energy ------------------------------ Total energy = -231.937013 1-e energy = -705.828643 2-e energy = 271.451090 HOMO = -0.283977 LUMO = 0.017158 Symmetry analysis of molecular orbitals - initial ------------------------------------------------- Numbering of irreducible representations: 1 a1g 2 a1u 3 a2g 4 a2u 5 b1g 6 b1u 7 b2g 8 b2u 9 e1g 10 e1u 11 e2g 12 e2u Orbital symmetries: 1 a1g 2 e1u 3 e1u 4 b1u 5 e2g 6 e2g 7 a1g 8 e1u 9 e1u 10 e2g 11 e2g 12 a1g 13 b1u 14 b2u 15 e1u 16 e1u 17 a2u 18 e2g 19 e2g 20 e1g 21 e1g 22 e2u 23 e2u 24 a1g 25 b2g 26 e1u 27 e1u 28 e2g 29 e2g 30 b1u 31 e2g Starting SCF solution at 1.3s ---------------------------------------------- Quadratically convergent ROHF Convergence threshold : 1.000E-04 Maximum no. of iterations : 20 Final Fock-matrix accuracy: 1.000E-07 ---------------------------------------------- Integral file = ./perm/c6h6-scf.aoints.0 Record size in doubles = 65536 No. of integs per rec = 43688 Max. records in memory = 6 Max. records in file = 141042 No. of bits per label = 8 No. of bits per value = 64 #quartets = 3.741D+04 #integrals = 1.410D+05 #direct = 0.0% #cached =100.0% iter energy gnorm gmax time ----- ------------------- --------- --------- -------- Usually it takes a few 1 -229.3668943486 7.17D-01 2.50D-01 5.5 iterations to converge 2 -229.4161883416 7.84D-02 2.32D-02 5.8 3 -229.4167722379 3.49D-03 1.08D-03 6.0 the HF equations 4 -229.4167733653 1.71D-06 5.91D-07 6.1 Final RHF results ------------------ Total Total SCF energy = -229.416773365268 Energy One-electron energy = -709.316417273146 Two-electron energy = 277.459104353356 Analysis Nuclear repulsion energy = 202.440539554522 Time for solution = 4.8s Symmetry analysis of molecular orbitals - final ----------------------------------------------- Numbering of irreducible representations: 1 a1g 2 a1u 3 a2g 4 a2u 5 b1g 6 b1u 7 b2g 8 b2u 9 e1g 10 e1u 11 e2g 12 e2u Orbital symmetries: 1 b1u 2 e2g 3 e2g 4 e1u 5 e1u 6 a1g 7 a1g 8 e1u 9 e1u 10 e2g 11 e2g 12 a1g 13 b1u 14 b2u 15 e1u 16 e1u 17 a2u 18 e2g 19 e2g 20 e1g 21 e1g 22 e2u 23 e2u 24 a1g 25 e1u 26 e1u 27 b2g 28 e2g 29 e2g 30 b1u 31 e2g Final eigenvalues ----------------- 1 1 -11.1828 2 -11.1825 3 -11.1825 4 -11.1822 5 -11.1822 6 -11.1816 7 -1.1450 8 -1.0094 9 -1.0094 10 -0.8210 11 -0.8210 12 -0.7116 Energy 13 -0.6408 Levels 14 -0.6171 15 -0.5885 16 -0.5885 17 -0.5006 18 -0.4902 19 -0.4902 20 -0.3357 21 -0.3357 22 0.1460 23 0.1460 24 0.2546 Orbital 25 0.3218 Analysis 26 0.3218 27 0.3644 28 0.3657 29 0.3657 30 0.3683 31 0.4991 ROHF Final Molecular Orbital Analysis ------------------------------------- Vector 7 Occ=2.000000D+00 E=-1.145005D+00 Symmetry=a1g MO Center= -4.1D-17, -1.7D-18, -8.9D-36, r^2= 2.1D+00 Bfn. Coefficient Atom+Function Bfn. Coefficient Atom+Function ----- ------------ --------------- ----- ------------ --------------- 42 0.184587 5 C s 33 0.184587 4 C s 15 0.184587 2 C s 51 0.184587 6 C s 24 0.184587 3 C s 6 0.184587 1 C s Vector 8 Occ=2.000000D+00 E=-1.009436D+00 Symmetry=e1u MO Center= 3.6D-17, -2.8D-16, 1.1D-18, r^2= 2.9D+00 Bfn. Coefficient Atom+Function Bfn. Coefficient Atom+Function ----- ------------ --------------- ----- ------------ --------------- 24 0.299828 3 C s 51 -0.299828 6 C s 33 0.253459 4 C s 6 -0.253459 1 C s Vector 9 Occ=2.000000D+00 E=-1.009436D+00 Symmetry=e1u MO Center= -2.6D-16, 1.8D-16, -1.2D-18, r^2= 2.9D+00 Bfn. Coefficient Atom+Function Bfn. Coefficient Atom+Function ----- ------------ --------------- ----- ------------ --------------- 42 0.319441 5 C s 15 -0.319441 2 C s 33 -0.199877 4 C s 6 0.199877 1 C s Vector 10 Occ=2.000000D+00 E=-8.210207D-01 Symmetry=e2g MO Center= -3.0D-16, 2.8D-17, -2.1D-21, r^2= 3.7D+00 Bfn. Coefficient Atom+Function Bfn. Coefficient Atom+Function ----- ------------ --------------- ----- ------------ --------------- 51 0.342851 6 C s 24 0.342851 3 C s 33 -0.201167 4 C s 6 -0.201167 1 C s 13 0.153965 2 C py 40 -0.153965 5 C py Vector 11 Occ=2.000000D+00 E=-8.210207D-01 Symmetry=e2g MO Center= 9.3D-17, -6.1D-17, -3.8D-21, r^2= 3.7D+00 Bfn. Coefficient Atom+Function Bfn. Coefficient Atom+Function ----- ------------ --------------- ----- ------------ --------------- 15 0.314089 2 C s 42 0.314089 5 C s 33 -0.279746 4 C s 6 -0.279746 1 C s 21 0.172949 3 C px 48 -0.172949 6 C px Vector 12 Occ=2.000000D+00 E=-7.116373D-01 Symmetry=a1g MO Center= -1.0D-17, -3.5D-17, -2.6D-35, r^2= 4.2D+00 Bfn. Coefficient Atom+Function Bfn. Coefficient Atom+Function ----- ------------ --------------- ----- ------------ --------------- 39 0.163127 5 C px 12 -0.163127 2 C px 49 0.163127 6 C py 22 -0.163127 3 C py Vector 13 Occ=2.000000D+00 E=-6.408308D-01 Symmetry=b1u MO Center= -9.0D-17, -9.0D-17, 2.8D-34, r^2= 5.3D+00 Bfn. Coefficient Atom+Function Bfn. Coefficient Atom+Function ----- ------------ --------------- ----- ------------ --------------- 6 0.195323 1 C s 33 -0.195323 4 C s 15 0.195323 2 C s 42 -0.195323 5 C s 24 0.195323 3 C s 51 -0.195323 6 C s Vector 14 Occ=2.000000D+00 E=-6.171063D-01 Symmetry=b2u MO Center= -1.2D-16, -6.3D-17, 1.0D-36, r^2= 2.8D+00 Bfn.
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