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Understanding Molecule Representation and Calculations in Computational Chemistry

This guide explores the representation and computational methods used in quantum chemistry for molecules, particularly focusing on molecules defined using Cartesian and Z-matrix coordinates. It outlines the necessary coordinates to describe a methane (CH4) molecule, including bond lengths, angles, and torsion. Additionally, the document reviews different file formats (.pdb, .com, .gjf) used in computational chemistry, detailing their compatibility and the data they contain. Methods such as Density Functional Theory (DFT) and various ab initio techniques are also discussed.

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Understanding Molecule Representation and Calculations in Computational Chemistry

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  1. Application Myfirst Gaussian input http://www.kollewin.com/blog/density-functional-theory/

  2. Definition of a molecule communication

  3. Cartesiancoordinates 5 1 2 4 3 x y z C 0.000000 0.000000 0.000000 H 1.070000 0.000000 0.000000 H -0.356662 1.008807 0.000000 H -0.356670 -0.504398 -0.873652 H -0.356670 -0.504398 0.873652 3N coordinates No symmetryconsidered

  4. Internalcoordinates No symmetryconsidered: - Z-matrix (bond) 5 length angle torsion 1 C H 1 B1 H 1 B2 2 A1 H 1 B3 3 A2 2 D1 H 1 B4 3 A3 2 D2 B1 1.070 B2 1.070 B3 1.070 B4 1.070 A1 109.471 A2 109.471 A3 109.471 D1 -120.000 D2 120.000 2 4 3 Symmetryconsidered: C H 1 B1 H 1 B1 2 A1 H 1 B1 3 A1 2 D1 H 1 B1 3 A1 2 -D1 B1 1.070 A1 109.471 D1 -120.000 Howmanycoordinates doesoneneedtodefine a CH4 molecule?

  5. Internalcoordinates 5 • Classification: • Type: • (bond)length (C1-H2) • (bond)angle (C1-H2-H3) • torsion angle (H2-H3-C1-H4) • Measurableproperties: • proper (C1-H2) • improper (H2-H5) • The set of coordinates has to be consistent and obvious!!! 1 2 4 3

  6. Program independent file formats (.pdb)

  7. 7 4 8 1 5 3 2 6 Ethane.pdb 1 2 3 4 5 6 7 8 12345678901234567890123456789012345678901234567890123456789012345678901234567890 COMPND ethane AUTHOR Created by Dave Woodcock at Okanagan University College AUTHOR email:djw_bcca@yahoo.ca AUTHOR Date revised: Mon Sep 4 08:23:32 2000 GENERATED BY BABEL 1.6 HETATM 1 C BEN A 1 0.000 0.000 0.000 1.00 0.00 C HETATM 2 H BEN A 1 -0.360 -0.514 -0.891 1.00 0.00 H HETATM 3 H BEN A 1 -0.360 1.029 0.000 1.00 0.00 H HETATM 4 H BEN A 1 -0.360 -0.514 0.891 1.00 0.00 H HETATM 5 C BEN A 1 1.533 0.000 0.000 1.00 0.00 C HETATM 8 H BEN A 1 1.893 0.514 -0.891 1.00 0.00 H HETATM 7 H BEN A 1 1.893 0.514 0.891 1.00 0.00 H HETATM 6 H BEN A 1 1.893 -1.029 0.000 1.00 0.00 H CONECT 1 2 3 4 5 CONECT 2 1 CONECT 3 1 CONECT 4 1 CONECT 5 1 6 7 8 CONECT 6 2 CONECT 7 2 CONECT 8 2 MASTER 0 0 0 0 0 0 0 0 8 0 8 0 END chain x y type z element resname resID No More detailed: http://www.wwpdb.org/documentation/Format_v32_A4.pdf

  8. Program dependent file formats (.com /.gjf /.hin)

  9. Someexamples • Gaussian (.inp, .com, .gjf) • HyperChem (.hin) • Orca (.inp) • Molpro (.inp) • MRCC (.inp) • Dalton (.dal) Differentextensionsmaymeandifferentinformationcontent! Sameextensiondoesnotmeanthatthosefilesarecompatible!

  10. Gaussian09 • www.gaussian.com/ • Windows OS, Linux OS, Mac X OS • Methods/Model: • MM, • Semiempiricalmethods (PM3, AM1) • ab initio (HF, MP2, MP3, MP4, CCSD, CCSD(T), CIS, CIS(D) QCISD, QCISD(T)), • DFT, • compositemodels (CBS-n, Gn) • Weusethis

  11. Definition of a molecule… • Moleculespecification (Cartesian, Z-matrix…) • Net charge • Arrangement of theelectrons (Electronicstate) • Electron spin: s=½ • Net spin quantumnumber: S • Multiplicity: Ms=2S+1 • Examples: H 1e- (↑) S=½ → S=½Ms=2 (doublet) H2 2•1e- (↑↓) S=2•½ =1 → S=0Ms=1 (singlet) O2 2•8e- (↑↑) S=1 → S=1Ms=3 (triplet) O2 2•8e- (↑↓) S=0 → S=0Ms=1 (singlet)

  12. E Fewcalculations H 1s1 1e-S=0.5 → Ms=2 H2 2e-S=0 → Ms=1 # B3LYP/6-31G*Opt H 0 2 H 0.00.0 0.0 1 Hartree = 2625.5 kJ/mol Doublet ΔE=Efinal-Einitial Hartree SCF Done: E(UB3LYP) = -0.500272784191 A.U. after 5 cycles [-1.17548238441 -(2×-0.500272784191)] ×2625.5 =-459.3 kJ/mol E # B3LYP/6-31G* Opt H2 0 1 H 0.0 0.0 0.0 H0.740.0 0.0 AO AO MO Singlet Hartree SCF Done: E(RB3LYP) = -1.17548238441 A.U. after 3 cycles

  13. Few more calculations C 6e-S=1 → Ms=3 O 8e-S=1 → Ms=3 # B3LYP/6-31G* Opt C 0 3 C 0.00.0 0.0 Triplet SCF Done: E(UB3LYP) = -37.8462804085 A.U. after 9 cycles # B3LYP/6-31G* Opt O 0 3 O 0.00.0 0.0 Triplet SCF Done: E(UB3LYP) = -75.0606231181 A.U. after 10 cycles

  14. Two more calculations O2 16e-S=1 → Ms=1 O2 16e-S=0 → Ms=3 # B3LYP/6-31G* Opt O2 0 1 O-1.11118534 1.97770357 0.01134399 O -2.27278534 1.97770357 0.01134399 excitedstate Singlet SCF Done: E(RB3LYP) = -150.257426636 A.U. after 6 cycles [-150.257426636 –(-150.320042076)] ×2625.5 = 164.4 kJ/mol # ROB3LYP/6-31G* Opt O2 0 3 O-1.11118534 1.97770357 0.01134399 O -2.27278534 1.97770357 0.01134399 Triplet groundstate SCF Done: E(UB3LYP) = -150.320042076 A.U. after 7 cycles

  15. Calculations of atoms

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