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Computational Chemistry

by: Tierra Ernser

Computational Chemistry CHEM 6485

Tierra Ernser

GPA 3.99

Charles Sherrill

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Charles Sherrill
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This 0 page Class Notes was uploaded by Tierra Ernser on Monday November 2, 2015. The Class Notes belongs to CHEM 6485 at Georgia Institute of Technology - Main Campus taught by Charles Sherrill in Fall. Since its upload, it has received 17 views. For similar materials see /class/234327/chem-6485-georgia-institute-of-technology-main-campus in Chemistry at Georgia Institute of Technology - Main Campus.


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Date Created: 11/02/15
Introduction to Nondynamical Correlation C David Sherrill School of Chemistry and Biochemiotry Georgia Institute of Technology Two Types of Electron Correlation Basis Set Correlation for H20 with a DZ Basis Geometry ECOM hartree Re O148028 15 R6 O210992 20 R6 O310067 Data from Harrision 1983 Dynamical correlation electrons instantaneously avoiding each other should become less important at stretched ge ometries since the electrons are further apart However the correlation energy increases With stretching There must be a nondynamical correlation What Causes the Nondynamical Correlation 0 Recall the correlation energy is the difference between Full Cl and Hartree Fock 0 We know Hartree Fock neglects instantaneous electron electron repulsions dynamical correlation o What else is it missing It does not account for nearly degenerate electron con gurations Simplest Example of Degeneracy Stretched H2 For minimal basis H2 only two 1s functions one on each H atom gbA gbB Restricted Hartree Fock orbitals determined completely by symmetry Let overbars denote 5 spin 1 0 m 14 3 1 gbw m 14 B 1 Ml 0 U a I gt V5 M2 cba 1 2 aagt Expansion of the Determinant 01Ea2 a2gt01gt 2 1 S12 4M2 ch 2gtgtlt Alt1gtBlt1gtgt A1A2 A1 B2 4 A1 Blt1gtgtlt6Alt2gt Blt2gtgt Simpli ed Notation for Expanded Determinant The expanded determinant looks like the sum of four determi nants made of atomic spin orbitals l U ogt 2 m Ms ms mm BBgtl Sowhat s the problem The rst and last terms are ionic valence bond structures and shoalcl not contribute to the wavefunction they place both electrons on one of the hydrogens as RAB gt 00 However they are required by RHF T hus RHF cloes not work for bondbreaking processes in general RHF Energy Much Too High for BondBreaking o The RHF energy associated With determinant 050 is ERHF 2h J00 0 However as RAB gt 00 we should have ERHF gt 2EH atom as RAB 00 This isjust hAAhBB which at in nity is also just ZhO U hAA hAB hBA hBB hAA hBB 0 Energy is overestimated by spurious term J00 at long distances Thinking about Degeneracy Another way to View the problem of RHF With dissociation is to realize we have a degeneracy problem as RAB gt oo Recall Hartree Fock assumes only one electron con gura tion is dominant RHF energies of the 02 and 02 con gurations are both equal to ZhO U J00 at RAB 00 They are completely degenerate Solution need to miX in the other determinant by con g uration interaction TwoDeterminant CI Fixes Minimal Basis H2 Dissociation chCIgt C1 00gt C2 Uagt EC ltltIgtCIIHltIgtCIgt H11 H12 1 Cl Cl C2 L H21 H22 J C2 0311711 031122 2ClC2H12 Evaluating the CI Energy We can use Slater s Rules see Intro to Electron Correlation to evaluate the matrix elements H I J We obtain H11 lt UEUIH UEUgt 2h00 J00 H12 lt UEUIHI UEUgt 0000 H21 cbwgw H 050gt 0000 H22 Warsaw 2h00 J00 EC C 2h00 i J00 i C 2h00 i J0U i 2C1C2039039039039 One can plug in for gba and 096 realizing integrals mixing A 85 B vanish as RAB gt 00 to show EC hAA hBB if Cl Cg At dissociation 5050 miX of 02 and 02 Dynamical Correlation Does Not Fix Things In General 0 Although doing Cl works for minimal basis H2 it does not work in general 0 The orbitals need to be determined not for the one determinant Mada but for both determinants at the same time 0 With regular RHF orbitals even correlated methods MP2 CISD CCSD CCSDT can fail Energy hartrees 2495 2505 251 2515 252 2525 Dissociation of BH DZP basis RHF MP2 I CISD E CCSD 9 CCSDT A Full CI AH 2 3 4 5 6 7 8 Bond length bohr Energy hartrees 778 779 78 781 782 783 784 785 786 DZP Energies for Twisted Ethylene RHF MP2 I e E A 0 15 30 45 60 75 90 105120135150165180 Twisting angle other coordinates fixed NearDegeneracies Invalidate Perturbative Treatments The a and 0 orbitals beoorne degenerate at large distances this is bad for energy denominators in perturbation theory AEMP2 Z M altbrlts 6a 6b 6i 6j The 02 con guration needs to be treated on an equal footing With 02 not as a perturbation Nondynamical Correlation Accounts for NearDegeneracies We need to include all nearly degenerate electron con gurations or determinants in our starting reference wavefunction Need to nd orbitals which minimize the energy of the mirture of near degenerate determinants this is multi con gurational self consistent eld MCSCF A special case of MCSCF which takes all possible determinants full CI in a given active orbital space is completeactive space self consistent eld CASSCF Need to use multi con gurational references for subsequent treatment of dynamical correlation multireference Cl multi reference PT multireference CC CASPT2 A Simpler Cheat Solution Multi reference methods are extraordinarily complex to program and to use Sometimes we can get good energies using unrestricted HartreeFock references especially when dynamical corre lation is treated subsequently This has the major disadvantage that any spin dependent properties are completely wrong the wavefunction becomes a 5050 mixture of singlet and triplet at dissociation Hard to nd a UHF solution for a singlet which breaks spin symmetry need to use GUESSJVIIX option and have good luck Energy hartrees 7785 779 DZP Energies for Twisted Ethylene RHF UHF i TCSCF 43 VOOCCD 9 CASSCF ee 30 45 60 75 90 105 120 135 150 165 180 Twisting angle other coordinates fixed


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