The correlation-consistent composite approach: Implementation of the resolution-of-the-identity approximation

Jeremy LaiTexas Academy of Mathematics and ScienceDr. Angela K. Wilson, Department of ChemistryCollege of Arts and Sciences University of North Texas

Computational ChemistryIndustries:

◦Materials Science◦Petrochemicals◦Medicine

Computers can work overnight!Especially useful for

◦Dangerous reactions◦Short-lived reactions◦Expensive reactions

Ab initio MethodsExtremely accurateNo experimental evidenceComputational cost

◦CPU Time◦Disk Space Requirements◦Memory Requirements

Why so expensive?Schrodinger Equation:

Can’t solve that, we make approximations◦Hartree-Fock Theory ◦Møller-Plesset perturbation theory◦Coupled-Cluster theory◦For two electron interaction:

Coulomb Integral

H2 has 2 electronsC2H6O has 20 electronsC6H12 has 36 electrons

Cyclohexane C6H12

Protein

Protein Dimer

The correlation-consistent composite approach (ccCA)3.3 years or 20 days?ccCA made medium-sized

molecules more practical4 additive steps

◦Reference Energy (MP2)◦Correlation Energy (CCSD(T))◦Core-Valence Energy (MP2)◦Scalar-Relativistic Energy (MP2)

Resolution-of-the-Identity ApproximationUnity operator

Theoretically reduces computational cost by 2 orders of magnitude

ExperimentTested RI-ccCA with G2/97 Test

SetOver 100 second-row and third-

row moleculesUsed Molpro, a computation

chemistry software packageUsed the Department of

Chemistry’s CRUNTCh supercomputers

Does it work?

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CPU Timings

Molecular Size (correlates to number of non-hydrogen atoms)

Perc

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Does it work? (cont.)

75

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Disk Space

Molecular Size (correlates to number of non-hydrogen atoms)

Perc

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avin

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1 2 3 4 5

Summary of RI-ccCAFavorable relationship with

molecular sizeReduces CPU timeReduces Disk SpaceReduces Wall TimeMakes large-sized molecules more

practical◦Carbon nanotubes◦Small proteins◦Next-generation fuels

Summary of RI-ccCA (cont.)More efficient for

small-sized molecules and medium-sized

This means we can now use

$1000 Computer instead of $100,000 Supercomputer

AcknowledgementsDr. Angela K. Wilson

◦Principal InvestigatorDr. Brian P. Prascher

◦Graduate StudentCenter for the Advancement of

Scientific Computing and Modeling (CASCaM)

University of North TexasTAMS Summer Research

Scholarship