# Introduction to Møller-Plesset Perturbation Theory

## Presentation on theme: "Introduction to Møller-Plesset Perturbation Theory"— Presentation transcript:

Introduction to Møller-Plesset Perturbation Theory
Kelsie Betsch Chem 381 Spring 2004

Møller-Plesset: Subset of Perturbation Theory
Rayleigh-Schrödinger Perturbation Theory H = H<0> + V Møller-Plesset Assumption that H<0> is Hartree-Fock hamiltonian

Parts of the hamiltonian
H<0> is Hartree-Fock operator Counts electron-electron repulsion twice V corrects using Coulomb and exchange integrals gij = fluctuation potential

Complete Hamiltonian and Energy Expression
Hartree-Fock energy is sum of zeroth- and first-order corrections Expression for correlation energy EHF = E0<0> + E0<1>

Calculating Correlation Energies
Promote electrons from occupied to unoccupied (virtual) orbitals Electrons have more room Decreased interelectronic repulsion lowers energy MP with 2nd order correction (MP2) Two-electron operator Single, triple, quadruple excitations contribute nothing Corrections to other orders may have S,D,T,Q, etc. contributions Select methods may leave some contributions out (MP4(SDQ))

How close do the methods come?
MP2 ~ 80-90% of correlation energy MP3 ~ 90-95% MP4 ~ 95-98% Higher order corrections are not generally employed Time demands

How to make an MP calculation
Select basis set Carry out Self Consistent Field (SCF) calculation on basis set Obtain wavefunction, Hartree-Fock energy, and virtual orbitals Calculate correlation energy to desired degree Integrate spin-orbital integrals in terms of integrals over basis functions

Basis Set Selection Ideally, complete basis set
Yields an infinite number of virtual orbitals More accurate correlation energy Complete basis sets not available Finite basis sets lead to finite number of virtual orbitals Less accurate correlation energy Smallest basis set used: 6-31G* Error due to truncation of basis set is always greater than that due to truncation of MP perturbation energy (MP2 vs. MP3)

PT calculations not variational Difficult to make comparisons No such upper bound to exact energy in PT as in variational calculations PT often overestimates correlation energies Energies lower than experimental values

Interest in relative energies Variational calculations, such as CI, are poor MP perturbation theory is size-extensive Gives MPPT superiority MP calculations much faster than CI Most ab initio programs can do them MP calculations good close to equilibrium geometry, poor if far from equilibrium

Summary Møller-Plesset perturbation theory assumes Hartree-Fock hamiltonian as the zero-order perturbation Hartree-Fock energy is sum of zeroth- and first-order energies Correlation energy begins with second-order perturbation How an MP calculation is carried out Strengths and weaknesses of MP vs. CI

Acknowledgements Dr. Brian Moore Dr. Arlen Viste

References P. Atkins and J. de Paula, Physical Chemistry, 7th ed. W.H. Freeman and Company, New York, 2002. A. Szabo and N.S. Ostlund, Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory, Dover Publications, Inc., Mineola, NY, 1989. C. Møller and M.S. Plesset, Phys. Rev., 46:618 (1934). F.L. Pilar, Elementary Quantum Chemistry, 2nd ed. Dover Publications, Inc., Mineola, NY, 1990. F. Jensen, Introduction to Computational Chemistry, John Wiley & Sons, Chichester, 1999. E. Lewars, Introduction to the Teory and Applications of Molecular and Quantum Mechanics, Kluwer Academic Publishers, Boston, 2003. I.N. Levine, Quantum Chemistry, 5th ed. Prentice Hall, Upper Saddle River, NJ,