Molecular response properties in equation of motion coupled cluster theory: A time-dependent perspective

Sonia Coriani, Filip Pawlowski, Jeppe Olsen, Poul Jørgensen

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Molecular response properties for ground and excited states and for transitions between these states are defined by solving the time-dependent Schrodinger equation for a molecular system in a field of a time-periodic perturbation. In equation of motion coupled cluster (EOM-CC) theory, molecular response properties are commonly obtained by replacing, in configuration interaction (CI) molecular response property expressions, the energies and eigenstates of the CI eigenvalue equation with the energies and eigenstates of the EOM-CC eigenvalue equation. We show here that EOM-CC molecular response properties are identical to the molecular response properties that are obtained in the coupled cluster-configuration interaction (CC-CI) model, where the time-dependent Schrodinger equation is solved using an exponential (coupled cluster) parametrization to describe the unperturbed system and a linear (configuration interaction) parametrization to describe the time evolution of the unperturbed system. The equivalence between EOM-CC and CC-CI molecular response properties only holds when the CI molecular response property expressions-from which the EOM-CC expressions are derived-are determined using projection and not using the variational principle. In a previous article [F. Pawlowski, J. Olsen, and P. Jorgensen, J. Chem. Phys. 142, 114109 (2015)], it was stated that the equivalence between EOM-CC and CC-CI molecular response properties only held for a linear response function, whereas quadratic and higher order response functions were mistakenly said to differ in the two approaches. Proving the general equivalence between EOM-CC and CC-CI molecular response properties is a challenging task, that is undertaken in this article. Proving this equivalence not only corrects the previous incorrect statement but also first and foremost leads to a new, time-dependent, perspective for understanding the basic assumptions on which the EOM-CC molecular response property expressions are founded. Further, the equivalence between EOM-CC and CC-CI molecular response properties highlights how static molecular response properties can be obtained from finite-field EOM-CC energy calculations.
Original languageEnglish
Article number024102
JournalJournal of Chemical Physics
Issue number2
Number of pages11
Publication statusPublished - 2016
Externally publishedYes

Bibliographical note

© 2016 AIP Publishing LLC.


  • response function theory
  • Coupled cluster response theory
  • Physics and Astronomy (all)
  • Physical and Theoretical Chemistry
  • Cluster analysis
  • Eigenvalues and eigenfunctions
  • Functions
  • Numerical methods
  • Quantum chemistry
  • Configuration interactions
  • Eigenvalue equations
  • Equation of motion coupled clusters
  • Equation-of-motion coupled cluster theories
  • Linear response functions
  • Periodic perturbation
  • Unperturbed systems
  • Variational principles
  • Equations of motion
  • Coupled cluster calculations (atoms and molecules)
  • Electron correlation and CI calculations (atoms and molecules)
  • Solutions of wave equations: bound state in quantum theory
  • configuration interactions
  • coupled cluster calculations
  • eigenvalues and eigenfunctions
  • excited states
  • ground states
  • Schrodinger equation
  • linear response function
  • variational principle
  • coupled cluster configuration interaction model
  • eigenstates
  • EOM-CC theory
  • time periodic perturbation
  • time dependent Schrodinger equation
  • time dependent perspective
  • motion equation coupled cluster theory
  • molecular response

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