First-order nonadiabatic coupling matrix elements between excited states: A Lagrangian formulation at the CIS, RPA, TD-HF, and TD-DFT levels

• Published in: The Journal of chemical physics Vol. 141; no. 1; p. 014110
• Main Authors: Li, Zhendong, Liu, Wenjian
• Format: Journal Article
• Language: English
• Published: United States American Institute of Physics 07.07.2014
• Subjects: ATOMIC AND MOLECULAR PHYSICS; Basis functions; Configuration interaction; COUPLING; Coupling (molecular); DENSITY FUNCTIONAL METHOD; Density functional theory; Derivatives; Energy gradient; EQUATIONS OF MOTION; EXCITED STATES; HARTREE-FOCK METHOD; INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; LAGRANGIAN FUNCTION; Mathematical analysis; MATRIX ELEMENTS; MOLECULES; PARTICLES; RANDOM PHASE APPROXIMATION; TIME DEPENDENCE
• ISSN: 0021-9606; 1089-7690; 1089-7690
• DOI: 10.1063/1.4885817

Analytic expressions for the first-order nonadiabatic coupling matrix elements between electronically excited states are first formulated exactly via both time-independent equation of motion and time-dependent response theory, and are then approximated at the configuration interaction singles, particle-hole/particle-particle random phase approximation, and time-dependent density functional theory/Hartree-Fock levels of theory. Note that, to get the Pulay terms arising from the derivatives of basis functions, the standard response theory designed for electronic perturbations has to be extended to nuclear derivatives. The results are further recast into a Lagrangian form that is similar to that for excited-state energy gradients and allows to use atomic orbital based direct algorithms for large molecules.