A multiconfigurational time-dependent Hartree-Fock method for excited electronic states. I. General formalism and application to open-shell states

Journal Article · Tue Jun 28 04:00:00 EDT 2011 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.3600397· OSTI ID:21560307

Miranda, R P; Fisher, A J ^[1]; Stella, L ^[2]; Horsfield, A P ^[3]

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1. UCL Department of Physics and Astronomy and London Centre for Nanotechnology, University College London, Gower Street, London WC1E 6BT (United Kingdom)
2. Nano-Bio Spectroscopy Group and ETSF Scientific Development Centre, Dpto. Fisica de Materiales, Universidad del Pais Vasco, Centro de Fisica de Materiales CSIC-UPV/EHU-MPC and DIPC, Av. Tolosa 72, E-20018 San Sebastian (Spain)
3. Department of Materials, Imperial College London, South Kensington Campus, London SW7 2AZ (United Kingdom)

The solution of the time-dependent Schroedinger equation for systems of interacting electrons is generally a prohibitive task, for which approximate methods are necessary. Popular approaches, such as the time-dependent Hartree-Fock (TDHF) approximation and time-dependent density functional theory (TDDFT), are essentially single-configurational schemes. TDHF is by construction incapable of fully accounting for the excited character of the electronic states involved in many physical processes of interest; TDDFT, although exact in principle, is limited by the currently available exchange-correlation functionals. On the other hand, multiconfigurational methods, such as the multiconfigurational time-dependent Hartree-Fock (MCTDHF) approach, provide an accurate description of the excited states and can be systematically improved. However, the computational cost becomes prohibitive as the number of degrees of freedom increases, and thus, at present, the MCTDHF method is only practical for few-electron systems. In this work, we propose an alternative approach which effectively establishes a compromise between efficiency and accuracy, by retaining the smallest possible number of configurations that catches the essential features of the electronic wavefunction. Based on a time-dependent variational principle, we derive the MCTDHF working equation for a multiconfigurational expansion with fixed coefficients and specialise to the case of general open-shell states, which are relevant for many physical processes of interest.

• OSTI ID: 21560307
• Journal Information: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 24 Vol. 134; ISSN JCPSA6; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
74 ATOMIC AND MOLECULAR PHYSICS
ACCOUNTING
ACCURACY
APPROXIMATIONS
CALCULATION METHODS
CONSTRUCTION
CORRELATIONS
DEGREES OF FREEDOM
DENSITY FUNCTIONAL METHOD
DIFFERENTIAL EQUATIONS
EFFICIENCY
ELECTRONS
ELEMENTARY PARTICLES
ENERGY LEVELS
EQUATIONS
EXCITED STATES
EXPANSION
FERMIONS
FUNCTIONALS
FUNCTIONS
HARTREE-FOCK METHOD
LEPTONS
MATHEMATICAL SOLUTIONS
PARTIAL DIFFERENTIAL EQUATIONS
SCHROEDINGER EQUATION
SHELLS
TIME DEPENDENCE
VARIATIONAL METHODS
WAVE EQUATIONS
WAVE FUNCTIONS