Transition moments and dynamic polarizabilities in a second order polarization propagator approach
TL;DR: In this paper, a polarization propagator approach was proposed to yield excitation energies, transition moments, and dynamic polarizabilities which are consistent through second order in the electronic repulsion.
Abstract: We have formulated a polarization propagator approach which yields excitation energies, transition moments, and dynamic polarizabilities which are consistent through second order in the electronic repulsion. Certain terms are proven to be missing in our previous second order calculations of transition moments and dynamic polarizabilities and in the equation‐of‐motion calculations of the same quantities. Numerical calculations on carbon monoxide are performed. The calculations show that the major difference between the polarizability (and some transition moments) in the RPA and in the second order polarization propagator approximation is due to these terms. The total effect of all correction terms has been to improve considerably the agreement between theoretical and experimental estimates of the excitation properties for carbon monoxide.
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TL;DR: The M06-2X meta-exchange correlation function is proposed in this paper, which is parametrized including both transition metals and nonmetals, and is a high-non-locality functional with double the amount of nonlocal exchange.
Abstract: We present two new hybrid meta exchange- correlation functionals, called M06 and M06-2X. The M06 functional is parametrized including both transition metals and nonmetals, whereas the M06-2X functional is a high-nonlocality functional with double the amount of nonlocal exchange (2X), and it is parametrized only for nonmetals.The functionals, along with the previously published M06-L local functional and the M06-HF full-Hartree–Fock functionals, constitute the M06 suite of complementary functionals. We assess these four functionals by comparing their performance to that of 12 other functionals and Hartree–Fock theory for 403 energetic data in 29 diverse databases, including ten databases for thermochemistry, four databases for kinetics, eight databases for noncovalent interactions, three databases for transition metal bonding, one database for metal atom excitation energies, and three databases for molecular excitation energies. We also illustrate the performance of these 17 methods for three databases containing 40 bond lengths and for databases containing 38 vibrational frequencies and 15 vibrational zero point energies. We recommend the M06-2X functional for applications involving main-group thermochemistry, kinetics, noncovalent interactions, and electronic excitation energies to valence and Rydberg states. We recommend the M06 functional for application in organometallic and inorganometallic chemistry and for noncovalent interactions.
22,326 citations
TL;DR: In this paper, the performance of time-dependent density-functional response theory (TD-DFRT) for the calculation of high-lying bound electronic excitation energies of molecules is evaluated.
Abstract: This paper presents an evaluation of the performance of time-dependent density-functional response theory (TD-DFRT) for the calculation of high-lying bound electronic excitation energies of molecules. TD-DFRT excitation energies are reported for a large number of states for each of four molecules: N2, CO, CH2O, and C2H4. In contrast to the good results obtained for low-lying states within the time-dependent local density approximation (TDLDA), there is a marked deterioration of the results for high-lying bound states. This is manifested as a collapse of the states above the TDLDA ionization threshold, which is at ??HOMOLDA (the negative of the highest occupied molecular orbital energy in the LDA). The ??HOMOLDA is much lower than the true ionization potential because the LDA exchange-correlation potential has the wrong asymptotic behavior. For this reason, the excitation energies were also calculated using the asymptotically correct potential of van Leeuwen and Baerends (LB94) in the self-consistent field step. This was found to correct the collapse of the high-lying states that was observed with the LDA. Nevertheless, further improvement of the functional is desirable. For low-lying states the asymptotic behavior of the exchange-correlation potential is not critical and the LDA potential does remarkably well. We propose criteria delineating for which states the TDLDA can be expected to be used without serious impact from the incorrect asymptotic behavior of the LDA potential
4,480 citations
TL;DR: In this article, the Tamm-Dancoff approximation to time-dependent density functional theory is proposed and implemented for molecular excited states, which yields excitation energies for several closed-and open-shell molecules that are essentially of the same quality as those obtained from time dependent density functional theories itself, when the same exchange correlation functional is used.
1,617 citations
TL;DR: In this article, an approximate coupled cluster singles and doubles model is presented, denoted CC2, where the total energy is of second-order Moller-Plesset perturbation theory (MP2) quality.
1,549 citations
TL;DR: An overview of TDDFT from its theoretical foundations to several applications both in the linear and in the nonlinear regime is given.
Abstract: Time-dependent density functional theory (TDDFT) can be viewed as an exact reformulation of time-dependent quantum mechanics, where the fundamental variable is no longer the many-body wave function but the density. This time-dependent density is determined by solving an auxiliary set of noninteracting Schrodinger equations, the Kohn-Sham equations. The nontrivial part of the many-body interaction is contained in the so-called exchange-correlation potential, for which reasonably good approximations exist. Within TDDFT two regimes can be distinguished: (a) If the external time-dependent potential is "small," the complete numerical solution of the time-dependent Kohn-Sham equations can be avoided by the use of linear response theory. This is the case, e.g., for the calculation of photoabsorption spectra. (b) For a "strong" external potential, a full solution of the time-dependent Kohn-Sham equations is in order. This situation is encountered, for instance, when matter interacts with intense laser fields. In this review we give an overview of TDDFT from its theoretical foundations to several applications both in the linear and in the nonlinear regime.
1,283 citations
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TL;DR: In this article, an accurate method for calculating the nuclear wave functions and vibrational-rotational energies of diatomic molecules with some economy in the number of values of the internuclear potential required is presented.
Abstract: 1. Introduction. The wave equation for the nuclear motion of a diatomic molecule, in the Born-Oppenheimer approximation, is one which is encountered frequently in quantum-theoretical calculations. Numerical methods for its solution have been developed and used [1, 2, 3, 4] over many years for atomic problems where the potential is one obtained by Hartree-Fock self-consistent fields or the Thomas-Fermi-Dirac statistical field methods. Only relatively recently have computational techniques and the application of electronic computers enabled one to obtain accurate theoretical internuclear potentials at enough internuclear distances to calculate the wave functions for the motion of the nuclei and use them to obtain averages, over the nuclear motion, of molecular properties. The present investigation is concerned with obtaining an accurate method for calculating the nuclear wave functions and vibrational-rotational energies of diatomic molecules with some economy in the number of values of the internuclear potential required. An improved formula for the correction of trial eigenvalues, which does not depend so much for its accuracy upon the smallness of the stepsize in the radial coordinate, and an analysis of the convergence of the procedure are given. A computer subroutine was written and numerical results obtained from it are described for a case where exact analytical solutions are known. In what follows, the vibrational quantum number v, v = 0, 1, 2, , will be used as a subscript to index the eigenvalues Ev with the usual convention that Eo < E1 ? E2 ?
1,118 citations
1,063 citations
754 citations
Book•
01 Jan 2004
TL;DR: In this article, the authors introduce the Pariser-Parr-Pople model and the double-time Green's functions. But they do not consider the effect of temperature dependent perturbation.
Abstract: 1. Introduction. 2. Differential Equations. 3. Propagators and Second Quantization. 4. Double-Time Green's Functions. 5. The Excitation Propagator. 6. Interaction of Radiation and Matter. 7. Temperature Dependent Perturbation Theory. 8. Molecules in Magnetic Fields. 9. Electron Propagator in Higher Order Treatments. 10. Atomic and Molecular Orbitals. 11. The Pariser-Parr-Pople Model. 12. The Excitation Propagator in Higher Orders. 13. Propagators and Chemical Reaction Rate. Appendix A: Complex Calculus Primer. Appendxi B: First and Second Quantization. Appendix C: Stability of Hartree-Fock Solutions. Appendix D: Third-Order Self-Energy. Appendix E: Temperatures-Dependent Propagators. Appendix F: The Eckart Potential and its Propagator. Index.
585 citations