Equations-of-motion method including renormalization and double-excitation mixing

Abstract

The equations-of-motion method is discussed as an approach to calculating excitation energies and transition moments directly. The proposed solution [T. V. McKoy, Phys. Rev. A 2, 2208 (1970)) of these equations is extended in two ways. First we include the proper renormalization of the equations with respect to the ground state particle-hole densities. We then show how to include the effects of two-particlehole components in excited states which are primarily single-particle-hole states. This is seen to be equivalent to a single-particle-hole theory with a normalized interaction. Applications to various diatomic and polyatomic molecules indicate that the theory can predict excitation energies and transition moments accurately and economically.

Equations of motion method: Excitation energies and intensities in formaldehyde

“…We have derived several approximations to the solution of the equations of motion for the operator 0): which generates the state J:>c) from the ground state JO). In the equations of motion method the approximation which includes single particle-hole (1p-1h) and two particle-two hole (2p-2h) components 3 in 0~, referred to as the (1p-1h)+(2p-2h) approximation, gives results for transition frequencies and intensities in N 2 , CO, C 2 H 4 , 2 C 6 H 6 , 4 and C0 2 5 in good agreement with experiment.…”

“…The calculated results listed in the third column agree well with the observed values in the fourth column. The experimental values for transitions to the 1 A 2 (n-1T*) and 3 A 2 (n -11*) states are the estimated vertical excitation energies. 11 The 1 A 1 -3 A 1 (7T -11*) has not been observed experimentally but could probably be seen quite easily in low-energy high-angle electron scattering off formaldehyde.…”

Assignments in the electronic spectrum of water

“…19 At this level of approximation we have obtained accurate excitation energies and oscillator strengths for transitions in N2' 21 CO, 21 CzH4' 21 H2CO, 22 C02' za and C Jia . 24 We now discuss the application of this method to the spectrum of the water molecule.…”

“…29 Table I shows the excitation energies for ten transitions in water along with the oscillator strengths for the four dipole-allowed transitions. These are results of the calculation using the 1p-1h plus 2p-2h (1p-1h + 2p-2h) approximation 19 to the solution of the equation of motion, Eq. (1), and the basis set containing the polarization functions.…”

Theory and computations of two-photon absorbing photochromic chromophores

“…As a result, the 2Ag state acquires the double excited character, and its energy is considerably lowered. Although double excitations could be included in extended or higher-order RPA formalisms [57], these methods did not receive wide attention. Instead, LR has been applied to correlated ground states, including MultiConfiguration Self Consistent Field (MCSCF) [58], and Coupled Cluster (CC) [59][60][61] methods.…”