Equation-of-motion EOM methods

The operator sets q = (qi qj 3 ) used in the last section contain products of 1,2,3. creation/annihilation operators, which act on an N-electron reference state 0), say, to produce other elements of Fock space, which describe the system (or its ions) with N, N 1. electrons. These elements are not eigenstates of the Hamiltonian, but of course may be combined to give approximations to actual state vectors, for both the neutral system and its ions. In the EOM approach generalized operators are introduced, which work on the ground state 0) to produce any desired excited state n), neutral or ionic, and an attempt is made to determine these operators directly. 

A typical operator, which creates an excitation, may be defined formally by 

The effect of the superoperator A, acting on 0j, is to produce [H, OiJ], and for exact state vectors it follows at once that 

In Other words, when acting on the exact ground state, 

Thus 01 is an eigenoperator of A, with the exact excitation energy as its eigenvalue. 

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More recently Equation Of Motion (EOM) methods have been used in connection with other types of wave functions, most notably coupled cluster.Such EOM methods are closely related to propagator methods, and give working equations which are similar to those encountered in propagator theory. 

More recently Equation Of Motion (EOM) methods have been used in cormection... 

The second-order polarization propagator approximation is closely related to the equation-of-motion (EOM) method (McCurdy et al., 1977). The equations that determine the excitation energies are the same up through the... 

The simplest polarization propagator corresponds to choosing an HF reference and including only the h2 operator, known as the Random Phase Approximation (RPA), which is identical to Time-Dependent Hartree-Fock (TDHF), with the corresponding density functional version called Time-Dependent Density Functional Theory (TDDFT). For the static case co= 0) the resulting equations are identical to those obtained from a coupled Hartree-Fock approach (Section 10.5). When used in conjunction with coupled cluster wave functions, the approach is usually called Equation Of Motion (EOM) methods. ... 

A similar study at the MP (4th order) basis set level by different researchers finds I and IX to be the stable structures (IX, a nonplanar double-bridged structure is similar to IV) the latter is less stable than the former by 2.3 kcal/mol [3]. Yet another study treats the system similarly and identifies the charge centroids for the species. The bridge hydrogen atoms are shown to be appropriately considered as protonated double bonds. Structural parameters for XI are calculated, in this study, to be r(B-B)=1.601, r(B-H)=1.22 and 1.178 A <(Ht-B-B)=105.9 [4]. An ab initio determination of the B-B coupling constant for B2H4 gives values of 77.61 and 64.91 Hz, when the coupled-Hartree-Fock (CHF) and equations-of-motion (EOM) methods, respectively, are used. For J(B,H), values of 122.99 and 104.51 Hz are similarly obtained [5]. 

PROPAGATOR AND EQUATION-OF-MOTION METHODS 13.6 EQUATION-OF-MOTION (EOM) METHODS... 

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