EOM-MBPT

The partitioned equation-of-motion second-order many-body perturbation theory [P-EOM-MBPT(2)] [67] is an approximation to equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) [17], which will be fully described in Section 2.4. The EOM-CCSD method diagonalizes the coupled-cluster effective Hamiltonian H = [HeTl+T2) in the singles and doubles space, i.e.,... 

It may be noticed that by virtue of being a dressed Hamiltonian including the effect of correlation, diagrams 37-39 account for some of the CIS(D)-type correlation corrections (22-24) to CIS (diagrams 35 and 36). There is no need to make ad hoc adjustments to diagrams to ensure size correctness because diagram 37 (unlinked) cancels exactly between the ground and excited states. In other words, P-EOM-MBPT(2) has the factorization approximation built in. 

The zeroth-order wavefunction of an excited state in an extended system cannot be described by a single determinant since the energies of the excited determinants form continuous bands. The states associated with the same band are degenerate since the energy difference between two adjacent states is an infinitesimal number. Thus, to calculate the energy spectrum of excited states, one needs to use degenerate MBPT, two-particle green function theory or a method like EOM-CC [5],... 

Orbital MBPT(4) CCSD CCSDT-1 QRHF-CCSD QRHF-CCSDT-1 EOM-CCSD EOM- CCSD+T (3) ... 

FC, PSO and SD terms were calculated with the EOM-CC method in HF, N2 and CO, where it is known that noncontact contributions are important, and results were compared with those reported in refs 164,186,187. In the last two cases, couplings were also calculated by Vahtras et Good agreement with other correlated calculations was obtained. Couplings in H2O, NH3 and HCl were also discussed and results were compared with Fukui s MBPT(2), showing that both methods reproduce the experimental 7(0,H) and /(N,H) values within 2%, but for V(H,H) significant differences with experiment were obtained. It is worth noting that / (H,Cl) = 30.03 Hz, which compares favourably with 7 om-<=<=(H,C1) = 35.03 Hz and with / (H,C1) = 37.7 Hz. ... 

In the second part of the chapter, the correlation will be less visible, since it will be accounted for by appUcation of linear combinations of the Slater determinants. We will discuss the variational methods (VB, Cl, MC SCF), and then the non-variational ones (CC, EOM-CC, MBPT). 

EOM-CC method (p. 548) deexcitations (p. 550) many body perturbation theory (MBPT) (p.551)... 

P —2co co,co) calculations on ammonia, and used them to scale static MBPT(2), CCSD, and CCSD(T) values. They also calculated EOM-CC fi(—co co, 0) directly. They obtained EOM-CC P —2co CO, (o) by using the dispersion relations and scaling the static CCSD(T) P(—2co co, co). Rice and Handy performed TDCHF and MP(2) calculations for fi(—co co,0) and P —2co co, co). There have also been MCSCF QRF calculations of P —2(0-, CO, co), and there is an experimental value. These results are compared in Tables 2 and 3. It is clear that there is a long way to go before these calculations can be said to be converged. 

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