Sekino-Bartlett approach

Abstract The modified equation-of-motion coupled cluster approach of Sekino and Bartlett is extended to computations of the mixed electric-dipole/magnetic-dipole polarizability tensor associated with optical rotation in chiral systems. The approach - referred to here as a linearized equation-of-motion coupled cluster (EOM-CCl) method - is a compromise between the standard EOM method and its linear response counterpart, which avoids the evaluation of computationally expensive terms that are quadratic in the field-perturbed wave functions, but still yields properties that are size-extensive/intensive. Benchmark computations on five representative chiral molecules, including (P)-hydrogen peroxide, (5)-methyloxirane, (5 )-2-chloropropioniuile, (/ )-epichlorohydrin, and (75,45)-norbornenone, demonstrate typically small deviations between the EOM-CCl results and those from coupled cluster linear response theory, and no variation in the signs of the predicted rotations. In addition, the EOM-CCl approach is found to reduce the overall computing time for multi-wavelength-specific rotation computations by up to 34%. 

The purpose of this work is to extend Sekino and Bartlett s approach - which we will refer to as a linearized EOM coupled cluster (EOM-CCl) method - to computations of the frequency-dependent optical rotations of chiral molecules. The development of coupled cluster methods in this field has been dedicated to the implementation of streamlined models of chiroptical properties that are applicable to large molecules[27,28], and this work represents apossible step toward that goal. We will compare the performance of the EOM-CCl approach to its linear-response counterpart - both in terms of theoretical predictions and computational efficiency - for the rigid chiral molecules (5 )-methyloxirane, (5)-2-chloropropionitrile, and (1S,4S)-norbornenone, as well as the conformationally flexible species (/ )-epichlorohydrin. 

In their 1999 paper[26], Sekino and Bartlett defined several models to ameliorate the size-extensivity error of the EOM-CC approach, while simultaneously avoiding the evaluation of the expensive quadratic term in the full second-order CCLR expression in Eq. (21). One of these, dubbed Model III, eliminated the size-extensivity error of EOM-CC completely by (a) retaining only the term linear in T in Eq. (21), (b) dropping the commutator. 

Following Sekino and Bartlett[26], the EOM-CCl approach to optical rotation involves elimination of (a) the quadratic terms in Eq. (25) (b) the commutator between the perturbation operator and the perturbed cluster operators in the linear term and (c) the disconnected contributions to the A equations consistent with Eq. (23), resulting in the simpler expression. 

The efficient computation of molecular response properties such as optical rotation is of paramount importance, and schemes for reducing the computational effort required for high-accuracy methods such as coupled cluster theory become even more crucial for larger, chemically relevant molecules. However, algorithmic improvements must not come at the expense of the overall accuracy of the theory, and the EOM-CCl approach of Sekino and Bartlett provides a reasonable com-... 

Faster computers and development of better numerical algorithms have created the possibility to apply RPA in combination with semiempirical Hamiltonian models to large molecular sterns. Sekino and Bartlett - derived the TDHF expressions for frequency-dependent off-resonant optical polarizabilities using a perturbative expansion of the HF equation (eq 2.8) in powers of external field. This approacii was further applied to conjugated polymer (iialns. The equations of motion for the time-dependent density matrix of a polyenic chain were first derived and solved in refs 149 and 150. The TDHF approach based on the PPP Hamiltonian - was subsequently applied to linear and nonlinear optical response of neutral polyenes (up to 40 repeat units) - and PPV (up to 10 repeat units). " The electronic oscillators (We shall refer to eigenmodes of the linearized TDHF eq with eigenfrequencies Qv as electronic oscillators since they represent collective motions of electrons and holes (see Section II))... 

A method closely related to the CCSD linear response function approach but derived differently is the equation-of-motion coupled cluster approach (EOM-CCSD) (Sekino and Bartlett, 1984 Geertsen et al, 1989 Stanton and Bartlett, 1993). The EOM-CCSD excitation energies are identical to the excitation energies obtained from the CCSD linear response function, but the transition moments and second-order properties, like frequency-dependent polarizabihties of spin-spin coupling constants, differ somewhat. 

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