Local correlation domains for coupled cluster theory: optical rotation and magnetic-field perturbations.

An approach is described for selecting local-correlation orbital domains appropriate for computing response properties such as optical rotation using frequency-dependent coupled-cluster linear-response theory. This scheme is an extension of our earlier idea [N. J. Russ and T. D. Crawford, Chem. Phys. Lett., 2004, 400, 104] based on an atom-by-atom decomposition of the coupled-perturbed Hartree-Fock (CPHF) response of the component molecular orbitals to external electric and magnetic fields. We have applied this domain-selection scheme to a series of chiral molecules, including pseudo-linear structures (hydrogen molecule helices, fluoroalkanes, and [n]triangulanes), cage-like structures (beta-pinene, methylnorbornanone, and bisnoradamantan-2-one), and aromatic rings (1-phenylethanol). We find that the crossover points between the canonical- and local-correlation approaches are larger than for the conventional Boughton-Pulay domain scheme, in agreement with our earlier analysis of dipole-polarizabilities. Localization errors are reasonably small (a few percent) for pseudo-linear structures with domain sizes of approximately six to eight atoms. Cage-like molecules are significantly more problematic, requiring natural domain sizes of ten or more to obtain the most reliable localization errors.

Coupled cluster calculations of optical rotatory dispersion of (S)-methyloxirane.

Coupled cluster (CC) and density-functional theory (DFT) calculations of optical rotation, [alpha](lambda), have been carried out for the difficult case of (S)-methyloxirane for comparison to recently published gas-phase cavity ringdown polarimetry data. Both theoretical methods are exquisitely sensitive to the choice of one-electron basis set, and diffuse functions have a particularly large impact on the computed values of [alpha](lambda). Furthermore, both methods show a surprising sensitivity to the choice of optimized geometry, with [alpha](355) values varying by as much as 15 deg dm(-1) (g/mL)(-1) among molecular structures that differ only negligibly. Although at first glance the DFT/B3LYP values of [alpha](355) appear to be superior to those from CC theory, the success of DFT in this case appears to stem from a significant underestimation of the lowest (Rydberg) excitation energy in methyloxirane, resulting in a shift of the first-order pole in [alpha](lambda) (the Cotton effect) towards the experimentally chosen incident radiation lines. This leads to a fortuitous positive shift in the value of [alpha](355) towards the experimental result. The coupled cluster singles and doubles model, on the other hand, correctly predicts the position of the absorption pole (to within 0.05 eV of the experimental result), but fails to describe correctly the shape/curvature of the ORD region lambda=355, resulting in an incorrect prediction of both the magnitude and the sign of the optical rotation.

Real versus artifactual symmetry-breaking effects in Hartree-Fock, density-functional, and coupled-cluster methods.

We have examined the relative abilities of Hartree-Fock, density-functional theory (DFT), and coupled-cluster theory in describing second-order (pseudo) Jahn-Teller (SOJT) effects, perhaps the most commonly encountered form of symmetry breaking in polyatomic molecules. As test cases, we have considered two prototypical systems: the 2Sigmau+ states of D( infinity h) BNB and C3+ for which interaction with a low-lying 2Sigmag+ excited state leads to symmetry breaking of the nuclear framework. We find that the Hartree-Fock and B3LYP methods correctly reproduce the pole structure of quadratic force constants expected from exact SOJT theory, but that both methods appear to underestimate the strength of the coupling between the electronic states. Although the Tamm-Dancoff (CIS) approximation gives excitation energies with no relationship to the SOJT interaction, the random-phase-approximation (RPA) approach to Hartree-Fock and time-dependent DFT excitation energies predicts state crossings coinciding nearly perfectly with the positions of the force constant poles. On the other hand, the RPA excited-state energies exhibit unphysical curvature near their crossings with the ground (reference) state, a problem arising directly from the mathematical structure of the RPA equations. Coupled-cluster methods appear to accurately predict the strength of the SOJT interactions between the 2Sigmau+ and 2Sigmag+ states, assuming that the inclusion of full triple excitations provides a suitable approximation to the exact wave function, and are the only methods examined here which predict symmetry breaking in BNB. However, coupled-cluster methods are plagued by artifactual force constant poles arising from the response of the underlying reference molecular orbitals to the geometric perturbation. Furthermore, the structure of the "true" SOJT force constant poles predicted by coupled-cluster methods, although correctly positioned, has the wrong structure.

Potential energy surface discontinuities in local correlation methods.

We have examined the occurrence of discontinuities in bond-breaking potential energy surfaces given by local correlation methods based on the Pulay-Saebø orbital domain approach. Our analysis focuses on three prototypical dissociating systems: the C-F bond in fluoromethane, the C-C bond in singlet, ketene, and the central C-C bond in propadienone. We find that such discontinuities do not occur in cases of homolytic bond cleavage due to the inability of the Pipek-Mezey orbital localization method to separate singlet-coupled charges on distant fragments. However, for heterolytic bond cleavage, such as that observed in singlet ketene and propadienone, discontinuities occur both at stretched geometries and near equilibrium. These discontinuities are usually small, but may be of the same order of magnitude as the localization error in some cases.