Full optical rotation tensor at coupled cluster with single and double excitations level in the modified velocity gauge

Abstract

This work presents the first simulations of the full optical rotation (OR) tensor at coupled cluster with single and double excitations (CCSD) level in the modified velocity gauge (MVG) formalism. The CCSD-MVG OR tensor is origin independent, and each tensor element can in principle be related directly to experimental measurements on oriented systems. We compare the CCSD results with those from two density functionals, B3LYP and CAM-B3LYP, on a test set of 22 chiral molecules. The results show that the functionals consistently overestimate the CCSD results for the individual tensor components and for the trace (which is related to the isotropic OR), by 10%-20% with CAM-B3LYP and 20%-30% with B3LYP. The data show that the contribution of the electric dipole-magnetic dipole polarizability tensor to the OR tensor is on average twice as large as that of the electric dipole-electric quadrupole polarizability tensor. The difficult case of (1S,4S)-(-)-norbornenone also reveals that the evaluation of the former polarizability tensor is more sensitive than the latter. We attribute the better agreement of CAM-B3LYP with CCSD to the ability of this functional to better reproduce electron delocalization compared with B3LYP, consistent with previous reports on isotropic OR. The CCSD-MVG approach allows the computation of reference data of the full OR tensor, which may be used to test more computationally efficient approximate methods that can be employed to study realistic models of optically active materials.

Origin invariant full optical rotation tensor in the length dipole gauge without London atomic orbitals

“…10, and calculate β and A tensors accordingly. 17,24 The downside of this approach is that it has an unphysical static limit that needs to be evaluated explicitly and subtracted out, a procedure known as modified velocity gauge (MVG). 17,24 Note that the LG-GIAOs and MVG approaches provide different numerical values of the B tensor and specific rotation for approximate methods, and that MVG is computationally more expensive than the LG-GIAOs approach.…”

“…Accurate quantum mechanical (QM) methods based on density functional theory (DFT) and coupled cluster (CC) theory have been developed for the calculation of chiroptical properties, [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] using response theory to evaluate the appropriate OR tensor. 15,[19][20][21][22][23][24] However, given the steep computational scaling of electronic QM calculations, all of these methods only provide an approximate solution to the Schrödinger equation using an incomplete basis expansion for the electron density. Thus, the numerical results depend on the choice of gauge for the electric dipole and quadrupole operators.…”

“…15,[25][26][27] Two typical choices are the length gauge (LG), which is more intuitive but provides an origin-dependent tensor, and the velocity gauge (VG), with which the OR tensor is origin-invariant but has an unphysical static limit. 17,24 For the LG and variational methods such as Hartree-Fock (HF) and DFT, the origin-dependence issue is resolved using London orbitals, also known as gauge includa) Electronic mail: mcaricato@ku.edu.…”

“…6,19,28,29 However, GIAOs cannot be utilized with standard CC methods because orbital relaxation is neglected to avoid unphysical poles in the linear response (LR) function due to the reference wave function. 21,22 On the other hand, the modified VG (MVG) 17,24 recipe requires the explicit evaluation and removal of the unphysical static limit, and so far it has been the preferred approach for OR calculations at CC level. 15,16,30,31 We recently proposed a strategy to overcome the origin-dependence issue of LG calculations of specific rotation without the complication of London orbitals, an approach we called LG(OI).…”

Electronic Currents Induced by Optical Fields and Rotatory Power Density in Chiral Molecules

“…Quite recently, newer methods, improving a procedure proposed for the formalism [ 41 ] by applying a singular value decomposition of in the gauge, have been discussed to achieve origin invariant optical rotation in formalism without London atomic orbitals [ 47 , 48 , 49 ]. Relations applicable to other gauges, including mixed dipole acceleration pictures reported elsewhere [ 41 ], could also be implemented allowing for singular value decomposition.…”