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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.

 

In this work, we describe a simple approach to select the most important molecular orbitals (MOs) to compute the optical rotation tensor through linear response (LR) Kohn‐Sham density functional theory (KS‐DFT). Taking advantage of the iterative nature of the algorithms commonly used to solve the LR equations, we select the MOs with contributions to the guess perturbed density that are larger than a certain threshold and solve the LR equations with the selected MOs only. We propose two criteria for the selection, and two definitions of the selection threshold. We then test the approach with two functionals (B3LYP and CAM‐B3LYP) and two basis sets (aug‐cc‐pVDZ and aug‐cc‐pVTZ) on a set of 51 organic molecules with specific rotation spanning five orders of magnitude, 10⁰–10⁴deg (dm⁻¹(g/mL)⁻¹). We show that this approach indeed can provide very accurate values of specific rotation with estimated speedup that ranges from 2 to 8× with the most conservative selection criterion, and up to 20 to 30× with the intermediate criterion.

 

Reliable simulations of molecules in condensed phase require the combination of an accurate quantum mechanical method for the core region, and a realistic model to describe the interaction with the environment. Additionally, this combination should not significantly increase the computational cost of the calculation compared to the corresponding in vacuo case. In this review, we describe the combination of methods based on coupled cluster (CC) theory with polarizable classical models for the environment. We use the polarizable continuum model (PCM) of solvation to discuss the equations, but we also show how the same theoretical framework can be extended to polarizable force fields. The theory is developed within the perturbation theory energy and singles‐T density (PTES) scheme, where the environmental response is computed with the CC single excitation amplitudes as an approximation for the full one‐particle reduced density. The CC‐PTES combination provides the best compromise between accuracy and computational effort for CC calculations in condensed phase, because it includes the response of the environment to the correlation density at the same computational cost of in vacuo CC. We discuss a number of numerical applications for ground and excited state properties, based on the implementation of CC‐PTES with single and double excitations (CCSD‐PTES), which show the reliability and computational efficiency of the method in reproducing experimental or full‐CC data.

This article is characterized under:

Electronic Structure Theory > Ab Initio Electronic Structure Methods

Electronic Structure Theory > Combined QM/MM Methods

Software > Quantum Chemistry

 

The environment may significantly affect molecular properties. Thus, it is desirable to account explicitly for these effects on the wave function and its derivatives, especially when the latter are evaluated with accurate methods, such as those belonging to coupled cluster (CC) theory. In this tutorial review, we discuss how to combine CC methods with the polarizable continuum model of solvation (PCM). We describe useful approximations that include the solvent response to the correlation and excited state equations while maintaining the computational cost comparable to in vacuo calculations. Although applied to PCM, the theoretical framework presented in this review is general and can be used with any polarizable embedding model. Representative applications of the CC‐PCM method to ground and excited state properties of solvated molecules are presented, and comparisons with experiment, and between the full and approximate schemes are discussed.

 

This paper reports the derivation and implementation of the electric dipole-magnetic dipole and electric dipole-electric quadrupole polarizability tensors at the density functional theory level with periodic boundary conditions (DFT-PBC). These tensors are combined to evaluate the Buckingham/Dunn tensor that describes the optical rotation (OR) in oriented chiral systems. We describe several aspects of the derivation of the equations and present test calculations that verify the correctness of the tensor formulation and their implementation. The results show that the full OR tensor is completely origin invariant as for molecules and that PBC calculations match molecular cluster calculations on 1D chains. A preliminary investigation on the choice of density functional, basis set, and gauge indicates a similar dependence as for molecules: the functional is the primary factor that determines the OR magnitude, followed by the basis set and to a much smaller extent the choice of gauge. However, diffuse functions may be problematic for PBC calculations even if they are necessary for the molecular case. A comparison with experimental data of OR for the tartaric acid crystal shows reasonable agreement given the level of theory employed. The development presented in this paper offers the opportunity to simulate the OR of chiral crystalline materials with general-purpose DFT-PBC methods, which, in turn, may help to understand the role of intermolecular interactions on this sensitive electronic property.

 

We present a method for obtaining origin-independent electronic circular dichroism (ECD) in the length-gauge representation LG(OI) without the usage of London atomic orbitals. This approach builds upon the work by Caricato [J. Chem. Phys. 153, 151101 (2020)] and is applied to rotatory strengths and ECD spectra from damped response theory. Numerical results are presented for time-dependent Hartree–Fock and density-functional theory, the second-order algebraic diagrammatic construction method, and linear-response coupled-cluster theory with singles and approximate doubles. We can support the finding that the common choice of placing the gauge origin in the center of mass of a molecule in conventional length-gauge calculations involving chiroptical properties might not be optimal and show that LG(OI) is a valuable alternative for the origin-independent calculation of ECD spectra. We show that, for a limited test set, the convergence of the rotatory strengths calculated with the LG(OI) approach toward the basis-set limit tends to be faster than for the established velocity gauge representation. Relationships between the sum-over-states expression of the optical rotation in the LG(OI) framework and its representation in terms of response functions are analyzed.