Brueckner doubles coupled cluster method with the polarizable continuum model of solvation

We present the theory and implementation for computing the (free) energy and its analytical gradients with the Brueckner doubles (BD) coupled cluster method in solution, in combination with the polarizable continuum model of solvation (PCM). The complete model, called PTED, and an efficient approximation, called PTE, are introduced and tested with numerical examples. Implementation details are also discussed. A comparison with the coupled-cluster singles and doubles CCSD-PCM-PTED and CCSD-PCM-PTE schemes, which use Hartree-Fock (HF) orbitals, is presented. The results show that the two PTED approaches are mostly equivalent, while BD-PCM-PTE is shown to be superior to the corresponding CCSD scheme when the HF reference wave function is unstable. The BD-PCM-PTE scheme, whose computational cost is equivalent to gas phase BD, is therefore a promising approach to study molecular systems with complicated electronic structure in solution

Noncollinear density functional theory having proper invariance and local torque properties

Noncollinear spins are among the most interesting features of magnetic materials, and their accurate description is a central goal of density functional theory applied to periodic solids. However, these calculations typically yield a magnetization vector that is everywhere parallel to the exchange-correlation magnetic field. No meaningful description of spin dynamics can emerge from a functional constrained to have vanishing local magnetic torque. In this contribution we present a generalization to periodic systems of the extension of exchange-correlation functionals to the noncollinear regime, proposed by Scalmani and Frisch [J. Chem. Theory Comput. 8, 2193 (2012)]. This extension does afford a nonvanishing local magnetic torque and is free of numerical instabilities. As illustrative examples, we discuss frustrated triangular and kagome lattices evaluated with various density functionals, including screened hybrid functionals

Electronic Couplings for Resonance Energy Transfer from CCSD Calculations: From Isolated to Solvated Systems

Quantum mechanical (QM) calculations of electronic couplings provide great insights for the study of resonance energy transfer (RET). However, most of these calculations rely on approximate QM methods due to the computational limitations imposed by the size of typical donor-acceptor systems. In this work, we present a novel implementation that allows computing electronic couplings at the coupled cluster singles and doubles (CCSD) level of theory. Solvent effects are also taken into account through the polarizable continuum model (PCM). As a test case, we use a dimer of indole, a common model system for tryptophan, which is routinely used as an intrinsic fluorophore in Förster resonance energy transfer studies. We consider two bright π → π* states, one of which has charge transfer character. Lastly, the results are compared with those obtained by applying TD-DFT in combination with one of the most popular density functionals, B3LYP

Electronic excitation energies in solution at equation of motion CCSD level within a state specific polarizable continuum model approach

We present a study of excitation energies in solution at the equation of motioncoupled cluster singles and doubles (EOM-CCSD) level of theory. The solvent effect is introduced with a state specific polarizable continuum model (PCM), where the solute-solvent interaction is specific for the state of interest. Three definitions of the excited state one-particle density matrix (1PDM) are tested in order to gain information for the development of an integrated EOM-CCSD/PCM method. The calculations show the accuracy of this approach for the computation of such property in solution. Solvent shifts between nonpolar and polar solvents are in good agreement with experiment for the test cases. The completely unrelaxed 1PDM is shown to be a balanced choice between computational effort and accuracy for vertical excitation energies, whereas the response of the ground state CCSD amplitudes and of the molecular orbitals is important for other properties, as for instance the dipole moment

A variational formulation of the polarizable continuum model

Continuum solvation models are widely used to accurately estimate solvent effects on energy, structural and spectroscopic properties of complex molecular systems. The polarizable continuum model (PCM) is one of the most versatile among the continuum models because of the variety of properties that can be computed and the diversity of methods that can be used to describe the solute from molecular mechanics (MM) to sophisticated quantum mechanical (QM) post-self-consistent field methods or even hybrid QM/MM methods. In this contribution, we present a new formulation of PCM in terms of a free energy functional whose variational parameters include the continuum polarization (represented by the apparent surface charges), the solute’s atomic coordinates and—possibly—its electronic density. The problem of finding the optimized geometry of the (polarized) solute, with the corresponding self-consistent reaction field, is recast as the minimization of this free energy functional, simultaneously with respect to all its variables. The numerous potential applications of this variational formulation of PCM are discussed, including simultaneous optimization of solute’s geometry and polarization charges and extended Lagrangian dynamics. In particular, we describe in details the simultaneous optimization procedure and we include several numerical examples

Assessment of the efficiency of long-range corrected functionals for some properties of large compounds

Using the long-range correction (LC) density functional theory (DFT) scheme introduced by Iikura et al. [J. Chem. Phys. 115, 3540 (2001)] and the Coulomb-attenuating model (CAM-B3LYP) of Yanai et al. [Chem. Phys. Lett. 393, 51 (2004)], we have calculated a series of properties that are known to be poorly reproduced by standard functionals: Bond length alternation of pi-conjugated polymers, polarizabilities of delocalized chains, and electronic spectra of extended dyes. For each of these properties, we present cases in which traditional hybrid functionals do provide accurate results and cases in which they fail to reproduce the correct trends. The quality of the results is assessed with regard to experimental values and/or data arising from electron-correlated wave function approaches. It turns out that (i) both LC-DFT and CAM-B3LYP provide an accurate bond length alternation for polyacetylene and polymethineimine, although for the latter they decrease slightly too rapidly with chain length. (ii) The LC generalized gradient approximation and MP2 polarizabilities of long polyphosphazene and polymethineimine oligomers agree almost perfectly. In the same way, CAM-B3LYP corrects the major part of the B3LYP faults. (iii) LC and CAM techniques do not help in correcting the nonrealistic evolution with chain length of the absorption wavelengths of cyanine derivatives. In addition, though both schemes significantly overestimate the ground to excited state transition energy of substituted anthraquinone dyes, they provide a more consistent picture once a statistical treatment is performed than do traditional hybrid functionals.The authors gratefully acknowledge the financial support of the FNRS-FRFC and the “Loterie Nationale” for Convention No. 2.4578.02, and of the FUNDP

Formation and relaxation of excited states in solution: A new time dependent polarizable continuum model based on time dependent density functional theory

In this paper a novel approach to study the formation and relaxation of excited states in solution is presented within the integral equation formalism version of the polarizable continuum model. Such an approach uses the excited state relaxed density matrix to correct the time dependent density functional theory excitation energies and it introduces a state-specific solvent response, which can be further generalized within a time dependent formalism. This generalization is based on the use of a complex dielectric permittivity as a function of the frequency, εˆ(ω). The approach is here presented in its theoretical formulation and applied to the various steps involved in the formation and relaxation of electronic excited states in solvated molecules. In particular, vertical excitations (and emissions), as well as time dependent Stokes shift and complete relaxation from vertical excited states back to ground state, can be obtained as different applications of the same theory. Numerical results on two molecular systems are reported to better illustrate the features of the model

Two-Component Noncollinear Time-Dependent Spin Density Functional Theory for Excited State Calculations

We present a linear response formalism for the description of the electronic excitations of a noncollinear reference defined via Kohn-Sham spin density functional methods. A set of auxiliary variables, defined using the density and noncollinear magnetization density vector, allows the generalization of spin density functional kernels commonly used in collinear DFT to noncollinear cases, including local density, GGA, meta-GGA and hybrid functionals. Working equations and derivations of functional second derivatives with respect to the noncollinear density, required in the linear response noncollinear TDDFT formalism, are presented in this work. This formalism takes all components of the spin magnetization into account independent of the type of reference state (open or closed shell). As a result, the method introduced here is able to afford a nonzero local xc torque on the spin magnetization while still satisfying the zero-Torque theorem globally. The formalism is applied to a few test cases using the variational exact-Two-component reference including spin-orbit coupling to illustrate the capabilities of the method