Abstract:In this work we demonstrate how different modern quantum chemical methods can be efficiently combined and applied for the calculation of the vibrational modes and spectra of large molecules. We are aiming at harmonic force fields, and infrared as well as Raman intensities within the double harmonic approximation, because consideration of higher order terms is only feasible for small molecules. In particular, density functional methods have evolved to a powerful quantum chemical tool for the determination of the electronic structure of molecules in the last decade. Underlying theoretical concepts for the calculation of intensities are reviewed, emphasizing necessary approximations and formal aspects of the introduced quantities, which are often not explicated in detail in elementary treatments of this topic. It is shown how complex quantum chemistry program packages can be interfaced to new programs in order to calculate IR and Raman spectra. The advantages of numerical differentiation of analytical gradients, dipole moments, and static, as well as dynamic polarizabilities, are pointed out. We carefully investigate the influence of the basis set size on polarizabilities and their spatial derivatives. This leads us to the construction of a hybrid basis set, which is equally well suited for the calculation of vibrational frequencies and Raman intensities. The efficiency is demonstrated for the highly symmetric C 60 , for which we present the first all-electron density functional calculation of its Raman spectrum.

Subsystem density-functional theory (subsystem DFT) has developed into a powerful alternative to Kohn-Sham DFT for quantum chemical calculations of complex systems. It exploits the idea of representing the total electron density as a sum of subsystem densities. The optimum total density is found by minimizing the total energy with respect to each of the subsystem densities, which breaks down the electronic-structure problem into effective subsystem problems. This enables calculations on large molecular aggregates and even (bio-)polymers without systemspecific parameterizations. We provide a concise review of the underlying theory, typical approximations, and embedding approaches related to subsystem DFT such as frozen-density embedding (FDE). Moreover, we discuss extensions and applications of subsystem DFT and FDE to molecular property calculations, excited states, and wave function in DFT embedding methods. Furthermore, we outline recent developments for reconstruction techniques of embedding potentials arising in subsystem DFT, and for using subsystem DFT to incorporate constraints into DFT calculations. C 2013 John Wiley & Sons, Ltd.

A subsystem formulation of time-dependent density functional theory (TDDFT) within the frozen-density embedding (FDE) framework and its practical implementation are presented, based on the formal TDDFT generalization of the FDE approach by Casida and Wesolowski [Int. J. Quantum Chem. 96, 577 (2004)]. It is shown how couplings between electronic transitions on different subsystems can be seamlessly incorporated into the formalism to overcome some of the shortcomings of the approximate TDDFT-FDE approach in use so far, which was only applicable for local subsystem excitations. In contrast to that, the approach presented here allows to include couplings between excitations on different subsystems, which become very important in aggregates composed of several similar chromophores, e.g., in biological or biomimetic light-harvesting systems. A connection to Forster- and Dexter-type excitation energy coupling expressions is established. A hybrid approach is presented and tested, in which excitation energy couplings are selectively included between different chromophore fragments, but neglected for inactive parts of the environment. It is furthermore demonstrated that the coupled TDDFT-FDE approach can cure the inability of the uncoupled FDE approach to describe induced circular dichroism in dimeric chromophores, a feature known as a "couplet," which is also related to couplings between (nearly) degenerate electronic transitions.

We investigate the usefulness of a frozen-density embedding scheme within density-functional theory ͓J. Phys. Chem. 97, 8050 ͑1993͔͒ for the calculation of solvatochromic shifts. The frozen-density calculations, particularly of excitation energies have two clear advantages over the standard supermolecule calculations: ͑i͒ calculations for much larger systems are feasible, since the time-consuming time-dependent density functional theory ͑TDDFT͒ part is carried out in a limited molecular orbital space, while the effect of the surroundings is still included at a quantum mechanical level. This allows a large number of solvent molecules to be included and thus affords both specific and nonspecific solvent effects to be modeled. ͑ii͒ Only excitations of the system of interest, i.e., the selected embedded system, are calculated. This allows an easy analysis and interpretation of the results. In TDDFT calculations, it avoids unphysical results introduced by spurious mixings with the artificially too low charge-transfer excitations which are an artifact of the adiabatic local-density approximation or generalized gradient approximation exchange-correlation kernels currently used. The performance of the frozen-density embedding method is tested for the well-studied solvatochromic properties of the n → * excitation of acetone. Further enhancement of the efficiency is studied by constructing approximate solvent densities, e.g., from a superposition of densities of individual solvent molecules. This is demonstrated for systems with up to 802 atoms. To obtain a realistic modeling of the absorption spectra of solvated molecules, including the effect of the solvent motions, we combine the embedding scheme with classical molecular dynamics ͑MD͒ and Car-Parrinello MD simulations to obtain snapshots of the solute and its solvent environment, for which then excitation energies are calculated. The frozen-density embedding yields estimated solvent shifts in the range of 0.20-0.26 eV, in good agreement with experimental values of between 0.19 and 0.21 eV.

An extensive study of fundamental frequencies and anharmonic vibrational constants for polyatomic molecules obtained from Becke three parameter Lee–Yang–Parr (B3LYP) and Becke–Perdew (BP86) density functional calculations is presented. These calculations are based on standard perturbation theory, and are compared to correlation-corrected vibrational self-consistent field (CC-VSCF) calculations for the water dimer. The anharmonic corrections obtained from density-functional calculations compare well with experimental values and with results from correlated ab initio methods. While fundamental frequencies from B3LYP calculations are reliable, they are considerably too small for BP86 calculations. Consequently, the good agreement of unscaled harmonic frequencies from BP86 calculations with experimental frequencies is due to an error cancellation effect. This is of importance for the prediction of vibrational spectra for large molecules, because the perturbation theory approach naturally becomes unreliable for very large molecules due to the increasing number of anharmonic resonance effects. These resonances seriously limit the applicability of perturbation theoretical approaches to anharmonic vibrational constants, whereas the computational effort for the calculation of cubic and quartic force constants, is feasible because calculations can be performed very efficiently by a parallelized calculation of harmonic force constants for several structures, which are distorted along the normal coordinates, followed by numerical differentiation.