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We have investigated the functional derivative of the nonadditive kinetic-energy bifunctional, which appears in the embedding potential that is used in the frozen-density embedding formalism, in the limit that the separation of the subsystems is large. We have derived an exact expression for this kinetic-energy component of the embedding potential and have applied this expression to deduce its exact form in this limit. Comparing to the approximations currently in use, we find that while these approximations are correct at the nonfrozen subsystem, they fail completely at the frozen subsystem. Using test calculations on two model systems, a H2O...Li+ complex and a cluster of aminocoumarin C151 surrounded by 30 water molecules, we show that this failure leads to a wrong description of unoccupied orbitals, which can lead to convergence problems caused by too low-lying unoccupied orbitals and which can further have serious consequences for the calculation of response properties. Based on our results, a simple correction is proposed, and we show that this correction is able to fix the observed problems for the model systems studied.

We have extended the frozen-density embedding (FDE) scheme within density-functional theory [T. A. Wesolowski and A. Warshel, J. Phys. Chem. 97, 8050 (1993)] to include external magnetic fields and applied this extension to the nonrelativistic calculation of nuclear magnetic resonance (NMR) shieldings. This leads to a formulation in which the electron density and the induced current are calculated separately for the individual subsystems. If the current dependence of the exchange-correlation functional and of the nonadditive kinetic-energy functional are neglected, the induced currents in the subsystems are not coupled and each of them can be determined without knowledge of the induced current in the other subsystem. This allows the calculation of the NMR shielding as a sum of contributions of the individual subsystems. As a test application, we have calculated the solvent shifts of the nitrogen shielding of acetonitrile for different solvents using small geometry-optimized clusters consisting of acetonitrile and one solvent molecule. By comparing to the solvent shifts obtained from supermolecular calculations we assess the accuracy of the solvent shifts obtained from FDE calculations. We find a good agreement between supermolecular and FDE calculations for different solvents. In most cases it is possible to neglect the contribution of the induced current in the solvent subsystem to the NMR shielding, but it has to be considered for aromatic solvents. We demonstrate that FDE can describe the effect of induced currents in the environment accurately.

We investigate the performance of two discrete solvent models in connection with density functional theory (DFT) for the calculation of molecular properties. In our comparison we include the discrete reaction field (DRF) model, a combined quantum mechanics and molecular mechanics (QM/MM) model using a polarizable force field, and the frozen-density embedding (FDE) scheme. We employ these solvent models for ground state properties (dipole and quadrupole moments) and response properties (electronic excitation energies and frequency-dependent polarizabilities) of a water molecule in the liquid phase. It is found that both solvent models agree for ground state properties, while there are significant differences in the description of response properties. The origin of these differences is analyzed in detail and it is found that they are mainly caused by a different description of the ground state molecular orbitals of the solute. In addition, for the calculation of the polarizabilities, the inclusion of the response of the solvent to the polarization of the solute becomes important. This effect is included in the DRF model, but is missing in the FDE scheme. A way of including it in FDE calculations of the polarizabilities using finite field calculations is demonstrated.

The orbital-free frozen-density embedding scheme within density-functional theory [T. A. Wesolowski and A. Warshel, J. Phys. Chem. 97, 8050 (1993)] is applied to the calculation of induced dipole moments of the van der Waals complexes CO2...X (X = He, Ne, Ar, Kr, Xe, Hg). The accuracy of the embedding scheme is investigated by comparing to the results of supermolecule Kohn-Sham density-functional theory calculations. The influence of the basis set and the consequences of using orbital-dependent approximations to the exchange-correlation potential in embedding calculations are examined. It is found that in supermolecular Kohn-Sham density-functional calculations, different common approximations to the exchange-correlation potential are not able to describe the induced dipole moments correctly and the reasons for this failure are analyzed. It is shown that the orbital-free embedding scheme is a useful tool for applying different approximations to the exchange-correlation potential in different subsystems and that a physically guided choice of approximations for the different subsystems improves the calculated dipole moments significantly.

The absorption spectra of aminocoumarin C151 in water and n-hexane solution are investigated by an explicit quantum chemical solvent model. We improved the efficiency of the frozen-density embedding scheme, as used in a former study on solvatochromism (J. Chem. Phys. 2005, 122, 094115) to describe very large solvent shells. The computer time used in this new implementation scales approximately linearly (with a low prefactor) with the number of solvent molecules. We test the ability of the frozen-density embedding to describe specific solvent effects due to hydrogen bonding for a small example system, as well as the convergence of the excitation energy with the number of solvent molecules considered in the solvation shell. Calculations with up to 500 water molecules (1500 atoms) in the solvent system are carried out. The absorption spectra are studied for C151 in aqueous or n-hexane solution for direct comparison with experimental data. To obtain snapshots of the dye molecule in solution, for which subsequent excitation energies are calculated, we use a classical molecular dynamics (MD) simulation with a force field adapted to first-principles calculations. In the calculation of solvatochromic shifts between solvents of different polarity, the vertical excitation energy obtained at the equilibrium structure of the isolated chromophore is sometimes taken as a guess for the excitation energy in a nonpolar solvent. Our results show that this is, in general, not an appropriate assumption. This is mainly due to the fact that the solute dynamics is neglected. The experimental shift between n-hexane and water as solvents is qualitatively reproduced, even by the simplest embedding approximation, and the results can be improved by a partial polarization of the frozen density. It is shown that the shift is mainly due to the electronic effect of the water molecules, and the structural effects are similar in n-hexane and water. By including water molecules, which might be directly involved in the excitation, in the embedded region, an agreement with experimental values within 0.05 eV is achieved.

An attempt is made to improve the currently accepted muonic value for the 197Au nuclear quadrupole moment [+0.547(16)x10(-28) m2] for the 3/2+ nuclear ground state obtained by Powers et al. [Nucl. Phys. A230, 413 (1974)]. From both measured Mossbauer electric quadrupole splittings and solid-state density-functional calculations for a large number of gold compounds a nuclear quadrupole moment of +0.60x10(-28) m2 is obtained. Recent Fourier transform microwave measurements for gas-phase AuF, AuCl, AuBr, and AuI give accurate bond distances and nuclear quadrupole coupling constants for the 197Au isotope. However, four-component relativistic density-functional calculations for these molecules yield unreliable results for the 197Au nuclear quadrupole moment. Relativistic singles-doubles coupled cluster calculations including perturbative triples [CCSD(T) level of theory] for these diatomic systems are also inaccurate because of large cancellation effects between different field gradient contributions subsequently leading to very small field gradients. Here one needs very large basis sets and has to go beyond the standard CCSD(T) procedure to obtain any reliable field gradients for gold. From recent microwave experiments by Gerry and co-workers [Inorg. Chem. 40, 6123 (2001)] a significantly enhanced (197)Au nuclear quadrupole coupling constant in (CO)AuF compared to free AuF is observed. Here, these cancellation effects are less important, and relativistic CCSD(T) calculations finally give a nuclear quadrupole moment of +0.64x10(-28) m2 for 197Au. It is argued that it is currently very difficult to improve on the already published muonic value for the 197Au nuclear quadrupole moment.