Density functional self-consistent quantum mechanics/molecular mechanics theory for linear and nonlinear molecular properties: Applications to solvated water and formaldehyde

A combined quantum mechanics/molecular mechanics (QM/MM) method is described, where the polarization between the solvent and solute is accounted for using a self-consistent scheme linear in the solvent polarization. The QM/MM method is implemented for calculation of energies and molecular response properties including the calculation of linear and quadratic response functions using the density-functional theory (DFT) and the Hartree-Fock (HF) theory. Sample calculations presented for ground-state energies, first-order ground-state properties, excitation energies, first-order excited state properties, polarizabilities, first-hyperpolarizabilities, and two-photon absorptions strengths of formaldehyde suggests that DFT may in some cases be a sufficiently reliable alternative to high-level theory, such as coupled-cluster (CC) theory, in modeling solvent shifts, whereas results obtained with the HF wave function deviate significantly from the CC results. Calculations carried out on water gives results that also are comparable with CC calculations in accuracy for ground-state and first-order properties. However, to obtain such accuracy an exchange-correlation functional capable of describing the diffuse Rydberg states must be chosen.     

Microscopic and macroscopic polarization within a combined quantum mechanics and molecular mechanics model

A polarizable quantum mechanics and molecular mechanics model has been extended to account for the difference between the macroscopic electric field and the actual electric field felt by the solute molecule. This enables the calculation of effective microscopic properties which can be related to macroscopic susceptibilities directly comparable with experimental results. By separating the discrete local field into two distinct contribution we define two different microscopic properties, the so-called solute and effective properties. The solute properties account for the pure solvent effects, i.e., effects even when the macroscopic electric field is zero, and the effective properties account for both the pure solvent effects and the effect from the induced dipoles in the solvent due to the macroscopic electric field. We present results for the linear and nonlinear polarizabilities of water and acetonitrile both in the gas phase and in the liquid phase. For all the properties we find that the pure solvent effect increases the properties whereas the induced electric field decreases the properties. Furthermore, we present results for the refractive index, third-harmonic generation (THG), and electric field induced second-harmonic generation (EFISH) for liquid water and acetonitrile. We find in general good agreement between the calculated and experimental results for the refractive index and the THG susceptibility. For the EFISH susceptibility, however, the difference between experiment and theory is larger since the orientational effect arising from the static electric field is not accurately described.     

The first hyperpolarizability of p-nitroaniline in 1,4-dioxane: a quantum mechanical/molecular mechanics study

In this work we have investigated the first hyperpolarizability of pNA in 1,4-dioxane solution using a quantum mechanics/molecular mechanics (QM/MM) model. The particular model adopted is the recently developed discrete solvent reaction field (DRF) model. The DRF model is a polarizable QM/MM model in which the QM part is treated using time-dependent density-functional theory and local-field effects are incorporated. This allows for direct computation of molecular effective properties which can be compared with experimental results. The solvation shift for the first hyperpolarizability is calculated to be 30% which is in good agreement with the experimental results. However, the calculated values, both in the gas phase and in solution, are by a factor of 2 larger than the experimental ones. This is in contrast to the calculation of the first hyperpolarizability for several small molecules in the gas phase where fair agreement is found with experimental. The inclusion of local-field effects in the calculations was found to be crucial and neglecting them led to results which are significantly larger. To test the DRF model the refractive index of liquid 1,4-dioxane was also calculated and found to be in good agreement with experiment.     

Time-dependent density functional theory/discrete reaction field spectra of open shell systems: The visual spectrum of [FeIII(PyPepS)2]- in aqueous solution

We report the calculated visible spectrum of [FeIII(PyPepS)2]- in aqueous solution. From all-classical molecular dynamics simulations on the solute and 200 water molecules with a polarizable force field, 25 solute/solvent configurations were chosen at random from a 50 ps production run and subjected the systems to calculations using time-dependent density functional theory (TD-DFT) for the solute, combined with a solvation model in which the water molecules carry charges and polarizabilities. In each calculation the first 60 excited states were collected in order to span the experimental spectrum. Since the solute has a doublet ground state several excitations to states are of type "three electrons in three orbitals," each of which gives rise to a manifold of a quartet and two doublet states which cannot properly be represented by single Slater determinants. We applied a tentative scheme to analyze this type of spin contamination in terms of Delta and Delta transitions between the same orbital pairs. Assuming the associated states as pure single determinants obtained from restricted calculations, we construct conformation state functions (CFSs), i.e., eigenfunctions of the Hamiltonian Sz and S2, for the two doublets and the quartet for each Delta,Delta pair, the necessary parameters coming from regular and spin-flip calculations. It appears that the lower final states remain where they were originally calculated, while the higher states move up by some tenths of an eV. In this case filtering out these higher states gives a spectrum that compares very well with experiment, but nevertheless we suggest investigating a possible (re)formulation of TD-DFT in terms of CFSs rather than determinants.     

The calculation of ground and excited doublet state molecular polarizabilities by the CNDO/S-CI method

The calculation of ground and excited state molecular polarizabilities by the CNDO/S-CI method has been extended to include doublet states. As incorporated, the second order perturbation scheme usually predicts average state polarizabilities of molecular cation ground states to be lower than the corresponding singlet ground states. Average anion polarizabilities are generally found to be higher than those of the corresponding singlet states. Excited doublet state polarizabilities are presented for the molecular cation of formaldehyde, benzene, 1,3,5-trans-hexatriene, and naphthalene. Due to the unavailability of experimental data it is currently impossible to assess appropriately the quality of these results.     

NMR solvent shifts of acetonitrile from frozen density embedding calculations

We present a density functional theory (DFT) study of solvent effects on nuclear magnetic shielding parameters. As a test example we have focused on the sensitive nitrogen shift of acetonitrile immersed in a selected set of solvents, namely water, chloroform, and cyclohexane. To include the effect of the solvent environment in an accurate and efficient manner, we employed the frozen-density embedding (FDE) scheme. We have included up to 500 solvent molecules in the NMR computations and obtained the cluster geometries from a large set of conformations generated with molecular dynamics. For small solute-solvent clusters comparison of the FDE results with conventional supermolecular DFT calculations shows close agreement. For the large solute-solvent clusters the solvent shift values are compared with experimental data and with values obtained using continuum solvent models. For the water --> cyclohexane shift the obtained value is in very good agreement with experiments. For the water --> chloroform NMR solvent shift the classical force field used in the molecular dynamics simulations is found to introduce an error. This error can be largely avoided by using geometries taken from Car-Parrinello molecular dynamics simulations.     

Intermolecular interactions with the direct reaction field method

The direct reaction field (DRF ) method, developed to incorporate the effects of a (large) semiclassical environment into the Hamiltonian of a quantum mechanical system, is briefly reviewed. It is shown that the DRF method behaves—at least—like a supermolecule SCF calculation. With the water dimer as an example, the similarity with the SCF procedure is demonstrated, and an application to the interaction between the active site of papain and the remaining 3000 or so atoms of this protein shows the inadequacy of dielectric constant models and the necessity of including atomic polarizabilities in model force fields.     

A smooth, nonsingular, and faithful discretization scheme for polarizable continuum models: the switching/Gaussian approach

Polarizable continuum models (PCMs) are a widely used family of implicit solvent models based on reaction-field theory and boundary-element discretization of the solute/continuum interface. An often overlooked aspect of these theories is that discretization of the interface typically does not afford a continuous potential energy surface for the solute. In addition, we show that discretization can lead to numerical singularities and violations of exact variational conditions. To fix these problems, we introduce the switching/Gaussian (SWIG) method, a discretization scheme that overcomes several longstanding problems with PCMs. Our approach generalizes a procedure introduced by York and Karplus [J. Phys. Chem. A 103, 11060 (1999)], extending it beyond the conductor-like screening model. Comparison to other purportedly smooth PCM implementations reveals certain artifacts in these alternative approaches, which are avoided using the SWIG methodology. The versatility of our approach is demonstrated via geometry optimizations, vibrational frequency calculations, and molecular dynamics simulations, for solutes described using quantum mechanics and molecular mechanics.     

The coupling constant polarizability and hyperpolarizabilty of 1J(NH) in N-methylacetamide, and its application for the multipole spin-spin coupling constant polarizability/reaction field approach to solvation

We present a benchmark study of a combined multipole spin-spin coupling constant (SSCC) polarizability/reaction field (MJP/RF) approach to the calculation of both specific and bulk solvation effects on SSCCs of solvated molecules. The MJP/RF scheme is defined by an expansion of the SSCCs of the solvated molecule in terms of coupling constant dipole and quadrupole polarizabilities and hyperpolarizabilities derived from single molecule ab initio calculations. The solvent electric field and electric field gradient are calculated based on data derived from molecular dynamics (MD) simulations thereby accounting for solute-solvent dynamical effects. The MJP/RF method is benchmarked against polarizable QM/MM calculations for the one-bond N-H coupling constant in N-methylacetamide. The best agreement between the MJP/RF and QM/MM approaches is found by truncating the electric field expansion in the MJP/RF approach at the linear electric field level. In addition, we investigate the sensitivity of the results due to the choice of one-electron basis set in the ab initio calculations of the coupling constant (hyper-)polarizabilities and find that they are affected by the basis set in a way similar to the coupling constants themselves.     

Calculation of nuclear magnetic resonance shieldings using frozen-density embedding

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.     

An improved iterative solution to solve the electrostatic problem in the polarizable continuum model

 We present a discrete iterative interpolation scheme (DIIS) to improve the convergence rate of electrostatic calculations in the polarizable continuum model (PCM) to describe solvent effects on molecular solutes. The electrostatic calculations may easily become the bottleneck of the calculation when the solute size is large. For large molecules iterative procedures turn out to be computationally more convenient than matrix inversion or closure methods. The DIIS scheme is compared here to another iterative procedure (DAMP) and to the biconjugate gradient (BCG) method. The comparisons show that DIIS leads to a sizeable saving of computational time for the C-PCM and IEF-PCM methods (average 40%) compared to DAMP, and more than 50% with respect to the BCG method. Received: 5 October 2000 / Accepted: 13 November 2000 / Published online: 19 January 2001