Kurt V. Mikkelsen

A multiconfigurational self‐consistent reaction‐field method

We present theory and implementation for a new approach for studying solvent effects: the multiconfigurational self‐consistent reaction‐field (MCSCRF) method. The atom, molecule, or supermolecule is assumed to be surrounded by a linear, homogeneous, continuous medium described by its macroscopic dielectric constant. The electronic structure of the compound is described by a multiconfigurational self‐consistent field (MCSCF) wave function. The wave function is fully optimized with respect to all variational parameters in the presence of the surrounding polarizable dielectric medium. We develop a second‐order convergent optimization procedure for the solvent states. The solvent integrals are evaluated by an efficient and general algorithm. The flexible description of the electronic structure allows us to accurately describe ground, excited, or ionized states of the solute. Deficiencies in the calculation can therefore be assigned to the cavity model rather than the description of the solute.

Multiconfigurational self‐consistent reaction field theory for nonequilibrium solvation

We present multiconfigurational self‐consistent reaction field theory and implementation for solvent effects on a solute molecular system that is not in equilibrium with the outer solvent. The approach incorporates two different polarization vectors for studying the influence of the solvent. The solute, an atom, a molecule or a supermolecule, is assumed to be surrounded by a linear, homogeneous medium described by two polarization vector fields, the optical polarization vector and the inertial polarization vector fields. The optical polarization vector is always in equilibrium with the actual electronic structure whereas the inertial polarization vector is not necessarily in equilibrium with the actual electronic structure. The electronic structure of the compound is described by a correlated electronic wave function—a multiconfigurational self‐consistent field (MCSCF) wave function. This wave function is fully optimized with respect to all variational parameters in the presence of the surrounding polariz...

Sign change of hyperpolarizabilities of solvated water

The experimental work by Levine and Bethea [J. Chem. Phys. 65, 2429 (1976)] and by Ward and Miller [Phys. Rev. A 19, 826 (1979)] on the hyperpolarizability of solvated water and water in the gas phase, respectively, showed a very substantial effect of the solvent on the measured hyperpolarizability. The sign of the hyperpolarizability of solvated water changed compared to gas phase and the numerical value increased by a factor of 1.5. This article presents a theoretical investigation of the solvent effects of the hyperpolarizabilities and their frequency dispersions for liquid water using the continuum, semicontinuum, and supermolecular models. Calculations involving the semicontinuum and supermolecular models give the sign change of the hyperpolarizabilities, indicating that the hydrogen bonds and the static dipole interaction have substantial impact on the hyperpolarizability of liquid water. Hyperpolarizabilities calculated by the supermolecular approach are about one third of those calculated by the s...

Response Theory and Calculations of Molecular Hyperpolarizabilities

Publisher Summary This chapter reviews the development and application of response theory with respect to a particular molecular property—the hyperpolarizability—and demonstrates the potential of this development with some illustrative examples. It reviews recent progress in ab initio calculations of hyperpolarizabilities that have turned into an important research area of quantum chemistry. It particularly emphasizes on the development of multi-configurational (MCSCF) theory. Hyperpolarizabilities can be expressed in terms of response functions that represent an elegant and efficient way of rationalizing the results of time-dependent perturbation theory. The chapter describes an analytic implementation of the linear and quadratic response functions for an MCSCF state. The implementation is direct in the sense that response matrices are never set up explicitly, only linear transformations of the response matrices on trial vectors and iterative techniques are used to solve the response matrix equations. One of the benefits of these techniques is that large, many-dimensional, and therefore accurate reference wave functions can be employed; calculations with configuration spaces containing several million determinants can, thus, routinely be carried out.

A self-consistent reaction field approach to liquid photoionization

Abstract A cluster-dielectric model with a self-consistent reaction field interaction is proposed and evaluated for liquid photoionization. The model is numerically applied to solvent binding energy shifts for some cations and anions in aqueous solutions. The role of medium interaction with the ion or with the ion dressed with its first solvation shell cluster is investigated by means of a self-consistent Hatree-Fock method employing a reaction field Fock operator. Total binding energy shifts and orbital energy shifts are obtained as functions of the dielectric constant. It is shown that for the range of values of the dielectric constant corresponding to the most common solvents, variation in the shifts results from structural effects rather than from pure dielectric effects. It is found that the Born approximation, which is poor for the prediction of the BE shift for the pure ion, works well for cations dressed with it first solvation shell cluster. For anions the model with only one solvation shell in addition to the dielectric is not as appropriate as for cations, which can be argued from comparison of present data with experimental and simulation data. The relation between the present method and a previously devised statistical method is established.

Rovibrationally averaged magnetizability, rotational g factor, and indirect spin–spin coupling of the hydrogen fluoride molecule

The magnetizability tensor, the rotational g factor, and the indirect nuclear spin–spin coupling constant of the hydrogen fluoride molecule have been calculated using large multiconfigurational self-consistent field wave functions and large basis sets. For a critical comparison with experiment, rovibrational corrections have also been calculated. For the magnetizability tensor and the spin–spin coupling constant, we present results with higher precision than available experimental data; for the rotational g factor, our results are in good agreement with experiment.

SOLVENT EFFECTS ON NUCLEAR SHIELDINGS AND SPIN-SPIN COUPLINGS OF HYDROGEN SELENIDE

Solvent effects on the nuclear shielding and indirect spin–spin coupling constants of H2Se have been calculated by modeling the surroundings as a continuous dielectric medium. Gauge-origin independence of the nuclear shieldings is ensured by using London atomic orbitals in combination with linear response theory. We present the linear response function of a solvated molecule subject to triplet perturbations and use a new implementation of this theory to evaluate the Fermi-contact and spin–dipole contributions to the indirect spin–spin coupling constants. We present high-level calculations of the nuclear shielding and indirect spin–spin coupling constants of H2Se in vacuum and different solvents. Our results represent the first ab initio calculations of the spin–spin coupling constants in H2Se as well as the first investigation of medium effects on these properties. It is demonstrated that the solvent shifts of the spin–spin couplings are caused by a polarization of the molecular electronic structure as we...

CALCULATION OF NUCLEAR SHIELDING CONSTANTS AND MAGNETIZABILITIES OF THE HYDROGEN FLUORIDE MOLECULE

Nuclear shielding constants and magnetizabilities of the hydrogen fluoride molecule have been calculated adopting the multiconfigurational self‐consistent field method. Effects of vibrational averaging are calculated by adopting a Gaussian function with variable width and position to describe the vibrational part of the wave function. The rovibrationally averaged 19F shielding constant is calculated to 407.4 ppm and its anisotropy to 111.2 ppm, both in good agreement with experimental results. Also the isotope effect, 〈σF(DF)〉−〈σF(HF)〉, which is calculated to 3.0 ppm agrees well with the available NMR experiment. The effective geometry, dipole moment, vibrational frequencies, and rotational constants are also calculated and discussed.

Self‐consistent reaction field calculations of photoelectron binding energies for solvated molecules

The multiconfigurational self‐consistent reaction field (MCSCRF) and the self‐consistent reaction field (SCRF) methods are applied for solvation shifts of molecular photoelectron spectra. Calculations are performed for cavity wave functions of water, benzene, methanol, and formamide surrounded by dielectric continua corresponding to various solvents. The cavity wave functions for single‐ or multiconfigurational closed‐ and open‐shell states are optimized self‐consistently with their reaction fields, using either a continuum approach with one solute molecule embedded in the dielectric medium or a semicontinuum approach with one solute molecule and a solvation shell of molecules surrounded by the dielectric medium. The application of the MCSCRF/SCRF model gives new insight into the effects of a solvent on ionization spectra. The origin of both absolute and differential shifts upon solvation is investigated. This includes studies of local vs delocalized ionization, role of dielectric polarization vs reaction...

Solvatochromatic shifts studied by multi-configuration self-consistent reaction field theory. Application to azabenzenes

Abstract We explore red and blue shifts of low-lying electronic excitation bands accompanying solvation by means of a self-consistent reaction field (SCRF) theory where the chromophore is treated quantum mechanically. A previously devised multi-configuration SCRF (MCSCRF) method has been enhanced to encompass restricted active space MCSCF wave functions, D 2h point group symmetries and higher multipole expansions of the charge and the reaction fields. Applications focus on the series of azabenzenes which show large solvation blue shifts for π→π* transitions but small solvation red shifts for n→π* transitions. It is found that the magnitude of the reaction field contributions to the shifts are of about the same order of magnitude as the polarization contri- butions and that the multipole expansion of the polarizing field cannot be truncated to include only a dipole. The solvation shifts are found to be sensitive to the parameters of the model, such as cavity radius and dielectric constant, but fairly insensitive to the parametrization of the solute wave functions. The role of symmetry broken, local descriptions of the excitations is discussed.