Eugene Kamarchik

Parametric two-electron reduced-density-matrix method applied to computing molecular energies and properties at nonequilibrium geometries

A parametric approach to the variational calculation of the two-electron reduced density matrix (2-RDM) for many-electron atoms and molecules has recently been developed in which the 2-RDM is parametrized to be both size consistent and nearly N-representable [C. Kollmar, J. Chem. Phys. 125, 084108 (2006); A. E. DePrince and D. A. Mazziotti, Phys. Rev. A 76, 049903 (2007)]. The parametric variational 2-RDM method is applied to computing ground-state molecular energies and properties at nonequilibrium geometries in significantly larger basis sets than previously employed. We study hydrogen abstraction from the hydroxide groups of H(2)O, NH(3)OH, and CH(3)OH. The 2-RDM method, parametrized by single and double excitations, shows significant improvement over coupled-cluster methods with similar excitations in predicting the shape of potential energy curves and bond-dissociation energies. Previous work completes the parametrization of the energy and 2-RDM by a system of n(2)h(2) normalization constraints, where n and h are the number of occupied and unoccupied orbitals, respectively. In the present paper, however, we show that the constraints can be eliminated by incorporating them into the energy and 2-RDM functions and, hence, the constrained optimization of the ground-state energy can be reformulated as an unconstrained optimization. The 2-RDMs from the parametric method are very nearly N-representable, and as measured by an l(2) norm, they are more accurate than the 2-RDMs from configuration interaction truncated at single and double excitations by an order of magnitude.

A novel Gaussian Binning (1GB) analysis of vibrational state distributions in highly excited H2O from reactive quenching of OH* by H2

As shown in experiments by Lester and co-workers [J. Chem. Phys. 110, 11117 (1999)], the reactive quenching of OH∗ by H2 produces highly excited H2O. Previous limited analysis of quasiclassical trajectory calculations using standard Histogram Binning (HB) was reported [B. Fu, E. Kamarchik, and J. M. Bowman, J. Chem. Phys. 133, 164306 (2010)]. Here, we examine the quantized internal state distributions of H2O in more detail, using two versions of Gaussian Binning (denoted 1GB). In addition to the standard version of 1GB, which relies on the harmonic energies of the states (1GB-H), we propose a new and more accurate technique based on exact quantum vibrational energies (1GB-EQ). Data from about 42,000 trajectories from previous calculations that give excited water molecules are used in the two versions of 1GB as well as HB. For the vibrationally hot molecules considered in this study, the classical internal energy distribution serves as a benchmark to estimate the accuracy of the different binning methods analyzed. The 1GB discretization methods, especially the one using exact quantum energies, reconstruct the classical distribution much more accurately than HB and also the original, more elaborate Gaussian Binning method. Detailed quantum state distributions are presented for pure overtone excitations as well as several antisymmetric stretch distributions. The latter are focused on because the antisymmetric stretch has the largest emission oscillator strength of the three water modes.

Reduced-Dimensional Quantum Approach to Tunneling Splittings Using Saddle-Point Normal Coordinates

We describe multidimensional extensions to a one-dimensional approach to tunneling splittings using a relaxed potential in the imaginary-frequency normal mode of the relevant saddle point (J. Chem. Phys. 2008 , 129 , 121103). Tests of these extensions are given for H(3)O(+) and NH(3) where full dimensional tunneling splittings are available and for the vinyl radical using a new full-dimensional potential energy surface.

Anharmonic state counts and partition functions for molecules via classical phase space integrals in curvilinear coordinates

An algorithm is presented for calculating fully anharmonic vibrational state counts, state densities, and partition functions for molecules using Monte Carlo integration of classical phase space. The algorithm includes numerical evaluations of the elements of the Jacobian and is general enough to allow for sampling in arbitrary curvilinear or rectilinear coordinate systems. Invariance to the choice of coordinate system is demonstrated for vibrational state densities of methane, where we find comparable sampling efficiency when using curvilinear z-matrix and rectilinear Cartesian normal mode coordinates. In agreement with past work, we find that anharmonicity increases the vibrational state density of methane by a factor of ∼2 at its dissociation threshold. For the vinyl radical, we find a significant (∼10×) improvement in sampling efficiency when using curvilinear z-matrix coordinates relative to Cartesian normal mode coordinates. We attribute this improved efficiency, in part, to a more natural curvilinear coordinate description of the double well associated with the H2C-C-H wagging motion. The anharmonicity correction for the vinyl radical state density is ∼1.4 at its dissociation threshold. Finally, we demonstrate that with trivial parallelizations of the Monte Carlo step, tractable calculations can be made for the vinyl radical using direct ab initio potential energy surface evaluations and a composite QCISD(T)/MP2 method.

Five ab initio potential energy and dipole moment surfaces for hydrated NaCl and NaF. I. Two-body interactions

We report full-dimensional, ab initio-based potentials and dipole moment surfaces for NaCl, NaF, Na(+)H2O, F(-)H2O, and Cl(-)H2O. The NaCl and NaF potentials are diabatic ones that dissociate to ions. These are obtained using spline fits to CCSD(T)/aug-cc-pV5Z energies. In addition, non-linear least square fits using the Born-Mayer-Huggins potential are presented, providing accurate parameters based strictly on the current ab initio energies. The long-range behavior of the NaCl and NaF potentials is shown to go, as expected, accurately to the point-charge Coulomb interaction. The three ion-H2O potentials are permutationally invariant fits to roughly 20,000 coupled cluster CCSD(T) energies (awCVTZ basis for Na(+) and aVTZ basis for Cl(-) and F(-)), over a large range of distances and H2O intramolecular configurations. These potentials are switched accurately in the long range to the analytical ion-dipole interactions, to improve computational efficiency. Dipole moment surfaces are fits to MP2 data; for the ion-ion cases, these are well described in the intermediate- and long-range by the simple point-charge expression. The performance of these new fits is examined by direct comparison to additional ab initio energies and dipole moments along various cuts. Equilibrium structures, harmonic frequencies, and electronic dissociation energies are also reported and compared to direct ab initio results. These indicate the high fidelity of the new PESs.