Volume 127, Issue 1, 07 July 2007
 ANNOUNCEMENTS
 ARTICLES

 Theoretical Methods and Algorithms

Computation and interpretation of molecular Omega intracules
View Description Hide DescriptionThe Omega intracule is a threedimensional function that describes the relative positions, momenta, and directions of motion of pairs of electrons in a system. In this paper, we describe the computation of the Omega intracule for a molecular system whose electronic wave function is expanded in a Gaussian basis set. This is followed by implementation details and numerical tests. Finally, we use the Omega intracules of a number of small systems to illustrate the power of this function to extract simple physical insights from complicated wave functions.

Perturbative treatment of the electroncorrelation contribution to the diagonal BornOppenheimer correction
View Description Hide DescriptionA perturbative scheme for the treatment of electroncorrelation effects on the diagonal BornOppenheimer correction (DBOC) is suggested. Utilizing the usual MøllerPlesset partitioning of the Hamiltonian formulas for first and second orders (termed as MP1 and MP2) are obtained by expanding the wave function in the corresponding coupledcluster expressions for the DBOC[J. Gauss et al., J. Chem. Phys.125, 144111 (2006)]. The obtained expressions are recast in terms of one and twoparticle density matrices in order to take advantage of existing analytic secondderivative implementations for manybody methods. Test calculations show that both MP1 and MP2 recover large fractions (on average 90% and 95%, respectively) of the coupledcluster singles and doubles (CCSD) electroncorrelation corrections to the DBOC and thus render the suggested MP treatments costeffective (though still accurate) alternatives to highlevel coupled cluster (CC) treatments. The applicability of the MP1 and MP2 schemes for treating DBOC is demonstrated in calculations for the atomization energies of benzene, naphthalene, anthracene, and tetracene. The corresponding corrections are surprisingly large (about for benzene, for naphthalene, for anthracene, and for tetracene) with the electroncorrelation corrections reducing the corresponding HartreeFock selfconsistent field values by 25%–30%.

Using redundant coordinates to represent potential energy surfaces with lowerdimensional functions
View Description Hide DescriptionWe propose a method for fitting potential energy surfaces with a sum of component functions of lower dimensionality. This form facilitates quantum dynamics calculations. We show that it is possible to reduce the dimensionality of the component functions by introducing new and redundant coordinates obtained with linear transformations. The transformations are obtained from a neural network. Different coordinates are used for different component functions and the new coordinates are determined as the potential is fitted. The quality of the fits and the generality of the method are illustrated by fitting reference potential surfaces of hydrogen peroxide and of the reaction.

Ab initio electron propagators in molecules with strong electronphonon interaction: II. Electron Green’s function
View Description Hide DescriptionAb initio electron propagator methods are developed to study electronic properties of molecular systems with strong electronelectron and electronphonon interactions. For the calculation of electron Green’s functions we apply a canonical small polaron transformation that intrinsically contains strong electronphonon effects. In the transformed Hamiltonian, the energy levels for the noninteracting particles are shifted down by the relaxation (solvation) energies. The Coulomb integrals are also renormalized by the electronphonon interaction. For certain values of the electronphonon coupling constants, the renormalized Coulomb integrals can be negative which implies the attraction between two electrons. Within the small polaron transformation we develop a diagrammatic technique for the calculation of electron Green’s function in which the electronphonon interaction is already included into the multiple phononcorrelation functions. Since the decoupling of the phononcorrelation functions is impossible, and therefore, a Wick’s theorem for such correlation functions is invalid, there is no Dyson equation for the electron Green’s function. To find the electron Green’s function, we use different approximations. One of them is a linkcluster approximation that includes diagonal transitions for the renormalized zeroth Green’s function. In the linkedcluster approach the Dyson equation is derived in the most general case, where the selfenergy operator is an arbitrary functional (not only in the HartreeFock approximation). It is shown that even a HartreeFock electron (hole) is not a particle any longer. It is a quasiparticle with a finite lifetime that depends on energy of particle and hole states in different ways. As a consequence of this, a standard description of a HartreeFock approximation in terms of wave functions becomes inappropriate in this problem. To challenge the linkedcluster approximation we develop a different approach: a sequential propagation approximation where scattering events occur only for sequential transitions. A selfconsistent HartreeFock equation for a fourindex Green’s function matrix is derived. In conclusion, the proposed schemes can be considered for future method developments for quantum chemical calculations for large molecules with strong nonadiabatic effects, correlated electron transfer reactions, and electron transport in molecular transport junctions.

Weak binding between two aromatic rings: Feeling the van der Waals attraction by quantum Monte Carlo methods
View Description Hide DescriptionWe report a systematic study of the weak chemical bond between two benzene molecules. We first show that it is possible to obtain a very good description of the dimer and the benzene molecule by using pseudopotentials for the chemically inert electrons and a resonating valence bondwave function as a variational ansatz, expanded on a relatively small Gaussian basis set. We employ an improved version of the stochastic reconfiguration technique to optimize the manybody wave function, which is the starting point for highly accurate simulations based on the lattice regularized diffusion Monte Carlo method. This projection technique provides a rigorous variational upper bound for the total energy, even in the presence of pseudopotentials, and substantially improves the accuracy of the trial wave function, which already yields a large fraction of the dynamical and nondynamical electron correlation. We show that the energy dispersion of two benzene molecules in the parallel displaced geometry is significantly deeper than the facetoface configuration. However, contrary to previous studies based on postHartreeFock methods, the binding energy remains weak also in this geometry, and its value is in agreement with the most accurate and recent experimental findings [H. Krause et al., Chem. Phys. Lett.184, 411 (1991)].

New results from the contact theorem for the charge profile for symmetric electrolytes
View Description Hide DescriptionIn this paper the contact value of the charge profile at a charged interface is presented as the sum of the normal component of the Maxwellelectrostatictensor and a new electrostaticproperty defined by the integral from the product of the gradient of the electrical potential and the singlet distribution function of coions (ions with sign of the charge equal to that of the interface). On physical arguments, it is conjectured that this new property is a monotonic function of the electrical charge at the wall and is limited by the bulk electrolyte pressure for large electrical charges at the wall. Using the contact theorems for the density and the charge profiles, the exact expressions for the contact values of the profiles of coions and counterions are derived and some related general properties are discussed.

Efficient calculation of van der Waals dispersion coefficients with timedependent density functional theory in real time: Application to polycyclic aromatic hydrocarbons
View Description Hide DescriptionThe van der Waals dispersion coefficients of a set of polycyclic aromatic hydrocarbons, ranging in size from the singlecycle benzene to circumovalene , are calculated with a realtime propagation approach to timedependent density functional theory (TDDFT). In the nonretarded regime, the CasimirPolder integral is employed to obtain , once the dynamic polarizabilities have been computed at imaginary frequencies with TDDFT. On the other hand, the numerical coefficient that characterizes the fully retarded regime is obtained from the static polarizabilities. This ab initio strategy has favorable scaling with the size of the system—as demonstrated by the size of the reported molecules—and can be easily extended to obtain higher order van der Waals coefficients.

New method for calculating bound states: The states of on the spinaligned potential energy surface
View Description Hide DescriptionIn this paper, we present a calculation for the bound states of symmetry on the spinaligned potential energy surface. We apply a mixture of discrete variable representation and distributed approximating functional methods to discretize the Hamiltonian. We also introduce a new method that significantly reduces the computational effort needed to determine the lowest eigenvalues and eigenvectors(bound state energies and wave functions of the full Hamiltonian). In our study, we have found the lowest 150 energy bound states converged to less than 0.005% error, and most of the excited energy bound states converged to less than 2.0% error. Furthermore, we have estimated the total number of the bound states of on the spinaligned potential surface to be 601.

New parametrization method for dissipative particle dynamics
View Description Hide DescriptionWe introduce an improved method of parametrizing the GrootWarren version of dissipative particle dynamics (DPD) by exploiting a correspondence between DPD and ScatchardHildebrand regular solutiontheory. The new parametrization scheme widens the realm of applicability of DPD by first removing the restriction of equal repulsive interactions between like beads, and second, by relating all conservative interactions between beads directly to cohesive energy densities. We establish the correspondence by deriving an expression for the Helmoltz free energy of mixing, obtaining a heat of mixing which is exactly the same form as that for a regular mixture (quadratic in the volume fraction) and an entropy of mixing which reduces to the ideal entropy of mixing for equal molar volumes. We equate the conservative interaction parameters in the DPD force law to the cohesive energy densities of the pure fluids, providing an alternative method of calculating the selfinteraction parameters as well as a route to the cross interaction parameter. We validate the new parametrization by modeling the binary system , which displays liquidliquid coexistence below an upper critical solution temperature around . A series of DPD simulations were conducted at a set of temperatures ranging from to above the experimental upper critical solution temperature using conservative parameters based on extrapolated experimental data. These simulations can be regarded as being equivalent to a quench from a high temperature to a lower one at constant volume. Our simulations recover the expected phase behavior ranging from solidliquid coexistence to liquidliquid coexistence and eventually leading to a homogeneous single phase system. The results yield a binodal curve in close agreement with the one predicted using regular solutiontheory, but, significantly, in closer agreement with actual solubility measurements.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Spacetime contours to treat intense fielddressed molecular states. I. Theory
View Description Hide DescriptionA molecular system exposed to an intense external field is considered. The strength of the field is measured by the number of electronic states that become populated during this process. In the present article the authors discuss a rigorous way, based on the recently introduced spacetime contours [R. Baer, et al., J. Chem. Phys.119, 6998 (2003)], to form coupled Schrödinger equations where , which maintains the effects due to the remaining populated states. It is shown that whereas the size of is unlimited, the main requirement concerning is that the original group of fieldfree states forms a Hilbert subspace in the spatial region of interest. From previous studies it is known that a group of states forms a Hilbert subspace if and only if the corresponding topological matrix is diagonal [M. Baer, et al., Farad, Discuss127, 337 (2004)].

Spacetime contours to treat intense fielddressed molecular states. II. Applications
View Description Hide DescriptionThis second article in the two backtoback articles presents a numerical application to support and strengthen two theoretical findings extensively discussed in the previous article (article I). In I, we found that introducing the spacetime contours enables to distinguish between , the number of nuclear Schrödinger equations to be solved, and , the number of fieldfree states that become populated by the external field (in the ordinary, perturbative approaches this distinction is not apparent). In the numerical study we show, employing the electronic transition probability matrix [which closely is related to the transformation matrix —see Eqs. (21) and (25) in I], that the case is rare and in most cases we have . Since the perturbative approach can be shown to follow when (see Sec. III C in I) the numerical study implies that in most cases the perturbative approach is not reliable. The second issue that is studied is related to the diabatization process. It is shown, numerically, that the case, in general, does not lead to fielddressed diabatic potentials which are single valued. However, if is chosen to be identical to the number of fieldfree states that yield fieldfree singlevalued diabatic potentials in a given spatial region then the corresponding fielddressed states also yield singlevalued (fielddressed) diabatic potentials. This result is independent of . The numerical study is carried out for an eigenvalue problem based on the Mathieu equation.

Ab initio molecular orbital study of ground and lowlying electronic states of CoCN
View Description Hide DescriptionThe ground and lowlying excited states of CoCN have been studied by ab initio multireference single and double excitation configuration interaction (MRSDCI) calculations with Davidson’s correction and CowanGriffin’s relativistic corrections. The electronic ground state of CoCN is and the equilibrium geometry is linear with bond lengths of and , substantially different from the experimentally derived values of and . The first excited state is , separated from the ground state by . Larger dynamical electron correlationenergy for the lowspin state than for the highspin state makes the state to be the ground state, which is discussed in terms of the differences in natural orbitals. A new spinorbit interaction scheme between the and states is proposed.

Production yields of H(D) atoms in the reactions of with , , and their deuterated variants
View Description Hide DescriptionThe production yields of H(D) atoms in the reactions of with , , and their deuterated variants were determined. was produced by excitation transfer between and groundstate followed by collisional relaxation. was produced by twophoton laser excitation of followed by concomitant amplified spontaneous emission. H(D) atoms were detected by using vacuumultraviolet laserinduced fluorescence(LIF). The H(D)atom yields were evaluated from the LIF intensities and the overall rate constants for the quenching, which were determined from the temporal profiles of the NO tracer emission. The absolute yields were evaluated by assuming that the yield for is 0.9. Although no isotope effects were observed in the overall rate constants, there were isotope effects in the H(D)atom yields. The Hatom yields for and were 0.52 and 0.30, respectively, while the Datom yields for and were 0.33 and 0.13, respectively. The presence of isotope effects in yields suggests that molecular elimination processes are competing and that molecular elimination is more dominant in deuterated species than in hydrides.

Dissociative recombination study of : Cross section and branching fraction measurements
View Description Hide DescriptionWe report an investigation into the dissociative recombination of the azide radical cation, . The reaction rate constant has been measured to be at room temperature. This value is smaller than those reported earlier for the ionelectron neutralization of at nitrogen atmospheric pressure. A strong propensity to dissociate through the channel has been observed.

In search of definitive signatures of the elusive NCCO radical
View Description Hide DescriptionPrevious experimental assignments of the fundamental vibrational frequencies of NCCO have been brought into question by subsequent unsuccessful attempts to observe IR signatures of this radical at these frequencies. Here we compute the fundamental vibrational frequencies by applying secondorder vibrational perturbation theory to the complete quartic force field computed at the allelectron (AE) coupled cluster singles, doubles, and perturbative triples level [CCSD(T)] with the correlationconsistent, polarized corevalence quadruplezeta (ccpCVQZ) basis set, which has tight functions to correctly describe core correlation. The AECCSD(T)/ccpCVQZ geometric parameters are , , , , and . Our CCSD(T)/ccpCVQZ values of the characteristic stretching frequencies and are 2171 and , respectively, in stark contrast to the experimentally derived values of 2093 and . Finally, focalpoint extrapolations using correlationconsistentbasis sets and electron correlation treatments as extensive as full coupled cluster singles, doubles, and triples (CCSDT) with perturbative accounting of quadruple excitations [CCSDT(Q)] determine the vibrationless barrier to linearity of NCCO and the dissociation energy of to be 8.4 and , respectively. Using our precisely determined dissociation energy, we recommend a new enthalpy of formation for NCCO of .

and double Rydberg anions: Predictions and comparisons with and
View Description Hide DescriptionA low barrier in the reaction pathway between the double Rydberg isomer of and a hydridewater complex indicates that the former species is more difficult to isolate and characterize through anion photoelectron spectroscopy than the well known double Rydberg anion (DRA), tetrahedral . Electron propagator calculations of vertical electron detachment energies (VEDEs) and isosurface plots of the electron localization function disclose that the transition state’s electronic structure more closely resembles that of the DRA than that of the hydridewater complex. Possible stabilization of the DRA through hydrogen bonding or iondipole interactions is examined through calculations on species. Three minima with , hydrogenbridged, and DRAmolecule structures resemble previously discovered species and have well separated VEDEs that may be observable in anion photoelectron spectra.

as a trap for noble gases  2: structure and energetics of complexes from to xenon
View Description Hide DescriptionThe affinity of to combine with noble gases X has been investigated from neon to xenon using ab initiocoupled cluster [CCSD and CCSD(T)] and density functional BH&HLYP levels of theory. For all noble gases, the stable structures belong to a symmetry with an apex of the triangle pointing to the noble gas. The structure of the complexes changes gradually from a practically pure arrangement to a situation close to . A topological analysis of the electron localization function is used to illustrate the changes in the bonding along the series. The lowest dissociation energies of and ( and ) correspond to the breaking of the complexes according to , while the lowest dissociation energies of and ( and ) correspond to the breaking according to . Rotational constants and harmonic frequencies are reported. Apart from whose dipole moment) may not be large enough, all the other complexes with dipole moments in the range of should be reasonable targets for detection by microwave spectroscopy. The present calculations are intended to stimulate both laboratory experiments and spatial observations since the possible sequestration of noble gases by may have strong implications on the composition of astrophysical objects.

Ground and asymmetric COstretch excited state tunneling splittings in the formic acid dimer
View Description Hide DescriptionThere has been some controversy concerning the assignment of measured tunneling splittings for the formic acid dimer in the vibrational ground state and the asymmetric COstretching excited state. The discussion is intimately related to the question whether the fundamental excitation of the COvibration promotes or hinders tunneling. Here we will address this issue on the basis of a fivedimensional reaction space Hamiltonian which includes three large amplitude coordinates as well as two harmonic modes whose linear superposition reproduces the asymmetric COvibrational mode. Within density functional theory using the B3LYP functional together with a basis set we obtain a ground statetunneling splitting which is about 2.4 larger than the one for the COstretching excited state.

Photoionization of molecular beam: Ab initio calculations
View Description Hide DescriptionLarge computations are performed on the cation in order to characterize its stable isomers and its lowest electronic excited states using configuration interaction methods and large basis sets. Several stable isomers are found including a linear , a rhombic (or cyclic), and a branched structure. Our calculations show a high density of electronic states for all of these isomers favoring their interactions. By combining the present ab initio data and those on neutral , the , , and vertical photoionization transition energies are computed at 10.87, 10.92, and , respectively. Photoionizing a molecular beam results on an onset at and then to a linear increase of the signal due to the opening of several ionization channels involving most of the and isomers and electronic states.