Phase dilemma in density matrix functional theory

For closed-shell systems, a particular parametrization of coefficients in a configuration interaction (CI) expansion provides a convenient formulation for the search over electronic wave functions constrained by a set of natural orbitals (NOs) and the corresponding occupation numbers that are invoked in every variational construction of the density matrix functional (DMF) V(ee)(Gamma) for the electron--electron repulsion energy. It produces an explicit expression for V(ee) in terms of the Coulomb and exchange integrals over NOs, and an idempotent matrix omega, diagonal elements of which equal the occupation numbers. At the same time, it reveals a very serious bottleneck affecting any rigorous approach to the DMF theory, namely the phase dilemma that stems from the necessity to carry out minimization over a large number of possible combinations of CI coefficient signs. While underscoring its lack of variational nature, a simple approximation for the phase factor products provides a strict derivation for the recently proposed Kollmar-Hess functional.     

An investigation into the use of expansion methods in the calculation of chemical shifts and diamagnetic susceptibilities

The chemical shift and the diamagnetic susceptibility of the hydrogenic atom with magnetic dipole and origin of the external magnetic field vector potential noncoincident with the hydrogenic nucleus have been calculated from perturbation theory using a set of expansion functions whose radial parts are single exponent associated Laguerre functions. In contrast to hydrogenic expansion functions these functions give rapid convergence to the exact values of the second-order energy summations when centred at the hydrogenic nucleus. The rate of convergence is fairly insensitive to the choice of expansion function exponent.     

A linear variation of the thermal expansivity with frequency shifts for the translational mode in ammonia solid II near the melting point

We examine here our spectroscopic modification of the Pippard relation which is a linear variation of the thermal expansivity alpha(p) with the frequency shifts (1/nu)(partial differentialnu/partial differentialp)(T) close to the melting point in ammonia solid II. For this we use our calculated frequencies for the Raman mode of nu (51 cm(-1)) in ammonia solid II for the pressures of 3.65, 5.02 and 6.57 kbars. We establish this linearity between alpha(p) and (1/nu)(partial differentialnu/ partial differentialp)(T) for the pressures studied in ammonia solid II close to the melting point. The observed behaviour of ammonia solid II is explained in terms of our spectroscopic relation given here.     

Evaluation of electronic correlation contributions for optical tensors of large systems using the incremental scheme

A new method is developed to calculate the optical tensors of large systems based on available wave function correlation approaches (e.g., the coupled cluster ansatz) in the framework of the incremental scheme. The convergence behaviors of static first- and second-order polarizabilities with respect to the order of the incremental expansion are examined and discussed for the model system Ga(4)As(4)H(18). The many-body increments of optical tensors originate from the dipole-dipole coupling effects and the corresponding contributions to the incremental expansion are compared among local domains with different distances and orientations. The weight factors for increments of optical tensors are found to be tensorial in accordance with the structural symmetry as well as the polarization and the external electric field directions. The long-term goal of the proposed approach is to incorporate the sophisticated molecular correlation methods into the accurate wave function calculation of optical properties of large compounds or even crystals.     

Accuracy and limitations of second-order many-body perturbation theory for predicting vertical detachment energies of solvated-electron clusters

Vertical electron detachment energies (VDEs) are calculated for a variety of (H(2)O)(n)(-) and (HF)(n)(-) isomers, using different electronic structure methodologies but focusing in particular on a comparison between second-order M?ller-Plesset perturbation theory (MP2) and coupled-cluster theory with noniterative triples, CCSD(T). For the surface-bound electrons that characterize small (H(2)O)(n)(-) clusters (n< or = 7), the correlation energy associated with the unpaired electron grows linearly as a function of the VDE but is unrelated to the number of monomers, n. In every example considered here, including strongly-bound "cavity" isomers of (H(2)O)(24)(-), the correlation energy associated with the unpaired electron is significantly smaller than that associated with typical valence electrons. As a result, the error in the MP2 detachment energy, as a fraction of the CCSD(T) value, approaches a limit of about -7% for (H(2)O)(n)(-) clusters with VDEs larger than about 0.4 eV. CCSD(T) detachment energies are bounded from below by MP2 values and from above by VDEs calculated using second-order many-body perturbation theory with molecular orbitals obtained from density functional theory. For a variety of both strongly- and weakly-bound isomers of (H(2)O)(20)(-) and (H(2)O)(24)(-), including both surface states and cavity states, these bounds afford typical error bars of +/-0.1 eV. We have found only one case where the Hartree-Fock and density functional orbitals differ qualitatively; in this case the aforementioned bounds lie 0.4 eV apart, and second-order perturbation theory may not be reliable.     

Towards benchmark second-order correlation energies for large atoms. II. Angular extrapolation problems

We have studied the use of the asymptotic expansions (AEs) for the angular momentum extrapolation (to l --> infinity) of atomic second-order Moller-Plesset (MP2) correlation energies of symmetry-adapted pairs (SAPs). The AEs have been defined in terms of partial wave (PW) increments to the SAP correlation energies obtained with the finite element MP2 method (FEM-MP2), as well as with the variational perturbation method in a Slater-type orbital basis. The method employed to obtain AEs from PW increments is general in the sense that it can be applied to methods other than MP2 and, if modified, to molecular systems. Optimal AEs have been determined for all types of SAPs possible in large atoms using very accurate FEM PW increments up to lmax = 45. The impact of the error of the PW increments on the coefficients of the AEs is computed and taken into account in our procedure. The first AE coefficient is determined to a very high accuracy, whereas the second involves much larger errors. The optimum l values (lopt) for starting the extrapolation procedures are determined and their properties, interesting from the practical point of view, are discussed. It is found that the values of the first AE coefficients obey expressions of the type derived by Kutzelnigg and Morgan [J. Chem. Phys. 96, 4484 (1992); 97, 8821(E) (1992)] for He-type systems in the bare-nucleus case provided they are modified by fractional factors in the case of triplet and unnatural singlet SAPs. These expressions give extremely accurate values for the first AE coefficient both for the STO and the FEM Hartree-Fock orbitals. We have compared the performance of our angular momentum extrapolations with those of some of the principal expansion extrapolations performed with correlation consistent basis sets employed in the literature and indicated the main sources of inaccuracy.     

Three methods for calculation of the hyper-Wiener index of molecular graphs

The hyper-Wiener index WW of a graph G is defined as WW(G) = (summation operator d (u, v)(2) + summation operator d (u, v))/2, where d (u, v) denotes the distance between the vertices u and v in the graph G and the summations run over all (unordered) pairs of vertices of G. We consider three different methods for calculating the hyper-Wiener index of molecular graphs: the cut method, the method of Hosoya polynomials, and the interpolation method. Along the way we obtain new closed-form expressions for the WW of linear phenylenes, cyclic phenylenes, poly(azulenes), and several families of periodic hexagonal chains. We also verify some previously known (but not mathematically proved) formulas.     

Cation-cation "attraction": when London dispersion attraction wins over Coulomb repulsion

London forces are omnipresent in nature and relevant to molecular engineering. Proper tuning of their energetic contribution may stabilize molecular aggregates, which would be otherwise highly unstable by virtue of other overwhelming repulsive terms. The literature contains a number of such noncovalently bonded molecular aggregates, of which the "binding mode" has never been thoroughly settled. Among those are the emblematic cationic complexes of tetrakis(isonitrile)rhodium(I) studied by a number of researchers. The propensity of these complexes to spontaneously produce oligomers has been an "open case" for years. For the dimer [(PhNC)(4)Rh](2)(2+), one of the archetypes of such oligomers, density functional theory methods (DFT-D3) and wave function based spin-component-scaled second-order M?ller-Plesset perturbation theory (SCS-MP2) quantum chemical calculations indicate that when the eight isonitrile ligands arrange spatially in an optimal π-stacked fashion, the energy due to dispersion not only overcomes coulombic repulsion but also the entropy penalty of complex formation. This central role of long-range electron correlation explains such cation-cation attractive interactions. Furthermore, the present findings relativize the role of the metal-metal "d(8)-d(8)" interactions, which are present on a relatively small scale compared to the effects of the ligands; d(8)-d(8) interactions represent about 10-15% of the total dispersion contribution to the binding energy.     

r 12-Dependent terms in the wave function as closed sums of partial wave amplitudes for large l

The ansatz = (1+1/2r₁₂)+ with the bare nuclear (or screened nuclear) wave function and expanded in products of one-electron functions is explored for second-order perturbation theory and for variational calculations of the ground state of Helium-like ions.The energy increments E _l ⁽²⁾ corresponding to the partial wave expansion of go asymptotically as l^–8, while conventional partial wave increments go as l^–4. is coupled to by a residual interaction U₁₂ that has no singularity for r₁₂=0. With the present ansatz it is sufficient to include l-values up to 5 in order to get the second-order energy accurate to one microhartree. For the same accuracy l4 is sufficient in a CI with correlated reference function while in conventional CI one must go to l50. The surprisingly faster convergence of the variational approach as compared to second-order perturbation theory is explained. The slow convergence of the traditional partial wave expansion is entirely due to the attempt to represent the quantity 1=¦r₁₂r₁₂ ^–1¦ by its partial wave expansion. The best reference function shows very little shielding and resembles closely the eigenstate of the bare nuclear Hamiltonian. The generalization to arbitrary systems is discussed and it is pointed out that the calculation of difficult integrals can be avoided without a significant loss in accuracy.     

A quantum wave packet dynamics study of the N(2D) + H2 reaction

We report a dynamics study of the reaction N((2)D) + H(2) (v=0, j=0-5) --> NH + H using the time-dependent quantum wave packet method and a recently reported single-sheeted double many-body expansion potential energy surface for NH(2)(1(2)A' ') which has been modeled from accurate ab initio multireference configuration-interaction calculations. The calculated probabilities for (v=0, j=0-5) are shown to display resonance structures, a feature also visible to some extent in the calculated total cross sections for (v=0, j=0). A comparison between the calculated centrifugal-sudden and coupled-channel reaction probabilities validate the former approximation for the title system. Rate constants calculated using a uniform J-shifting scheme and averaged over a Boltzmann distribution of rotational states are shown to be in good agreement with the available experimental values. Comparisons with other theoretical results are also made.     

Multidimensional quantum trajectories: applications of the derivative propagation method

In a previous publication [J. Chem. Phys. 118, 9911 (2003)], the derivative propagation method (DPM) was introduced as a novel numerical scheme for solving the quantum hydrodynamic equations of motion (QHEM) and computing the time evolution of quantum mechanical wave packets. These equations are a set of coupled, nonlinear partial differential equations governing the time evolution of the real-valued functions C and S in the complex action, S=C(r,t) + iS(r,t)/Planck's over 2pi, where Psi(r,t)=exp(S). Past numerical solutions to the QHEM were obtained via ensemble trajectory propagation, where the required first- and second-order spatial derivatives were evaluated using fitting techniques such as moving least squares. In the DPM, however, equations of motion are developed for the derivatives themselves, and a truncated set of these are integrated along quantum trajectories concurrently with the original QHEM equations for C and S. Using the DPM quantum effects can be included at various orders of approximation; no spatial fitting is involved; there is no basis set expansion; and single, uncoupled quantum trajectories can be propagated (in parallel) rather than in correlated ensembles. In this study, the DPM is extended from previous one-dimensional (1D) results to calculate transmission probabilities for 2D and 3D wave packet evolution on coupled Eckart barrier/harmonic oscillator surfaces. In the 2D problem, the DPM results are compared to standard numerical integration of the time-dependent Schrodinger equation. Also in this study, the practicality of implementing the DPM for systems with many more degrees of freedom is discussed.     

Spectroscopy of photovoltaic and photoconductive nanocrystalline Co2+-doped ZnO electrodes

Photocurrent and photoconductivity measurements have been used in combination with absorption and magnetic circular dichroism (MCD) spectroscopic measurements to elucidate the mechanism of photoinduced carrier generation in nanocrystalline Co(2+):ZnO electrodes. These experiments allowed direct observation of two broad Co(2+) charge transfer (CT) bands extending throughout the visible energy range. The lower energy CT transition is assigned as a Co(2+) --> conduction band excitation (ML(CB)CT). Sensitization of this ML(CB)CT level by (4)A(2) --> (4)T(1)(P) ligand-field excitation is concluded to be responsible for the distinctive structured photocurrent action spectrum of these electrodes at ca. 14 000 cm(-1). The higher energy CT transition is assigned as a valence band --> Co(2+) excitation (L(VB)MCT) and is found to have an internal quantum efficiency for charge separation that is approximately four times larger than that of the ML(CB)CT excitation. The different internal quantum efficiencies for the two CT excitations are related to differences in excited-state wave functions arising from configuration interaction with the 1S excitonic levels of ZnO. Whereas the ML(CB)CT excited state is best described as a localized Co(3+) + e(-)(CB) configuration, the L(VB)MCT excited state (Co(+) + h(+)(VB)) has a 4-fold greater admixture of delocalized excitonic (Co(2+) + h(+)(VB) + e(-)(CB)) character in its wave function, a conclusion supported by quantitative analysis of the CT absorption intensities. Practical factors controlling the overall photovoltaic efficiencies of the photoelectrochemical cells, including electrode conductivity and porosity, were also examined.     

Dynamics of (H(-), H(2)) collisions: a time-dependent quantum mechanical investigation on a new ab initio potential energy surface

A global analytical potential energy surface for the ground state of H(3)(-) has been constructed by fitting an analytic function to the ab initio potential energy values computed using coupled cluster singles and doubles with perturbative triples [CCSD(T)] method and Dunning's augmented correlation consistent polarized valence triple zeta basis set. Using this potential energy surface, time-dependent quantum mechanical wave packet calculations were carried out to calculate the reaction probabilities (P(R)) for the exchange reaction H(-)+H(2)(v, j)-->H(2)+H(-), for different initial vibrational (v) and rotational (j) states of H(2), for total angular momentum equal to zero. With increase in v, the number of oscillations in the P(R)(E) plot increases and the oscillations become more pronounced. While P(R) increases with increase in rotational excitation from j=0 to 1, it decreases with further increase in j to 2 over a wide range of energies. In addition, rotational excitation quenches the oscillations in P(R)(E) plots.     

Observation of partial wave structures in the integral cross section of the S((1)D2) + H2(j = 0) reaction

The integral cross section of the S((1)D(2)) + H(2)(j = 0) → SH + H reaction has been measured for the first time at collision energies from 0.820 down to 0.078 kJ mol(-1) in a high-resolution crossed beam experiment. The excitation function obtained exhibits a non-monotonic variation with collision energy and compares well with the results of high-level quantum calculations. In particular, the structures observed in the lower energy part, where only a few partial waves contribute, can be described in terms of the sequential opening of individual channels, consistent with the theoretical calculations.     

Impact of nuclear quantum effects on the molecular structure of bihalides and the hydrogen fluoride dimer

The structural impact of nuclear quantum effects is investigated for a set of bihalides, [XHX](-), X = F, Cl, and Br, and the hydrogen fluoride dimer. Structures are calculated with the vibrational self-consistent-field (VSCF) method, the second-order vibrational perturbation theory method (VPT2), and the nuclear-electronic orbital (NEO) approach. In the VSCF and VPT2 methods, the vibrationally averaged geometries are calculated for the Born-Oppenheimer electronic potential energy surface. In the NEO approach, the hydrogen nuclei are treated quantum mechanically on the same level as the electrons, and mixed nuclear-electronic wave functions are calculated variationally with molecular orbital methods. Electron-electron and electron-proton dynamical correlation effects are included in the NEO approach using second-order perturbation theory (NEO-MP2). The nuclear quantum effects are found to alter the distances between the heavy atoms by 0.02-0.05 A for the systems studied. These effects are of similar magnitude as the electron correlation effects. For the bihalides, inclusion of the nuclear quantum effects with the NEO-MP2 or the VSCF method increases the X-X distance. The bihalide X-X distances are similar for both methods and are consistent with two-dimensional grid calculations and experimental values, thereby validating the use of the computationally efficient NEO-MP2 method for these types of systems. For the hydrogen fluoride dimer, inclusion of nuclear quantum effects decreases the F-F distance with the NEO-MP2 method and increases the F-F distance with the VSCF and VPT2 methods. The VPT2 F-F distances for the hydrogen fluoride dimer and the deuterated form are consistent with the experimentally determined values. The NEO-MP2 F-F distance is in excellent agreement with the distance obtained experimentally for a model that removes the large amplitude bending motions. The analysis of these calculations provides insight into the significance of electron-electron and electron-proton correlation, anharmonicity of the vibrational modes, and nonadiabatic effects for hydrogen-bonded systems.     

Direct quantum mechanical calculation of the F + H2 → HF + H thermal rate constant

Accurate full-dimensional quantum mechanical thermal rate constant values have been calculated for the F+H₂→HF+H reaction on the Stark–Werner ab initio potential energy surface. These calculations are based on a flux correlation functions and employ a rigorous statistical sampling scheme to account for the overall rotation and the MCTDH scheme for the wave packet propagation. Our results shed some light on discrepancies on the thermal rate found for previous flux correlation based calculations with respect to accurate reactive scattering results. The resonance pattern of the all-J cumulative reaction probability is analyzed in terms of the partial wave contributions.     

Divide-and-conquer local correlation approach to the correlation energy of large molecules

A divide-and-conquer local correlation approach for correlation energy calculations on large molecules is proposed for any post-Hartree-Fock correlation method. The main idea of this approach is to decompose a large system into various fragments capped by their local environments. The total correlation energy of the whole system can be approximately obtained as the summation of correlation energies from all capped fragments, from which correlation energies from all adjacent caps are removed. This approach computationally achieves linear scaling even for medium-sized systems. Our test calculations for a wide range of molecules using the 6-31G or 6-31G( * *) basis set demonstrate that this simple approach recovers more than 99.0% of the conventional second-order Moller-Plesset perturbation theory and coupled cluster with single and double excitations correlation energies.     

Pulsed laser photolysis and quantum chemical-statistical rate study of the reaction of the ethynyl radical with water vapor

The rate coefficient of the gas-phase reaction C(2)H + H(2)O-->products has been experimentally determined over the temperature range 500-825 K using a pulsed laser photolysis-chemiluminescence (PLP-CL) technique. Ethynyl radicals (C(2)H) were generated by pulsed 193 nm photolysis of C(2)H(2) in the presence of H(2)O vapor and buffer gas N(2) at 15 Torr. The relative concentration of C(2)H radicals was monitored as a function of time using a CH* chemiluminescence method. The rate constant determinations for C(2)H + H(2)O were k(1)(550 K) = (2.3 +/- 1.3) x 10(-13) cm(3) s(-1), k(1)(770 K) =(7.2 +/- 1.4) x 10(-13) cm(3) s(-1), and k(1)(825 K) = (7.7 +/- 1.5) x 10(-13) cm(3) s(-1). The error in the only other measurement of this rate constant is also discussed. We have also characterized the reaction theoretically using quantum chemical computations. The relevant portion of the potential energy surface of C(2)H(3)O in its doublet electronic ground state has been investigated using density functional theory B3LYP6-311 + + G(3df,2p) and molecular orbital computations at the unrestricted coupled-cluster level of theory that incorporates all single and double excitations plus perturbative corrections for the triple excitations, along with the 6-311 + + G(3df,2p) basis set [(U)CCSD(T)6-311 + + G(3df,2p)] and using UCCSD(T)6-31G(d,p) optimized geometries. Five isomers, six dissociation products, and sixteen transition structures were characterized. The results confirm that the hydrogen abstraction producing C(2)H(2)+OH is the most facile reaction channel. For this channel, refined computations using (U)CCSD(T)6-311 + + G(3df,2p)(U)CCSD(T)6-311 + + G(d,p) and complete-active-space second-order perturbation theory/complete-active-space self-consistent-field theory (CASPT2/CASSCF) [B. O. Roos, Adv. Chem. Phys. 69, 399 (1987)] using the contracted atomic natural orbitals basis set (ANO-L) [J. Almlof and P. R. Taylor, J. Chem. Phys.86, 4070 (1987)] were performed, yielding zero-point energy-corrected potential energy barriers of 17 kJ mol(-1) and 15 kJ mol(-1), respectively. Transition-state theory rate constant calculations, based on the UCCSD(T) and CASPT2/CASSCF computations that also include H-atom tunneling and a hindered internal rotation, are in perfect agreement with the experimental values. Considering both our experimental and theoretical determinations, the rate constant can best be expressed, in modified Arrhenius form as k(1)(T) = (2.2 +/- 0.1) x 10(-21)T(3.05) exp[-(376 +/- 100)T] cm(3) s(-1) for the range 300-2000 K. Thus, at temperatures above 1500 K, reaction of C(2)H with H(2)O is predicted to be one of the dominant C(2)H reactions in hydrocarbon combustion.