Explicitly correlated Gaussian calculations of the (2)D Rydberg states of the boron atom

Accurate non-relativistic variational calculations are performed for the seven lowest members of the (2)D Rydberg series (1s(2)2s2p(2), and 1s(2)2s(2)nd, n = 3, [ellipsis (horizontal)], 8) of the boron atom. The wave functions of the states are expanded in terms of all-electron explicitly correlated Gaussian basis functions and the effect of the finite nuclear mass is directly included in the calculations allowing for determining the isotopic shifts of the energy levels. The Gaussian basis is optimized independently for each state with the aid of the analytic energy gradient with respect to the Gaussian parameters. The calculations represent the highest accuracy level currently achievable for the considered states. The computed energies are compared with the available experimental data.     

Structure and properties of metal-exchanged zeolites studied using gradient-corrected and hybrid functionals. II. Electronic structure and photoluminescence spectra

The influence of the choice of the exchange-correlation functional (semilocal gradient corrected or hybrid functionals) on the electronic properties of metal-exchanged zeolites has been investigated for Cu- and Co-exchanged chabazite. The admixture of exact exchange in hybrid functionals increases the fundamental gap of purely siliceous chabazite, leading to better agreement with experiment and many-body perturbation theory for close-packed SiO(2) polymorphs where detailed experimental information is available. For the metal-exchanged chabazite the increased exchange splitting strongly influences the position of the cation states relative to the framework bands-in general, gradient-corrected functionals locate the occupied cation states close to the valence-band maximum of the framework, while hybrid functionals shift the occupied cation states to larger binding energies and the empty states to higher energies within the fundamental gap. The photoluminescence spectra have been analyzed using fixed-moment total-energy calculations for excited spin states in structurally relaxed and frozen geometries. The geometrical relaxation of the excited states leads to large differences in excitation and emission energies which are more pronounced in calculations using hybrid functionals. Due to the stronger relaxation effects calculated with hybrid functionals, the large differences in the electronic spectra calculated with both types of functionals are not fully reflected in the photoluminescence spectra.     

An ab initio study of the low-lying electronic states of S3

Accurate calculations of the low-lying singlet and triplet electronic states of thiozone, S(3), have been carried out using large multireference configuration interaction wave functions. Cuts of the full potential energy surfaces along the stretching and bending coordinates have been presented, together with the vertical excitation spectra. The strong experimentally observed absorption around 395 nm is assigned to the 1 (1)B(2) state, which correlates to ground state products. Absorption at wavelengths shorter than 260 nm is predicted to lead to singlet excited state products, S(2) (a (1)Delta(g))+S((1)D). The spectroscopic properties of the X (3)Sigma(g) (-), a (1)Delta(g), and b (1)Sigma(g) (+) electronic states of the S(2) radical have also been accurately characterized in this work. The investigations of the low-lying electronic states were accompanied by accurate ground state coupled cluster calculations of the thermochemistry of both S(2) and S(3) using large correlation consistent basis sets with corrections for core-valence correlation, scalar relativity, and atomic spin-orbit effects. Resulting values for D(0)(S(2)+S) and SigmaD(0) for S(3) are predicted to be 61.3 and 162.7 kcal/mol, respectively, with conservative uncertainties of +/-1 kcal/mol. Analogous calculations predict the C(2v)-D(3h) (open-cyclic) isomerization energy of S(3) to be 4.4+/-0.5 kcal/mol.     

A theoretical and computational study of the anion, neutral, and cation Cu(H(2)O) complexes

An ab initio investigation of the potential energy surfaces and vibrational energies and wave functions of the anion, neutral, and cation Cu(H(2)O) complexes is presented. The equilibrium geometries and harmonic frequencies of the three charge states of Cu(H(2)O) are calculated at the MP2 level of theory. CCSD(T) calculations predict a vertical electron detachment energy for the anion complex of 1.65 eV and a vertical ionization potential for the neutral complex of 6.27 eV. Potential energy surfaces are calculated for the three charge states of the copper-water complexes. These potential energy surfaces are used in variational calculations of the vibrational wave functions and energies and from these, the dissociation energies D(0) of the anion, neutral, and cation charge states of Cu(H(2)O) are predicted to be 0.39, 0.16, and 1.74 eV, respectively. In addition, the vertical excitation energies, that correspond to the 4 (2)P<--4 (2)S transition of the copper atom, and ionization potentials of the neutral Cu(H(2)O) are calculated over a range of Cu(H(2)O) configurations. In hydrogen-bonded, Cu-HOH configurations, the vertical excitation and ionization energies are blueshifted with respect to the corresponding values for atomic copper, and in Cu-OH(2) configurations where the copper atom is located near the oxygen end of water, both quantities are redshifted.     

One- and two-body densities of carbon isoelectronic series in their low-lying multiplet states from explicitly correlated wave functions

The (3)P ground state and both the (1)D and (1)S excited states arising from the low-lying 1s(2)2s(2)2p(2) configuration of the carbon isoelectronic series are studied starting from explicitly correlated multiconfigurational wave functions. One- and two-body densities in position space have been calculated and different one- and two-body expectation values have been obtained. The effects of electronic correlations have been systematically studied. All the calculations have been done by means of variational Monte Carlo.     

Refinement of the experimental energy levels of higher 2D Rydberg states of the lithium atom with very accurate quantum mechanical calculations

Very accurate variational non-relativistic calculations are performed for four higher Rydberg (2)D states (1s(2)nd(1), n = 8,..., 11) of the lithium atom ((7)Li). The wave functions of the states are expanded in terms of all-electron explicitly correlated Gaussian functions and finite nuclear mass is used. The exponential parameters of the Gaussians are optimized using the variational method with the aid of the analytical energy gradient determined with respect to those parameters. The results of the calculations allow for refining the experimental energy levels determined with respect to the (2)S 1s(2)2s(1) ground state.     

A density-functional study of the structural, electronic, magnetic, and vibrational properties of Ti8C12 metallocarbohedrynes

Calculations are presented for the structural, electronic, and vibrational properties of the different Ti8C12 metallocarbohedrynes. (Please note that we adopt the name "metallocarbohedrynes" instead of "metallocarbohedrenes" to denote the acetylenic nature of C2 units in this class of clusters demonstrated by several contributions in literature.) The density-functional theory (DFT) calculations are performed with the all-electron projector augmented-wave method and generalized gradient approximation for the exchange-correlation functional. We study the seven low-energy isomers of the Ti8C12 metallocarbohedrynes using spin-polarized DFT, where we find a correlation between the number of rotated carbon dimers and the cohesive energy of the structure. The electronic density of states (eDOS) show that C3nu, D*3d, and D3d isomers are spin polarized. The partial eDOS shows that, depending on the dimer orientation, carbon atoms and a subgroup of the metal atoms form a covalent framework while other metal atoms are bonded to this framework more ionically. This picture is further supported by the charge density of the different structures, where we see that the Ti atoms with higher charge density show less contribution to the covalent bonding of the Ti-C framework. The vibrational spectra of the different structures are calculated using the frozen-vibration method. Also, we calculate the vibrational spectra of the C3nu and C2nu structures using molecular-dynamics simulations at two different temperatures. The results of the simulations demonstrate the local stability of the structures beyond the harmonic limit explored by the frozen-vibration method.     

Tetrahydrides of third-row transition elements: spin-orbit coupling effects on the stability of rhenium tetrahydride

The potential energy surfaces of low-lying states in rhenium tetrahydride (ReH(4)) were explored by using the multiconfiguration self-consistent field (MCSCF) method together with the SBKJC effective core potentials and the associated basis sets augmented by a set of f functions on rhenium atom and by a set of p functions on hydrogen atoms, followed by spin-orbit coupling (SOC) calculations to incorporate nonscalar relativistic effects. The most stable structure of ReH(4) was found to have a D(2d) symmetry and its ground state is (4)A(2). It is found that this is lower in energy than the dissociation limit, ReH(2)+H(2), after dynamic correlation effects are taken into account by using second-order multireference M?ller-Plesset perturbation (MRMP2) calculations. This reasonably agrees with previous results reported by Andrews et al. [J. Phys. Chem. 107, 4081 (2003)]. The present investigation further revealed that the dissociation reaction of ReH(4) cannot occur without electronic transition from the lowest quartet state to the lowest sextet state. This spin-forbidden transition can easily occur because of large SOC effects among low-lying states in such heavy metal-containing compounds. The minimum-energy crossing (MEX) point between the lowest quartet and sextet states is proved to be energetically and geometrically close to the transition state for the dissociation reaction on the potential energy surface of the lowest spin-mixed state. The MEX point (C(2) symmetry) was estimated to be 9184?cm(-1) (26.3 kcal/mol) higher than the (4)A(2) state in D(2d) symmetry at the MRMP2 level of theory. After inclusion of SOC effects, an energy maximum on the lowest spin-mixed state appears near the MEX point and is recognized as the transition state for the dissociation reaction to ReH(2)+H(2). The energy barrier for the dissociation, evaluated to be MEX in the adiabatic picture, was calculated to be 5643?cm(-1) (16.1 kcal/mol) on the lowest spin-mixed state when SOC effects were estimated at the MCSCF level of theory.     

Behavior of Ag3 clusters inside a nanometer-sized space of ZSM-5 zeolite

We found from DFT calculations that Ag-Ag orbital interactions as well as Ag-O electrostatic interactions determine the structures of three silver cations inside a nanometer-sized cavity of ZSM-5 (Ag(3)-ZSM-5) in lower and higher spin states. Both interactions strongly depend on the number of Al atoms substituted for Si atoms on the ZSM-5 framework (ZSM-5(Al(n))), where n ranges from 1 to 3. In smaller n, stronger Ag-Ag orbital interactions and weaker Ag-O electrostatic interactions operate. Accordingly, there are significant dependencies of the structures of three silver cations on the number of Al atoms. In lower spin states of Ag(3)-ZSM-5(Al(1)) and Ag(3)-ZSM-5(Al(2)), D(3h)-like triangle clusters are contained inside ZSM-5 whereas their higher spin states have triangle clusters distorted significantly from the D(3h) structure. In lower spin states, the totally symmetric orbital consisting of 5s(Ag) orbitals is responsible for cluster formation, whereas in higher spin states occupation of a 5s(Ag)-based orbital with one node results in significant distortion of the triangle clusters. The distortion can be partially understood by analogies to Jahn-Teller distortion of the bare D(3h) Ag(3)(+) cluster in the triplet spin state. When n is 3, we found that three silver cations are isolated in a lower spin state and that a linear cluster consisting of two silver cations is formed in a higher spin state. Thus, we demonstrate from DFT calculations that the number of Al atoms can control the properties of three silver cations inside a ZSM-5 cavity. Since the structural and electronic features of the enclosed silver clusters can link to their catalytic properties, the DFT findings can help us to understand the catalytic activity of Ag-ZSM-5.     

Towards accurate all-electron quantum Monte Carlo calculations of transition-metal systems: spectroscopy of the copper atom

In this work we present all-electron fixed-node diffusion Monte Carlo (FN-DMC) calculations of the low-lying electronic states of the copper atom and its cation. The states considered are those which are the most relevant for the organometallic chemistry of copper-containing systems, namely, the (2)S, (2)D, and (2)P electronic states of Cu and the (1)S ground state of Cu(+). We systematically compare our FN-DMC results to CCSD(T) calculations using very large atomic-natural-orbital-type all-electron basis sets. The FN-DMC results presented in this work provide, to the best of our knowledge, the most accurate nonrelativistic all-electron correlation energies for the lowest-lying states of copper and its cation. To compare our results to experimental data we include the relativistic contributions for all states through numerical Dirac-Fock calculations, which for copper (Z=29) provide almost the entire relativistic effects. It is found that the fixed-node errors using Hartree-Fock nodes for the lowest transition energies of copper and the first ionization potential of the atom cancel out within statistical fluctuations. The overall accuracy achieved with quantum Monte Carlo for the nonrelativistic correlation energy (statistical fluctuations of about 1600 cm(-1) and near cancelation of fixed-node errors) is good enough to reproduce the experimental spectrum when relativistic effects are included. These results illustrate that, despite the presence of the large statistical fluctuations associated with core electrons, accurate all-electron FN-DMC calculations for transition metals are nowadays feasible using extensive but accessible computer resources.     

Simulation studies of amide I IR absorption and two-dimensional IR spectra of beta hairpins in liquid water

Amide I IR absorption and two-dimensional (2D) IR photon echo spectra of a model beta hairpin in aqueous solution are theoretically studied and simulated by combining semiempirical quantum chemistry calculations and molecular dynamics simulation methods. The instantaneous normal-mode analysis of the beta hairpin in solution is performed to obtain the density of states and the inverse participation ratios of the one-exciton states. The motional and exchange narrowing processes are taken into account by employing the time-correlation function theory for the linear and nonlinear response functions. Numerically simulated IR absorption and 2D spectra are then found to be determined largely by the amide I normal modes delocalized on the peptides in the two strands. The site-specific isotope-labeling effects on the IR and 2D IR spectra are discussed. The simulation results for the ideal (A17) beta hairpin are directly compared with those of the realistic 16-residue (GB1) beta hairpin from an immunoglobulin G-binding protein. It was found that the characteristic features in IR and 2D spectra of both the ideal (A17) beta hairpin and the GB1 beta hairpin are the same. The simulated IR spectrum of the GB1 beta hairpin is found to be in good agreement with experiment, which demonstrates that the present computational method is quantitatively reliable.     

Theoretical spectroscopy of the calcium dimer in the A 1Sigma(u)+, c3Pi(u), and a3Sigma(u)+ manifolds: an ab initio nonadiabatic treatment

Nonadiabatic theory of molecular spectra of diatomic molecules is presented. It is shown that in the fully nonadiabatic framework, the rovibrational wave functions describing the nuclear motions in diatomic molecules can be obtained from a system of coupled differential equations. The rovibrational wave functions corresponding to various electronic states are coupled through the relativistic spin-orbit coupling interaction and through different radial and angular coupling terms, while the transition intensities can be written in terms of the ground state rovibrational wave function and bound rovibrational wave functions of all excited electronic states that are electric dipole connected with the ground state. This theory was applied in the nearly exact nonadiabatic calculations of energy levels, line positions, and intensities of the calcium dimer in the A (1)Sigma(u) (+)(1 (1)S+1 (1)D), c (3)Pi(u)(1 (3)P+1 (1)S), and a (3)Sigma(u) (+)(1 (3)P+1 (1)S) manifolds of states. The excited state potentials were computed using a combination of the linear response theory within the coupled-cluster singles and doubles framework for the core-core and core-valence electronic correlations and of the full configuration interaction for the valence-valence correlation, and corrected for the one-electron relativistic terms resulting from the first-order many-electron Breit theory. The electric transition dipole moment governing the A (1)Sigma(u) (+)<--X (1)Sigma(g) (+) transitions was obtained as the first residue of the frequency-dependent polarization propagator computed with the coupled-cluster method restricted to single and double excitations, while the spin-orbit and nonadiabatic coupling matrix elements were computed with the multireference configuration interaction wave functions restricted to single and double excitations. Our theoretical results explain semiquantitatively all the features of the observed Ca(2) spectrum in the A (1)Sigma(u) (+)(1 (1)S+1 (1)D), c (3)Pi(u)(1 (3)P+1 (1)S), and a (3)Sigma(u) (+)(1 (3)P+1 (1)S) manifolds of states.     

Prediction of the existence of the N2H- molecular anion

We predict the existence of the N(2)H(-) anion from first principle calculations. We present the three-dimensional potential energy surface and the bound states of the N(2)H(-)/D(-) van der Waals anion. The electronic calculations were performed using state-of-the-art ab initio methods and the nuclear motions were solved using a quantum close-coupling scattering theory. A T-shaped equilibrium structure was found, with a well depth of 349.1 cm(-1), where 18 bound states have been located for N(2)H(-) and 25 for N(2)D(-) for total angular momentum J = 0. We also present the absorption spectra of the N(2)H(-) complex. This anion could be formed after low energy collisions between N(2) and H(-) through radiative association. The importance of this prediction in astrophysics and the possible use of N(2)H(-) as a tracer of N(2) and H(-) in the interstellar medium is discussed.     

Effect of double-layer polarization on the forces that act on a nanosized cylindrical particle in an ac electrical field

The polarization of, the forces acting on, and the electroosmotic flow field around a cylindrical particle of radius a* and uniform zeta potential zeta* submerged in an electrolyte solution and subjected to alternating electric fields are computed by solving the Poisson-Nernst-Planck (PNP) equations (the standard model). The dipole coefficient and the electrostatic and hydrodynamic forces are calculated as functions of the electric field's frequency, the solute concentration, and the particle's surface charge. The calculations are not restricted to small Debye screening lengths (lambdaD*). At relatively low frequencies, the polarization coefficient is nearly frequency-independent. As the frequency increases above D*/a*(2), where D* is the effective diffusion coefficient, the polarization coefficient initially increases, attains a maximum, and then decreases to an asymptotic value (when the frequency exceeds (1+Du)D*/lambdaD(*2), where Du is the Dukhin number). At low frequencies, when (lambdaD*/a*)(2)e(|zeta*F*/(2R*T*)|) < 1, the PNP calculations are in excellent agreement with the predictions of the Dukhin-Shilov (DS) low-frequency theory. At high frequencies, when lambda D*/a* < 1, the PNP calculations are in excellent agreement with the Maxwell-Wagner-O'Konski (MWO) theory.     

Orbit-orbit relativistic corrections to the pure vibrational non-Born-Oppenheimer energies of H(2)

We report the derivation of the orbit-orbit relativistic correction for calculating pure vibrational states of diatomic molecular systems with sigma electrons within the framework that does not assume the Born-Oppenheimer (BO) approximation. The correction is calculated as the expectation value of the orbit-orbit interaction operator with the non-BO wave function expressed in terms of explicitly correlated Gaussian functions multiplied by even powers of the internuclear distance. With that we can now calculate the complete relativistic correction of the order of alpha(2) (where alpha=1/c). The new algorithm is applied to determine the full set of the rotationless vibrational levels and the corresponding transition frequencies of the H(2) molecule. The results are compared with the previous calculations, as well as with the frequencies obtained from the experimental spectra. The comparison shows the need to include corrections higher than second order in alpha to further improve the agreement between the theory and the experiment.     

Hydrogen molecule in the small dodecahedral cage of a clathrate hydrate: quantum five-dimensional calculations of the coupled translation-rotation eigenstates

We report quantum five-dimensional (5D) calculations of the energy levels and wave functions of the hydrogen molecule, para-H2 and ortho-H2, confined inside the small dodecahedral (H2O)20 cage of the sII clathrate hydrate. All three translational and the two rotational degrees of freedom of H2 are included explicitly, as fully coupled, while the cage is treated as rigid. The 5D potential energy surface (PES) of the H2-cage system is pairwise additive, based on the high-quality ab initio 5D (rigid monomer) PES for the H2-H2O complex. The bound state calculations involve no dynamical approximations and provide an accurate picture of the quantum 5D translation-rotation dynamics of H2 inside the cage. The energy levels are assigned with translational (Cartesian) and rotational quantum numbers, based on calculated root-mean-square displacements and probability density plots. The translational modes exhibit negative anharmonicity. It is found that j is a good rotational quantum number, while the threefold degeneracy of the j = 1 level is lifted completely. There is considerable translation-rotation coupling, particularly for excited translational states.     

Probing the structural and electronic factors affecting the adsorption and reactivity of alkenes in acidic zeolites using DFT calculations and multivariate statistical methods

Quantum mechanical (QM) cluster calculations have been performed on a model of ZSM-5 at DFT and MP2 levels. We investigated how the adsorption energies and the energetics of alkoxide intermediate formation of six different alkene substrates, ethene, propene, 1-butene, cis/trans butene, and isobutene, vary in this zeolite model. An analysis of the DFT geometric, electronic, and energetic parameters of the zeolite-substrate complexes, transition states, and alkoxide intermediates is performed using principal components analysis (PCA) and partial least squares (PLS). These deliver an insight into the correlated changes that occur between molecular structure and energy along the reaction coordinate between the physisorbed and chemisorbed species within the zeolite. To the best of our knowledge, this is the first occasion multivariate techniques such as PCA or PLS have been employed to profile the changes in electronics, distances, and angles in QM calculations of catalytic systems such as zeolites. We find the calculated adsorption and the alkoxide intermediate energies correlate strongly with the absolute charge on the substrate and the length of the substrate double bond. The transition states' energies are not affected by the zeolite framework as modeled, which explains why they correlate strongly with the gas-phase substrate protonation energy. Our cluster results show that for ethene, propene, 1-butene, and isobutene, the relative energetics associated with the formation of the alkoxide intermediate in ZSM-5 follow the same trends as calculations where the effects of the framework are included.     

Intermediate state representation approach to physical properties of electronically excited molecules

Propagator methods provide a direct approach to energies and transition moments for (generalized) electronic excitations from the ground state, but they do not usually allow one to determine excited state wave functions and properties. Using a specific intermediate state representation (ISR) concept, we here show how this restriction can be overcome in the case of the algebraic-diagrammatic construction (ADC) propagator approach. In the ISR reformulation of the theory the basic ADC secular matrix is written as a representation of the Hamiltonian (or the shifted Hamiltonian) in terms of explicitly constructable states, referred to as intermediate (or ADC) states. Similar intermediate state representations can be derived for operators other than the Hamiltonian. Together with the ADC eigenvectors, the intermediate states give rise to an explicit formulation of the excited wave functions and allow one to calculate physical properties of excited states as well as transition moments for transitions between different excited states. As for the ground-state excitation energies and transition moments, the ADC excited state properties are size consistent so that the theory is suitable for applications to large systems. The established hierarchy of higher-order [ADC(n)] approximations, corresponding to systematic truncations of the IS configuration space and the perturbation-theoretical expansions of the ISR matrix elements, can readily be extended to the excited state properties. Explicit ISR matrix elements for arbitrary one-particle operators have been derived and coded at the second-order [ADC(2)] level of theory. As a first computational test of the method we have carried out ADC(2) calculations for singlet and triplet excited state dipole moments in H(2)O and HF, where comparison to full CI results can be made. The potential of the ADC(2) method is further demonstrated in an exploratory study of the excitation energies and dipole moments of the low-lying excited states of paranitroaniline. We find that four triplet states, T1-T4, and two singlet states, S1 and S2, lie (vertically) below the prominent charge transfer (CT) excitation, S3. The dipole moment of the S3 state (17.0D) is distinctly larger than that of the corresponding T3 triplet state (11.7D).     

The open-shell interaction of He with the B 3Piu(0+) state of Br2: an ab initio study and its comparison with a diatomics-in-molecule perturbation model

The interaction of He with Br2 in electronically excited B 3Piu state is investigated using spin-unrestricted single and double coupled-cluster approach with noniterative perturbative treatment of triple excitations. Internal electrons of the Br atom are described by effective core pseudopotentials. The validity of this approach is analyzed by comparing the lowest 2Sigma+ and 2Pi electronic states of the HeBr molecule with those obtained in all electron calculations [J. Chem. Phys. 115, 10438 (2001)]. In this context, we examine the performance of different basis sets and saturation with bond functions. The comparison of theoretical blue-shifts with the experiment provides confidence about the present ab initio calculations. In addition, He-Br results of ab initio calculations at the same level are used to obtain approximate He-Br2 (3Piu) interactions in the framework of the diatomics-in-molecule first order perturbation theory (IDIM-PT1) [J. Chem. Phys. 104, 9913 (1996)]. Overall, the IDIM-PT1 model results show a good agreement with the ab initio ones, being the main difference the sensitivity to the elongation of the Br-Br bond.