Quantum mechanical modeling of a transannular interaction in a bicyclic amidinium ion

A transannular donor-acceptor interaction in a bicyclic azaamidinium salt was modeled by quantum mechanical calculations using a supermolecule complex consisting of a formamidinium cation and an ammonia molecule. Molecular properties are reported at various geometries. These results are compared with the results of similar calculations on the bicyclic cation itself. The model calculations and the bicyclic cation calculations are in good agreement, but both fail to reproduce the experimentally known structure. Results from ab initio calculations on the model system are discussed, as are results from calculations which included iodide as counterion.     

Bi-fidelity fitting and optimization

A common feature in computations of chemical and physical properties is the investigation of phenomena at different levels of computational accuracy. Less accurate computations are used to provide a relatively quick understanding of the behavior of a system and allow a researcher to focus on regions of initial conditions and parameter space where interesting phenomena are likely to occur. These inexpensive calculations are often discarded when more accurate calculations are performed. This paper demonstrates how computations at different levels of accuracy can be simultaneously incorporated to study chemical and physical phenomena with less overall computational effort than the most expensive level of computation. A smaller set of computationally expensive calculations is needed because the set of expensive calculations is correlated with the larger set of less expensive calculations. We present two applications. First, we demonstrate how potential energy surfaces can be fit by simultaneously using results from two different levels of accuracy in electronic structure calculations. In the second application, we study the optical response of metallic nanostructures. The optical response is generated with calculations at two different grid resolutions, and we demonstrate how using these two levels of computation in a correlated fashion can more efficiently optimize the response.     

Compact basis sets for LCAO-LSD calculations. Part II: Tests for Cr2 and Ni4

The compact orbital and auxiliary basis sets for LCAO-LSD calculations introduced in Part I are tested in molecular calculations on Cr₂ and Ni₄. The present results for spectroscopic constants and valence orbital energies obtained using medium size orbital expansions with a double-zeta representation for valence orbitals are in very good agreement with those previously calculated with very extended sets. Since the computational time of the present calculations is reduced severalfold compared with the extended basis set calculations, the present basis sets allow increased efficiency of the LCAO-LSD calculations and allow the method to be extended to larger systems.     

Order-<Emphasis Type="Italic">N</Emphasis> and embedded-cluster first-principles DFT calculations using SIESTA/Mosaico

Order-N and embedded-cluster first-principles DFT calculations have been performed with the Mosaico method for energy optimization (Seijo and Barandiarán in J Chem Phys 121:6698, 2004) for the first time. The Hamiltonian matrix elements have been computed with the SIESTA code. The order-N behavior of the method in DFT calculations was shown in total energy calculations performed on bulk silicon using supercells up to Si₈₀₀₀. The sizes of the orbital-specific-basis-sets needed for precise calculations have been explored in demanding (bulk silicon) and favorable (water clusters) cases for a method based on the calculation of localized molecular orbitals. Embedded-cluster calculations, which are much faster than full-system calculations, have been performed on an Si-vacancy of bulk silicon and on a water cluster with a displacing water molecule. The feasiability of calculations of this type with Mosaico has been demonstrated. The sizes of the variationally free, active clusters which are needed for an agreement with full-system calculations have been explored and result to be reasonably small. Contribution to the Serafin Fraga Memorial Issue.     

Pseudopotential and electron propagator methods for the calculation of the photoelectron spectra of anionic silicon clusters: predictions on Si10-

Photoelectron spectra of anionic clusters of silicon require reliable theoretical calculations for their assignment and interpretation. Electron propagator calculations in the outer valence Green's-function approximation with two well-characterized, all-electron basis sets on vertical electron detachment energies (VEDEs) of anions are compared to similar calculations that employ Stuttgart pseudopotentials. Tests on Si(n) (-) clusters with n=3-7 exhibit an encouraging agreement between the all-electron and pseudopotentials results and between electron propagator predictions and experiments and values obtained from coupled-cluster calculations. To illustrate the capabilities of the new approach based on a Si pseudopotential and electron propagator methods, VEDE calculations on Si(10) (-) are presented.     

13C and (15)N chemical shift tensors in adenosine,guanosine dihydrate, 2'-deoxythymidine,and cytidine

The (13)C and (15)N chemical shift tensor principal values for adenosine, guanosine dihydrate, 2'-deoxythymidine, and cytidine are measured on natural abundance samples. Additionally, the (13)C and (15)N chemical shielding tensor principal values in these four nucleosides are calculated utilizing various theoretical approaches. Embedded ion method (EIM) calculations improve significantly the precision with which the experimental principal values are reproduced over calculations on the corresponding isolated molecules with proton-optimized geometries. The (13)C and (15)N chemical shift tensor orientations are reliably assigned in the molecular frames of the nucleosides based upon chemical shielding tensor calculations employing the EIM. The differences between principal values obtained in EIM calculations and in calculations on isolated molecules with proton positions optimized inside a point charge array are used to estimate the contributions to chemical shielding arising from intermolecular interactions. Moreover, the (13)C and (15)N chemical shift tensor orientations and principal values correlate with the molecular structure and the crystallographic environment for the nucleosides and agree with data obtained previously for related compounds. The effects of variations in certain EIM parameters on the accuracy of the shielding tensor calculations are investigated.     

A critical study of basis set effects and the use of approximate natural orbitals in SCF-CI calculations of molecular geometries and heats of reaction

SCF-CI calculations have been performed on a number of chemical reactions between closed shell molecules in order to determine the heats of reaction. Contracted Gaussian type atomic basis sets of three different qualities were used and the CI calculations were performed in a truncated approximate natural orbital space. The conclusions to be drawn from these calculations are rather pessimistic. For heats of reaction, errors up to 6 kcal/mole are obtained on the SCF-level with a double zeta plus polarization atomic basis. A further improvement is only possible if extended basis sets are used. Correlation effects on heats of reaction are of the same size and CI calculations are therefore only meaningful with large atomic basis sets.For the CI calculations a one-electron space of approximate natural orbitals, obtained from second order RS perturbation theory, was used. Different truncations, using the occupation number as criterion, were tested. The general conclusion is that errors in energy differences obtained with a truncated basis set are of the same magnitude as the error in the total correlation energy. In practice this means that not more than 20–30% of the approximate natural orbitals can be deleted if the error is to be kept less than a few kcal/mole.Finally the truncation error in calculations of bond distances was tested for a few cases. Errors of around 10% of the total change due to correlation were found when 30% of the lowest occupied natural orbitals were deleted.     

Calculations on the diphenylmethyl anion

Semiempirical and ab initio calculations for the diphenylmethyl anion and related species are reported. MINDO/3 calculations indicate a coplanar anion with an enlarged bond angle of ～139° to counteract the steric repulsions. MNDO calculations reveal an expanded bond angle with somewhat greater twist (21°). The ab initio calculations (STO -3G level) reveal an expanded central bond angle with an intermediate degree of phenyl twist. The results are compared with experimental data for this and related anions.     

Application of fixed-nuclei scattering theory to electron methane elastic and inelastic differential cross sections at 10 eV impact energy

Quantum mechanical calculations are reported for electron-methane elastic scattering and rotational excitation cross sections at 10 eV impact energy. The calculations employ a fixed-nuclei close coupling formalism with full incorporation of symmetry and are used to test previous laboratory-frame calculations employing a direct coupling approximation. Good agreement is obtained. Additional comparisons to previous theoretical and experimental work are also presented, and the contributions of the various symmetries to the cross sections are analyzed in terms of representatve matrix elements of the interaction potential.     

A method for the rapid calculation of matrix elements with highly oscillatory JWKB radial wavefunctions

A method for the rapid computation of matrix elements with JWKB radial wavefunctions is discussed. The method consists of dividing the range of integration into segments determined by the nodes of the semiclassical wavefunction. The desired matrix elements are calculated by summing the contributions from each segment which are evaluated by integrating between nodes with a Gauss-Mehler quadrature formula. The results are compared with exact quantum mechanical calculations and were found to agree within 1–2%. The calculations with the present method were generally five to ten times faster than the quantum mechanical calculations.     

Comparison of AM1 and PM3 semiempirical to ab initio methods in the study of Diels-Alder reactions of butadiene and cyclopentadiene with cyanoethylenes

Assuming a concerted synchronous mechanism with one transition state of the Diels-Alder reactions, the structures of the transition states and the activation energies for the reactions of butadiene and cyclopentadiene with cyanoethylenes were calculated by AM1 and PM3 semiempirical methods. The structural parameters were compared with those obtained by high level Gaussian calculations, whereas the activation energies were compared both with the ab initio calculations and those obtained experimentally. The structural properties calculated with PM3 methods are in general in better agreement with the ab initio calculations. The low level ab initio calculations are in many cases worse than the semiempirical methods. All predicted activation energies with both semiempirical methods are up to 300% higher than the experimental values. The predicted reactivity is also opposite to the experimental data. Only the very high level Gaussian calculations are in good correlation with experimental results. The predicted selectivity of the reaction is also opposite to the experimental facts. Two explanations are offered for this discrepancy: AM1 and PM3 methods cannot handle the calculation of the concerted Diels-Alder transition states and are not recommended to be used for that purpose, or this Diels-Alder reaction is not concerted but is stepwise.     

Solving the electron and electron-nuclear Schrodinger equations for the excited states of helium atom with the free iterative-complement-interaction method

Very accurate variational calculations with the free iterative-complement-interaction (ICI) method for solving the Schrodinger equation were performed for the 1sNs singlet and triplet excited states of helium atom up to N=24. This is the first extensive applications of the free ICI method to the calculations of excited states to very high levels. We performed the calculations with the fixed-nucleus Hamiltonian and moving-nucleus Hamiltonian. The latter case is the Schrodinger equation for the electron-nuclear Hamiltonian and includes the quantum effect of nuclear motion. This solution corresponds to the nonrelativistic limit and reproduced the experimental values up to five decimal figures. The small differences from the experimental values are not at all the theoretical errors but represent the physical effects that are not included in the present calculations, such as relativistic effect, quantum electrodynamic effect, and even the experimental errors. The present calculations constitute a small step toward the accurately predictive quantum chemistry.     

Analysis of approximations and errors in equations of motion method calculations

We analyze a number of fundamental questions associated with the use of a finite one-particle orbital basis in equations of motion (EOM) method calculations of excitation energies etc., of atomic and molecular systems. This approximation yields an approximate n_e-electron ground state and say, N excited states, while there are (N + 1)² different possible basis operators for EOM calculations. We show that sets of at most 2N basis operators can contribute to the EOM calculations. Any set of 2N basis operators, satisfying certain conditions, provides the exact EOM energies which are equivalent to complete configuration interaction results within the same orbital basis. We investigate the use of particle-particle shifting operators which are not employed in EOM calculations in model calculations on He with operator bases smaller than the complete 2V to consider the convergence of the expansion. The dependence of EOM calculations on the quality of the approximate ground state wavefunction is studied through calculations for Be where additional support is provided for the frequent need for multiconfigurational zeroth order reference functions (as corrected perturbatively). Excited state EOM wavefunctions from EOM calculations are shown to not necessarily be orthogonal to either the exact or approximate ground state wavefunction, suggesting implications in the use of EOM methods to evaluate excited state properties. The He and Be examples and a simple two-level problem are also utilized to illustrate questions concerning the use of the EOM equations to obtain an iteratively improved ground state wavefunction.     

Multireference configuration interaction calculations for positronium halides

Multireference configuration interaction (MRCI) calculations of the positronium halides, PsF, PsCl, PsBr, and PsI, are carried out, to give positron ionization energies, positronium binding energies, and two-photon annihilation rates. All CI calculations consider only valence correlation effect with a frozen-core approximation, and use the orbitals with angular momentum up to 8. To incorporate the effects of many-body correlations in the energies and two-photon annihilation rates, the MRCI calculations are repeated with increasing reference configurations, and the full CI limits of these energies and annihilation rates are estimated. The contribution from orbitals having angular momentum greater than 8 to those values is also estimated. Relative to our previous single reference CI calculations, many-body correlation effects significantly increase the positron ionization energies, positronium binding energies, and two-photon annihilation rates. The structures of the positronium halides are also discussed.     

Computation of multiphase equilibrium phenomena with an equation of state

This paper presents a general approach to multiphase equilibrium computations using an equation of state. Various types of calculations are described: flash calculations, saturation-pressure and saturation-temperature calculations, and calculations of the feed composition corresponding to a given saturation pressure and temperature.A stagewise procedure for flash calculations using the QNSS method allows efficient computation of phase equilibria for systems with any number of phases. The initial guess of the composition of an extra phase which is required to start the iteration is obtained from an analysis of the Gibbs-energy surface.Newton's method is used to construct multiphase boundaries on various types of diagrams (pressure-temperature, pressure-composition and temperature-composition). Multiphase critical points on these boundaries are also estimated by interpolation.The algorithms developed are tested for a typical reservoir-oil-CO₂ mixture which exhibits three-phase liquid 1-liquid 2-vapor (L₁L₂V) separation. The predictions obtained using the Peng-Robinson of state are satisfactory.     

Multimode calculations of rovibrational energies and dipole transition intensities for polyatomic molecules with torsional motion: application to H2O2

We report rigorous calculations of rovibrational energies and dipole transition intensities for hydrogen peroxide using a new version of MULTIMODE as applied to molecules with torsional (reaction path) motion. The key features which permit such calculations for moderately sized polyatomic molecules of this general type are briefly described. A previous, accurate potential energy surface and a new high-level ab initio dipole moment surface are employed in these calculations. Detailed comparisons are made with high-resolution experimental spectral intensities from the HITRAN database.     

Gradient corrections in density functional theory calculations for surfaces: Co on Pd{110}

Ab initio total energy calculations have been performed for CO chemisorption on Pd{110}. Local density approximation (LDA) calculations yield chemisorption energies which are significantly higher than experimental values but inclusion of the generalised gradient approximation (GGA) gives better agreement. In general, sites with higher coordination of the adsorbate to surface atoms lead to a larger degree of overbinding with LDA, and give larger corrections with GGA. The reason is discussed using a first-order perturbation approximation. It is concluded that this may be a general failure of LDA for chemisorption energy calculations. This conclusion may be extended to many surface calculations, such as potential energy surfaces for diffusion.     

A TDDFT study of the optical response of DNA bases, base pairs, and their tautomers in the gas phase

We present calculations of the optical response of the DNA bases and base pairs both in their normal and tautomeric forms in the gas phase, using time-dependent density functional theory (TDDFT). These calculations are performed in real time within the adiabatic approximation with a basis of local orbitals. Our results for the individual bases are in good agreement with experiment and computationally more demanding calculations of chemical accuracy. The optical response of base pairs indicates that the differences between normal and tautomeric forms in certain cases are significant enough to provide a means of identification.     

An open-ended self-consistent field method. A simulation of a molecular orbital technique for small memory computers

The steps in a nonconventional algorithm for self-consistent field calculations are outlined, and calculations on cumulenes are given to demonstrate the convergence properties of the method. The approach is essentially open ended and is likely to be cost effective on computer systems with minimal core.     

Relativistic all-electron configuration interaction calculations on the gold atom

We present the results of relativistic and non-relativistic self-consistent field and configuration interaction calculations for the gold atom, using the spin-free no-pair Hamiltonian in a basis set expansion. A new basis set for the gold atom is discussed and its results in relativistic and non-relativistic self-consistent field calculations are compared to those of numerical Dirac-Hartree-Focic and Hartree-Fock calculations, respectively. Excitation energies, electron affinities and ionization potentials were calculated using a multi-reference configuration interaction technique and are in reasonable agreement with experiment in the relativistic case.