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.     

Conformational and vibrational analysis with the aid of normal coordinate calculations

Many organic compounds exist as equilibrium mixtures of two or more molecular conformations, and vibrational spectroscopy can be used to obtain information about the structure of those conformations. Normal coordinate calculations are often an aid to those conformational studies and to making vibrational assignments for the different conformers. However, sometimes those calculations are partially inconclusive, and a few results are briefly discussed in which both conclusive and inconclusive results were obtained from calculations. Calculations are then applied to some 1,2-dichloro- and 1,2-dibromo-alkanes. Previous calculations on 1,2-dichloropropane and 1,2-dichlorobutane are revised, and calculations are reported for 1,2-dibromopropane, 1,2-dibromopropane-d₆, and 1,2-dibromobutane. Spectra are given for the last two of these compounds. A modified valence force field was determined for each family of 1,2-dihaloalkane that should be transferable to other members of the family.     

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.     

The reaction rate for dissociative adsorption of N2 on stepped Ru(0001): six-dimensional quantum calculations

Quantum-mechanical calculations of the reaction rate for dissociative adsorption of N2 on stepped Ru(0001) are presented. Converged six-dimensional quantum calculations for this heavy-atom reaction have been performed using the multiconfiguration time-dependent Hartree method. A potential-energy surface for the transition-state region is constructed from density-functional theory calculations using Shepard interpolation. The quantum results are in very good agreement with the results of the harmonic transition-state theory. In contrast to the findings of previous model calculations on similar systems, the tunneling effect is found to be small.     

Recognition of amino acids in solution

The basic solvation shells of all the amino acids, of use in the study of their recognition in aqueous solutions, are determined by means of a method based on the use of 1/R expansions parameterized on the basis of the results from accurate SCF calculations. The accuracy of the calculations is tested in a more extensive study of the solvation of glycine, for which the results of Monte Carlo calculations are reproduced.     

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.     

A method for the calculation of transition moments between electronic states of molecules using a different one-electron basis set for each state

A state-specific approach to the calculation of transition moments between molecular electronic states requires that the wavefunction for each state is expanded in its optimum one-electron basis and that nonorthonormal basis techniques are used for the calculation of the transition moment integrals. A method has been developed for carrying out such nonorthonormal basis calculations, based on the corresponding orbitals transformation and appropriately defined density matrices, which may be used with configuration interaction (CI ) wavefunctions. Further improvements of the method have resulted in a decrease in the time required for the calculations and thus allow its application with moderately large CI expansions for each state. Nonorthonormal basis calculations on transition moments in H₂O have been carried out using the above method. The results are in agreement with those of large MRD -CI calculations.     

Density functional theory study of beta-hydride elimination of ethyl on flat and stepped Cu surfaces

Plane wave density functional theory calculations have been used to characterize the transition states for beta-hydride elimination of ethyl on Cu(100), Cu(110), Cu(111), and Cu(221). The reaction rates predicted by these calculations have been compared to experiments by including tunneling corrections within harmonic transition state theory. Tunneling corrections are found to be important in describing the peak temperatures observed using temperature programmed desorption experiments on Cu(110), Cu(111), and Cu(221). Once these corrections are included, the effective activation energies obtained from our calculations are in good agreement with previous experimental studies of this reaction on these four Cu surfaces. The transition states determined in our calculations are used to examine two general hypotheses that have been suggested to describe structure sensitivity in metal-catalyzed surface reactions.     

RHF and two-configuration SCF calculations are inappropriate for conjugated diradicals

Restricted Hartee Fock (RHF) and two-configuration self-consistent field (TCSCF) calculations provide qualitatively correct molecular orbitals for the two open-shell electrons in diradicals. Nevertheless, these calculations fail to give correct relative energies and in some cases they even lead to incorrect geometries. Examples of these failures are given for both singlet and triplet states of some conjugated diradicals. In several cases these failures are related to the “doublet instability problem” in RHF calculations on radicals. It is argued that unrestricted Hartee-Fock (UHF) calculations on triplet states are more likely that RHF to provide accurate geometries.     

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.     

Influence of electronic correlations on the ground-state properties of cerium dioxide

The electron-correlation effects on the ground-state properties of CeO(2) are studied by ab initio quantum-chemical methods. For this purpose the method of increments is applied. It combines Hartree-Fock calculations for periodic systems with correlation calculations requiring only information of the corresponding finite-cluster calculations. Using the coupled-cluster approach for the evaluation of the individual increments, we recover 93% of the experimental cohesive energy. The lattice constant and bulk modulus are found to be in good agreement with experimental values. For comparison also the results obtained with density functional methods 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.     

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.     

Efficient calculation of potential energy surfaces for the generation of vibrational wave functions

An automatic procedure for the generation of potential energy surfaces based on high level ab initio calculations is described. It allows us to determine the vibrational wave functions for molecules of up to ten atoms. Speedups in computer time of about four orders of magnitude in comparison to standard implementations were achieved. Effects due to introduced approximations--within the computation of the potential--on fundamental modes obtained from vibrational self-consistent field and vibrational configuration interaction calculations are discussed. Benchmark calculations are provided for formaldehyde and 1,2,5-oxadiazole (furazan).     

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.     

Calculating energy levels of isomerizing tetra-atomic molecules. II. The vibrational states of acetylene and vinylidene

A general, full-dimensional computational method for the accurate calculation of rotationally and vibrationally excited states of tetra-atomic molecules is further developed. The resulting computer program may be run in serial and parallel modes and is particularly appropriate for molecules executing wide-amplitude motions and isomerizations. An application to the isomerizing acetylene/vinylidene system is presented. Large-scale calculations using a coordinate system based on orthogonal satellite vectors have been performed in six dimensions and vibrational term values and wave functions for acetylene and vinylidene states up to approximately 23 000 cm(-1) above the potential minimum have been determined. This has permitted the characterization of acetylene and vinylidene states at and above the isomerization barrier. These calculations employ more extensive vibrational basis sets and hence consider a much higher density of states than in any variational calculations reported hitherto for this system. Comparison of the calculated density of states with that determined empirically suggests that our calculations are the most realistic achieved for this system to date. Indeed more states have been converged than in any previous study of this system. Calculations on lower lying excited states of acetylene based on HC-CH diatom-diatom coordinates give nearly identical results to those based on orthogonal satellite vectors. Comparisons are also made with calculations based on HH-CC diatom-diatom coordinates.     

Six-dimensional potential energy surface of the dissociative chemisorption of HCl on Au(111) using neural networks

We constructed a six-dimensional potential energy surface(PES)for the dissociative chemisorption of HCl on Au(111)using the neural networks method based on roughly 70000 energies obtained from extensive density functional theory(DFT)calculations.The resulting PES is accurate and smooth,based on the small fitting errors and good agreement between the fitted PES and the direct DFT calculations.Time-dependent wave packet calculations show that the potential energy surface is very well converged with respect to the number of DFT data points,as well as to the fitting process.The dissociation probabilities of HCl initially in the ground rovibrational state from six-dimensional quantum dynamical calculations are quite diferent from the four-dimensional fixed-site calculations,indicating it is essential to perform full-dimensional quantum dynamical studies for the title molecule-surface interaction system.     

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.     

The error function for fitting of models to immittance data

In statistical calculations for fitting a model to experimental immittance data (admittance and/or impedance data) the key issue is the error function, which as a result of calculations should attain its minimum value ( ? 0). Different formulae for the error function, recently used in calculations, are analyzed and a new formula is proposed. The principal feature of the new formula is that for the admittance data and the impedance data the same results of calculations are obtained; this formula takes into account the possibility of correlation of errors of the two components of the immittance vector.The usefulness of the proposed formula is experimentally verified and demonstrated on immittance data measured for two actual systems.     

Charge-conserving integral approximations for ab initio quantum chemistry

Two charge-conserving integral approximations are presented, one for neglecting and another for approximating the less important integrals that arise in quantum chemical calculations on molecular systems. Results are presented for test calculations on ethylene and glycine.