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.     

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.     

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.     

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.     

Bond centred functions in relativistic and non-relativistic calculations for diatomics

In this paper, we discuss the performance of molecular basis sets consisting of atomic centred (AC) functions augmented with bond centred (BC) functions in relativistic and non-relativistic calculations carried out at the Hartree–Fock and several correlated levels of approximation. While usually non-correlated calculations employing BC functions can be performed at a lower computational cost as compared with those making use of energy optimized AC basis sets, the correlated calculations are always more accurate and less expensive with the latter. It is demonstrated that both correlated or non-correlated calculations always benefit from the addition of a few BC functions with a moderate increase of computational effort. The performance of basis sets containing even-tempered BC functions is also studied and their usage is advocated in case of relativistic calculations.     

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.     

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.     

Ab initio study of (13)C(alpha) chemical shift anisotropy tensors in peptides

This study reports magnitudes and the orientation of the (13)C(alpha) chemical shift anisotropy (CSA) tensors of peptides obtained using quantum chemical calculations. The dependency of the CSA tensor parameters on the energy optimization of hydrogen atom positions and hydrogen bonding effects and the use of zwitterionic peptides in the calculations are examined. Our results indicate that the energy optimization of the hydrogen atom positions in crystal structures is necessary to obtain accurate CSA tensors. The inclusion of intermolecular effects such as hydrogen bonding in the calculations provided better agreement between the calculated and experimental values; however, the use of zwitterionic peptides in calculations, with or without the inclusion of hydrogen bonding, did not improve the results. In addition, our calculated values are in good agreement with tensor values obtained from solid-state NMR experiments on glycine-containing tripeptides. In the case of peptides containing an aromatic residue, calculations on an isolated peptide yielded more accurate isotropic shift values than the calculations on extended structures of the peptide. The calculations also suggested that the presence of an aromatic ring in the extended crystal peptide structure influences the magnitude of the delta(22) which the present level of ab initio calculations are unable to reproduce.     

Quantum Monte Carlo calculations of the dissociation energies of three-electron hemibonded radical cationic dimers

We report variational and diffusion quantum Monte Carlo (VMC and DMC) calculations of the dissociation energies of the three-electron hemibonded radical cationic dimers of He, NH3, H2O, HF, and Ne. These systems are particularly difficult for standard density-functional methods such as the local-density approximation and the generalized gradient approximation. We have performed both all-electron (AE) and pseudopotential (PP) calculations using Slater-Jastrow wave functions with Hartree-Fock single-particle orbitals. Our results are in good agreement with coupled-cluster CCSD(T) calculations. We have also studied the relative stability of the hemibonded and hydrogen-bonded water radical dimer isomers. Our calculations indicate that the latter isomer is more stable, in agreement with post-Hartree-Fock methods. The excellent agreement between our AE and PP results demonstrates the high quality of the PPs used within our VMC and DMC calculations.     

o-C8 Carbon: a New Allotrope of Superhard Carbon

An orthonormal crystal of carbon with PMMA space group (o-C₈) was found to be a stable superhard carbon allotrope by particle swarm optimization algorithm and density functional calculations. The phonon spectrum calculations demonstrate that the o-C₈ carbon phase is dynamically stable. The volume compression calculations show that it is highly incompressible, with bulk modulus of 298.6 GPa. The calculations demonstrate that it is a low-density superhard material with density of 2.993 g/cm³ and Vickers hardness of 82.4 GPa.     

Full spin-orbit configuration interaction calculations on electronic states of LiBe

Ab initio calculations are reported for the simplest heteronuclear metal cluster, LiBe. Full spin-orbit configuration interaction calculations in the context of relativistic effective core potentials lead to accurate potential energy curves for low-lying states. Results are compared with recent experimental observations and with all electron multi-reference configuration interaction calculations.     

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.     

Basis set selections for relativistic self-consistent field calculations

Practical methods of generating reliable and economic basis sets for relativistic self-consistent fields (RSCF) calculations are developed. Large component basis sets are generated from constrained optimizations of exponents in the nonrelativistic atomic calculations for light atoms. For heavy atoms, large component basis sets for inner core orbitals are generated by fitting numerical atomic spinors of Dirac-Hartree-Fock calculations with appropriate number of Slater-type functions. Small component basis sets are obtained by using the kinetic balance condition and other computational criteria. With judicious selections of the basis sets, virtual orbitals in RSCF calculations become very similar to those in nonrelativistic calculations, implying that relativistic virtual orbitals can be used in electron correlation calculations in the same manner as the conventional nonrelativistic virtual orbitals. It is also evident that the Koopmans' theorem is also valid in RSCF results.     

Quantum calculations of the O(3P)+H2-->OH+H reaction

Quantum scattering calculations are reported for the O(3P)+H2(v=0,1) reaction using chemically accurate potential energy surfaces of 3A' and 3A" symmetry. We present state-to-state reaction cross sections and rate coefficients as well as thermal rate coefficients for the title reaction using accurate quantum calculations. Our calculations yield reaction cross sections that are in quantitative accord with results of recent crossed molecular beam experiments. Comparisons with results obtained using the J-shifting calculations show that the J-shifting approximation is quite reliable for this system. Thermal rate coefficients from the exact calculations and the J-shifting approximation agree remarkably well with experimental results. Our calculations also reproduce the markedly different OH(v'=0)/OH(v'=1) branching in O(3P)+H2(v=1) reaction, observed in experiments that use different O(3P) atom sources. In particular, we show that the branching ratio is a strong function of the kinetic energy of the O(3P) atom.     

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.     

Rotational Isomerism in O-Methylphenol: Matrix-Isolation Infrared Study and MNDO Calculations

Rotational isomerism in o-methylphenol was studied by matrix-isolation infrared spectroscopy and MNDO calculations. Monomer molecules were isolated both in the argon matrix and in the nitrogen matrix near 10°K. The resolution of one weak band from the main hydroxyl absorption in the stretching and torsional regions evidently indicates the existence of two stable rotational isomers. Results of MNDO semi-empirical molecular orbital calculations with full geometry optimization indicate that only two stable conformations can exist with the trans (stag) conformation being more stable than the cis (stag) conformation by 3.32 KJ/mole. The present experimental data are interpreted with the aid of theoretical MNDO calculations. The agreement between experiment and theoretical calculations is excellent. However, it was found that the CNDO/2 calculations would give misleading predictions on the relative stabilities of rotational isomers in the present case.     

Unusual conformational-determining interactions in oxymethylpyridines: An ab initio study and an improved method for refining molecular mechanics parameters

The conformational preferences of oxymethylpyridines have been investigated by ab initio calculations and compared to similar calculations for oxymethylbenzene. The C? O bond in the pyridine compounds was found to prefer eclipsing with a C? C bond in the ring, in agreement with previous observations but in disaccord with tentative MM2 calculations. The effect was most pronounced in the 2-substituted pyridine. The benzene compound, on the other hand, showed good agreement between the energies from MM2, MM3, and ab initio calculations. The conformational preferences are discussed in terms of stereoelectronic interactions. New MM2 and MM3 parameters were determined from ab initio calculations on nonstationary points on the energy hypersurface. The parameterization method is discussed. © 1995 by John Wiley & Sons, Inc.     

Ground and excited states of NH4: Electron propagator and quantum defect analysis

Vertical excitation energies of the Rydberg radical NH4 are inferred from ab initio electron propagator calculations on the electron affinities of NH4+. The adiabatic ionization energy of NH4 is evaluated with coupled-cluster calculations. These predictions provide optimal parameters for the molecular-adapted quantum defect orbital method, which is used to determine Einstein emission coefficients and radiative lifetimes. Comparisons with spectroscopic data and previous calculations are discussed.     

Toward a consistent treatment of polarization in model QM/MM calculations

The concept of model chemistries within hybrid QM/MM calculations has been addressed through analysis of the polarization energy determined by two distinct approaches based on (i) induced charges and (ii) induced dipoles. The quantum mechanical polarization energy for four configurations of the water dimer has been determined for a range of basis sets using Morokuma energy decomposition analysis. This benchmark value has been compared to the fully classical polarization energy determined using the induced dipole approach, and the molecular mechanics polarization energy calculated using induced charges within the MM region of hybrid QM/MM calculations. From the water dimer calculations, it is concluded that the induced charge approach is consistent with medium sized basis set calculations whereas the induced dipole approach is consistent with large basis set calculations. This result is highly relevant to the concept of QM/MM model chemistries.     

Conformational studies of 2-methylbutyronitrile and 3-methyl-1-pentyne by vibrational spectroscopy and molecular mechanics

Vibrational spectra were obtained for the structurally similar compounds 2-methylbutyronitrile and 3-methyl-1-pentyne, and vibrational assignments were made with the aid of normal coordinate calculations. Molecular mechanics calculations were also made, and each compound was shown to exist as a mixture of three conformers, with the most stable conformer being the one with the two methyl groups trans to each other. Results of the calculations are given.