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Wim Klopper

Publications and source records attributed to Wim Klopper.

At least 19 recordsLinked to original sources
PubMed2006

Basis-set extensions for two-component spin-orbit treatments of heavy elements.

The accuracy of standard basis sets of quadruple-zeta and lower quality for the use in two-component self-consistent field procedures including spin-orbit coupling is investigated for the elements In-I and Au-At. Spin-orbit coupling leads to energetic and spatial splittings of inner shells, which are not described accurately with standard basis sets optimized for scalar relativistic calculations. This results in large errors in total atomic energies and significant errors in atomization energies of compounds containing these atoms. We show how these errors can be corrected by adding just a few steep sets of basis functions and demonstrate the quality of the resulting extended basis sets.

Astatine↗
PubMed2006

A comparison of linear and nonlinear correlation factors for basis set limit Møller-Plesset second order binding energies and structures of He2, Be2, and Ne2.

The basis set limit Møller-Plesset second-order equilibrium bond lengths of He2, Be2, and Ne2, accurate to 0.01a0, are computed to be 5.785a0, 5.11a0, and 6.05a0. The corresponding binding energies are 22.4+/-0.1, 2180+/-20, and 86+/-2 muE(h), respectively. An accuracy of 95% in the binding energy requires an aug-cc-pV6Z basis or larger for conventional Møller-Plesset theory. This accuracy is obtained using an aug-cc-pV5Z basis if geminal basis functions with a linear correlation factor are included and with an aug-cc-pVQZ basis if the linear correlation factor is replaced by exp(-gammar(12)) with gamma=1. The correlation factor r(12) exp(-gammar(12)) does not perform as well, describing the atom more efficiently than the dimer. The geminal functions supplement the orbital basis in the description of both the short-range correlation, at electron coalescence, and the long-range dispersion correlation and the values of gamma that give the best binding energies are smaller than those that are optimum for the atom or the dimer. It is important to sufficiently reduce the error due to the resolution of the identity approximation for the three- and four-electron integrals and we recommend the complementary auxiliary basis set method. The effect of both orbital and geminal basis set superposition error must be considered to obtain accurate binding energies with small orbital basis sets. In this respect, we recommend using exp(-gammar(12)) with localized orbitals and the original orbital-variant formalism.

Journal Article↗
PubMed2006

Extensions of r12 corrections to CC2-R12 for excited states.

As known since about two decades, R12 methods, which include terms linear in the interelectronic distance r(12) in the wave function, improve substantially the basis set convergence of the ground state correlation energy. In a previous study, however, it was found that the same approach does not give a similar systematic improvement if applied to excited states in the framework of coupled cluster response theory. In the present work, we examine the reason for this behavior and show that the inclusion of additional orbitals in the construction of the r(12) pair functions leads to an enhanced basis set convergence (and thus a balanced description) also for the excited states.

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PubMed2006

Growing graphene sheets from reactions with methyl radicals: a quantum chemical study.

Hydrogen abstraction reactions by methyl radicals on the zigzag and armchair edges of perylene are studied by density functional theory (DFT) to explore various growth pathways that seem to be in line with experimental observations. The DFT approach is validated by comparing the results obtained from calculations with six different functionals with those obtained from correlated ab initio methods, thereby emphasizing the calculation of reaction barriers. A useful compromise between accuracy and computational cost is provided by DFT, and possible pathways are studied in detail at this level of calculation. Our computational study is carried out by ordering, as a first step, all of the isomers that arise from the abstraction of one or two H atoms from 1,12-dimethyl-1,12-dihydroperylene and 3,4-dimethyl-3,4-dihydroperylene with respect to their energies. Subsequently, only those pathways that connect low-energy isomers are investigated. The calculations reveal that the selected pathways are favored thermodynamically, and also that the reaction barriers are somewhat higher than the energy locally available for the respective reaction. Notably, in the case of 3,4-dimethyl-3,4-dihydroperylene, the first two reaction steps have no or only a very low reaction barrier. The final conclusion of our study is that a cascade of reactions is possible that leads to the growth of a graphene sheet on a graphite surface.

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PubMed2006

Accurate computational determination of the binding energy of the SO3 x H2O complex.

Reliable thermochemical data for the reaction SO3 + H2O<-->SO3 x H2O (1a) are of crucial importance for an adequate modeling of the homogeneous H2SO4 formation in the atmosphere. We report on high-level quantum chemical calculations to predict the binding energy of the SO3 x H2O complex. The electronic binding energy is accurately computed to De = 40.9+/-1.0 kJ/mol = 9.8+/-0.2 kcal/mol. By using harmonic frequencies from density functional theory calculations (B3LYP/cc-pVTZ and TPSS/def2-TZVP), zero-point and thermal energies were calculated. From these data, we estimate D0 = -Delta H(1a)0(0 K) = 7.7+/-0.5 kcal/mol and Delta H(1a)0(298 K) = -8.3+/-1.0 kcal/mol.

Journal Article↗
PubMed2006

Basis-set extrapolation techniques for the accurate calculation of molecular equilibrium geometries using coupled-cluster theory.

To reduce remaining basis-set errors in the determination of molecular equilibrium geometries, a basis-set extrapolation (BSE) scheme is suggested for the forces used in geometry optimizations. The proposed BSE scheme is based on separating the Hartree-Fock and electron-correlation contributions and uses expressions obtained by straightforward differentiation of well established extrapolation formulas for energies when using basis sets from Dunning's hierarchy of correlation-consistent basis sets. Comparison with reference data obtained at the R12 coupled-cluster level [CCSD(T)-R12] demonstrates that BSE significantly accelerates the convergence to the basis-set limit, thus leading to improvements comparable to or even better than those obtained by increasing the cardinal number in the used basis set by one. However, BSE alone is insufficient to improve agreement with experiment, even after additional consideration of inner-shell correlation and quadruple-excitation effects (mean error and standard deviation with extrapolation are -0.014 and 0.047 pm in comparison with mean error and standard deviation of -0.002 and 0.036 pm without extrapolation). Improvement is obtained only when other contributions of similar magnitude as the BSE contributions (e.g., pentuple-excitation effects and relativistic effects) are also considered. A rather large discrepancy (of the order of a few tenths of a picometer) is observed for the F(2) molecule indicating an enhanced basis-set requirement for the various contributions in this case.

Journal Article↗
PubMed2006

A second-quantization framework for the unified treatment of relativistic and nonrelativistic molecular perturbations by response theory.

A formalism is presented for the calculation of relativistic corrections to molecular electronic energies and properties. After a discussion of the Dirac and Breit equations and their first-order Foldy-Wouthuysen [Phys. Rev. 78, 29 (1950)] transformation, we construct a second-quantization electronic Hamiltonian, valid for all values of the fine-structure constant alpha. The resulting alpha-dependent Hamiltonian is then used to set up a perturbation theory in orders of alpha(2), using the general framework of time-independent response theory, in the same manner as for geometrical and magnetic perturbations. Explicit expressions are given to second order in alpha(2) for the Hartree-Fock model. However, since all relativistic considerations are contained in the alpha-dependent Hamiltonian operator rather than in the wave function, the same approach may be used for other wave-function models, following the general procedure of response theory. In particular, by constructing a variational Lagrangian using the alpha-dependent electronic Hamiltonian, relativistic corrections can be calculated for nonvariational methods as well.

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PubMed2006

Density functional study of methyl chemisorption on polycyclic aromatic hydrocarbons.

The reactions of methyl radicals with large (up to C(96)H(24)) polycyclic aromatic hydrocarbons (PAHs) are studied by density functional calculations to shed light on the experimentally observed deposition of carbon on highly oriented pyrolytic graphite (HOPG), which occurs when hot HOPG (decorated by nanometre-sized defects) is exposed to methyl radicals. The equilibrium structures of the reaction products, together with transition structures for PAHs up to the size of phenanthroperylene, are determined using the density functionals B3LYP, TPSSh, BP86 and TPSS. The structures are analysed by computing the pi orbital axis vector (POAV) and the altitude of the reactive carbon above the molecular plane of the PAH. The strongest C-CH(3) bonds are found at the edges of the PAHs, where the s character of the C orbital involved in the bond is roughly 25 % (sp(3) hybrid orbital). Carbon atoms inside the PAH form bonds with the methyl radical through atomic orbitals with about 16 % s character in the POAV analysis. These bonds are much weaker than those at the edges of the PAH, while the reactive carbon has moved about 40 pm above the molecular plane. At the edges, the PAH carbon atoms do not leave the molecular plane to this extent. The computed barrier heights and geometrical parameters of the transition structures are in agreement with Hammond's postulate, and the relative energies of all of the equilibrium structures can be rationalized by Hückel molecular orbital (HMO) theory.

Journal Article↗
PubMed2006

Reactivity of titanium dimer and molecular nitrogen in rare gas matrices. Vibrational and electronic spectra and structure of Ti2N2.

The reactivity of diatomic titanium with molecular nitrogen has been investigated in rare gas matrices. The formation of Ti2N2 from the condensation of effusive beams of Ti and N2 in neon and argon matrices is observed after sample deposition. Our results also show that the in situ formation results from the spontaneous reaction at 9 K of ground state Ti2 with N2. Several low-lying excited states of Ti2N2 are also observed between 0.78 and 1.1 eV above the ground state, leading to a complex sequence of interacting vibronic transitions, merging into a broad continuum above 1.25 eV. Observations of Ti2(14)N2, Ti2(15)N2 and Ti2(14)N(15)N isotopic data enable the determination of all fundamental vibrations in the ground electronic state. Semi-empirical harmonic potential calculations lead to estimates of 3.22 N cm(-1) for the Ti-N bond force constant and 90 +/- 5 degrees for the bond angles. Comparisons with TiN diatomic data suggest a near square-planar structure with 175 +/- 3 pm TiN bond distance. Quantum chemical calculations at various levels indicate a 1A(g) ground state with a Ti-N distance close to 180 pm and 89 degrees for the NTiN bond angle, and give fundamental frequencies in excellent agreement with the experimentally observed values. Further MRCI calculations on all low-lying states enable an interpretation of the complex electronic spectrum in the NIR region.

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PubMed2006

A close look at short C-CH3...potassium contacts: synthetic and theoretical investigations of [M2Co2(mu3-OtBu)2(mu2-OtBu)4(thf)n] (M = Na, K, Rb, thf = tetrahydrofuran).

Agostic interactions of the type Si-CH3M+ (M = alkali metal) are frequently mentioned in discussions of solid-state structures of trimethylsilyl compounds and the purpose of this work was to elucidate if they also exist in the related tert-butyl species by using density functional theory. The compounds [M2Co2(mu3-OtBu)2(mu2-OtBu)4(thf)n] (M = Na, n = 2; M = K, n = 0; M = Rb, n = 1) have been synthesised and their crystal structures determined. Close contacts of methyl groups with K atoms are observed in the solid-state structure of [K2Co2(mu3-OtBu)2(mu2-OtBu)4], and calculations of the rotational barrier of a tert-butoxy group about the axis through the C-O bond were performed. It was shown that apparent short C-CH3K distances are in this case a consequence of the packing in the extended solid-state structure.

Journal Article↗
PubMed2006

Coupled-cluster response theory with linear-r12 corrections: the CC2-R12 model for excitation energies.

Coupled-cluster response theory for vertical excitation energies within the second-order approximate coupled-cluster singles-and-doubles model CC2, including linear-r(12) corrections, is derived and implemented for Ansatze 1 and 2 of R12 theory. An orthonormal auxiliary basis set is used for the resolution-of-the-identity approximation in order to calculate the three- and four-electron integrals needed in R12 theory. The basis set convergence is investigated for a selected set of atoms and small molecules and it is found that in many cases the convergence is not improved. An analysis of the different contributions to excitation energies shows that the present scheme for the construction of the R12 pair functions leads in response theory to an unbalanced description of ground- and excited-state wave functions and needs to be generalized to carry the high accuracy of R12 methods over to response theory.

Journal Article↗
PubMed2005

DFT study of fullerene dimers.

Several [2+2] dimerization products of a fullerene Cn (n=50, 52, 54, 56, 58, 60) in its most stable form are presented and discussed. In total, 34 dimers are studied. Only symmetric Cn-Cn dimers (no mixed products) are reported, and only dimers of the fullerenes C50 to C58 with bonds between C atoms in adjacent pentagons are considered. Geometries were optimized within the framework of density functional theory using the Becke-Perdew exchange-correlation functional (BP86) in combination with an empirical dispersive energy correction, which contributes significantly to the binding energy. The results are discussed in the context of the reactivity of adjacent pentagon sites. The lateral interaction between fullerenes is found to be stronger for C50 to C58 than for C60, which is consistent with recent experimental observations. Further, the possibility of polymer formation based on the investigated [2+2] reaction is addressed.

Journal Article↗
PubMed2005

Frequency-dependent hyperpolarizabilities of the Ne, Ar, and Kr atoms using the approximate coupled cluster triples model CC3.

The frequency-dependent electric field-induced second harmonic generation (ESHG) second hyperpolarizabilities gamma of neon, argon, and krypton are calculated using the approximate coupled cluster triples model CC3. Systematic basis set investigations are carried out to establish basis set limits, and scalar relativistic effects are accounted for by direct perturbation theory. To estimate higher-order correlation effects, full configuration-interaction results are used to benchmark the accuracy of CC3. The best theoretical estimates obtained thereby for the static second hyperpolarizabilities gamma(0) are 107.4, 1159, and 2589 a.u. for neon, argon, and krypton, respectively. These values as well as the results for the dispersion curve of the parallel component gamma( parallel) agree well with the latest experimental values from electric field-induced second harmonic generation. In addition, the dispersion of the perpendicular component gamma( perpendicular) and the hyperpolarizability ratios gamma( parallel)gamma( perpendicular) has been studied for the first time on a consistently correlated ab initio level. The analysis of the results indicates that, in particular for neon and krypton, the presently available experimental values are flawed.

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PubMed2005

New correlation factors for explicitly correlated electronic wave functions.

We have investigated the correlation factors exp(-zetar12), r12 exp(-zetar12), erfc(zetar12), and r12 erfc(zetar12) in place of the linear-r12 term for use in explicitly correlated electronic-structure methods. The accuracy obtained with all of these correlation factors is significantly greater than that obtained with the plain correlation factor r12. Polarization functions that are more diffuse than those of standard basis sets give even better results. The correlation factor exp(-zetar12) is very close to the optimum correlation factor for helium and outperforms the others.

Journal Article↗
PubMed2005

Solid C58 films.

A new solid material has been created in ultra high vacuum by utilizing the aggregation process of C58 molecules deposited onto highly oriented pyrolytic graphite from a mass selected low-energy ion beam comprising C58+. Cluster fluxes of up to 3x10(11) ions s-1 cm-2 with impinging kinetic energies of 6+/-0.5 eV were typically applied. Growth of the solid C58 phase proceeds according to the cluster-aggregation-based Volmer-Weber scenario where initially ramified 2D islands transform into 3D pyramid-like structures at higher coverages. The C58 films created exhibit much higher thermal stability than the C60 solid phase. Sublimation of C58 sets in at a temperature of 700 K. Ultraviolet photoionization spectra (He I, 21.2 eV) yield a molecular ionization potential in the range between 6.6 and 7 eV. Density functional and Hartree-Fock theories suggest that the formation of C58 dimers and higher multimers upon deposition/aggregation gives rise to the high thermal stability and unique electronic properties of this material.

Biomedical Engineering↗
PubMed2005

Analytic calculation of first-order molecular properties at the explicitly correlated second-order Moller-Plesset level: basis-set limits for the molecular quadrupole moments of BH and HF.

The analytic calculation of first-order properties has been implemented in the DALTON program at the level of explicitly correlated second-order Moller-Plesset perturbation theory (MP2-R12). The implementation has been accomplished for MP2-R12 theory based on standard approximations A, A', and B, using an auxiliary basis for the resolution-of-the-identity approximation, with and without a frozen core. MP2-R12 first-order molecular properties have been calculated analytically for a few small test molecules. For BH and HF, the MP2-R12 results were supplemented with explicitly correlated coupled-cluster calculations (but at this level from numerical derivatives) including vibrational and relativistic corrections.

Journal Article↗
PubMed2005

Global analytical potential energy surface for large amplitude nuclear motions in ammonia.

An analytical, full-dimensional, and global representation of the potential energy surface of NH(3) in the lowest adiabatic electronic state is developed, and parameters are determined by adjustment to ab initio data and thermochemical data for several low-lying dissociation channels. The electronic structure is calculated at the CASPT2 level within an [8,7] active space. The representation is compared to other recently published potential energy surfaces for this molecule. The present representation is distinguished by giving a qualitatively correct description of the potential energy for very large amplitude displacements of the nuclei from equilibrium. Other characteristic features of the present surface are the equilibrium geometries r(eq)(NH(3)) approximately 101.24 pm, r(eq)(NH(2)) approximately 102.60 pm, alpha(eq)(NH(3)) approximately 106.67 degrees, and the inversion barrier at r(inv)(NH(3)) approximately 99.80 pm and 1781 cm(-1) above the NH(3) minimum. The barrier to linearity in NH(2) is 11,914 cm(-1) above the NH(2)((2)B(1)) minimum. While the quartic force field for NH(3) from the present representation is significantly different from that of the other potential energy surfaces, the vibrational structures obtained from perturbation theory are quite similar for all representations studied here.

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