Frans B. van Duijneveldt

Accuracy of the Boys and Bernardi function counterpoise method

The performance of the Boys and Bernardi function counterpoise (FCP) method in eliminating the basis set superposition error (BSSE) is studied for He2, at R=5.6 a.u., within the supermolecular coupled electron pair approximation (CEPA‐1) method. A series of one‐electron Gaussian basis sets is designed that allows a systematic approach to the basis set limit value of the interaction energy. Every basis set contains a part suitable to reproduce the atomic correlation energy and a second part optimized for the dispersion interaction in He2. BSSE‐free correlated first‐order interaction energies [E(1)], calculated using perturbation theory, are reported for each of these sets. Extrapolation to the basis set limit yields a new value of 33.60±0.02 μH for E(1) at R=5.6 a.u. Extending previous work, the supermolecular CEPA‐1 interaction energies for each set are then compared to the total of E(1) and the BSSE‐free Mo/ller–Plesset second‐order dispersion energy reported previously. While for some basis sets the unc...

Gaussian basis sets which yield accurate Hartree—Fock electric moments and polarizabilities

Abstract Calculated dipole, quadrupole and octopole moments and dipole polarizabilities are reported for H2, CH4, NH3, H2O, HF, HCN, H2CO, H3CF and HCOOH in the Hartree—Fock approximation. Nine different basis sets are employed, ranging from a minimal basis to a large triply polarized basis. It is argued that in order to achieve an accuracy of 0.001 hartree in intermolecular interaction energies, the errors in computed monomer moments should be less than 0.03, 0.15 and 0.75 au for μ, θ and Ω, respectively, while α should be correct to within 2 a03. Measured by these standards, the DZPP and larger sets provide results close to the Hartree—Fock limit, but the commonly used energy-optimized DZP basis proves unsatisfactory. An alternative moment-optimized DZP′ basis is proposed which is shown to be the smallest basis yielding results acceptably close to the Hartree—Fock limit. Vibrational corrections are estimated for the hydrides and turn out to be small. Comparison w ith experiment then shows that correlation corrections are important, especially for μ and α. Details on contraction schemes and standard scale factors for the different basis sets are given in the Appendix.

Proper correction for the basis set superposition error in SCF calculations of intermolecular interactions

The effects of basis set extension to the space of the partner monomer in supermolecular SCF and perturbation calculations have been analysed for the model He2 and HeLi+ systems. In contrast to the suggestions of many authors it is demonstrated that the correction for the basis set superposition error should be calculated with the full basis set of the dimer without removing the occupied orbitals of the partner monomer. In fact, the enlargement of the monomer basis set by the partner occupied orbitals effectively improves the first-order exchange interaction energy. For the first-order electrostatic interaction energy any enlargement of a poor or medium size basis set of the monomer by the partner orbitals worsens its value.

Ab initio calculations on the geometry and OH vibrational frequency shift of cyclic water trimer

Abstract The equilibrium geometrical parameters R OO θ and χ of cyclic water trimer have been determined at the counterpoise corrected SCF+MP2 level in the ESPB basis within pseudo-C 3v symmetry. The final structure has short ( R OO =2.85 A) and strongly bent (θ=20°) hydrogen bonds. The non-bonded OH bonds are directed by χ=48° out of the OOO plane. The interaction energy (Δ E ) is −14.7 kcal mol −1 and the corresponding D 0 =10.2 kcal mol −1 . The likely error bars on these results are discussed. The second order polarization interactions in the trimer are markedly non-additive. The total non-additivity contributes −2.0 kcal mol −1 to the final Δ E , and it is responsible for a shortening of R OO by 0.07 A. Its largest effect (about −70 cm −1 ) is in the H-bonded OH vibrational frequency shift Δν OH , which at the equilibrium geometry is calculated to be −230 cm −1 . The shift is markedly sensitive to the angle χ, and vibrational averaging along this coordinate is expected to reduce Δν. The results therefore support Nelanders reassignment of the IR and Raman gas phase OH spectra, which implies Δν OH ≈ −175 cm −1 .

Ab initio potential energy surface for the low-frequency out-of-plane bending motions of the water trimer

Abstract A potential energy surface is presented for the out-of-plane bending angles χ 1 , χ 2 and χ 3 of the three non-hydrogen-bonded H atoms in the water trimer. Starting from a C 3h planar reference geometry interaction energies are evaluated using a previously developed SCF + MP2/ESPB approach at 69 geometries spanning the χ 1 , χ 2 , χ 3 space. These are fit to a sixth-degree 50-term polynomial expansion. The standard deviation of the fit is about 5 μ hartree. Stationary points are located and the barriers between them are determined. The physical origins of the barriers and the role of non-additivity are discussed on the basis of an energy partitioning of the interaction energy.

Methods for the calculation of n OH in OH-O hydrogen bonds

Ab initio calculations are reported for dimerization‐induced changes, Δk, in the harmonic force constant k of the H‐bonded OH in water dimer. Two dimer geometries are considered. Δk is obtained by considering the perturbation of a given monomer OH potential by the interaction energy in the dimer in question. The interaction energy is partitioned to identify the role of the various contributions to Δk. The sensitivity of Δk to the choice of the one‐electron basis set is studied by using five different basis sets, some of which have a set of bond functions in the HO bond. At the correlated level, correction for basis set superposition error is found to be essential. A comparison is made of the correlation contribution to Δk as given by the CEPA1, MP2, MP3, and MP4 methods. Of these, MP2 gives exaggerated results. Nevertheless, for economical and reasonably accurate calculations on large systems the MP2 approach in the ESPB basis set is advocated. The most accurate calculations yield a shift Δv0‐;1 of – 121 cm−1 for the uncoupled donor O‐H vibrational frequency in water dimer.

Ab initio calculations on weakly bonded systems

Large-basis CI calculations are performed on the van der Waals complexes Ar–HCl and (H2O)2. It is shown that a reasonable estimate of the CI basis-set superposition error is obtained from a ghost calculation involving the orbitals of the monomer and only the virtual orbitals of the ghost.Both basis-set superposition error corrections and size-consistency corrections are of vital importance to obtain a reliable potential-energy surface.For Ar–HCl the minima of the potential are predicted within 50 µhartree of the experimental surface, viz. –804 µhartree for the Ar–HCl orientation and –565 µhartree for the HCl–Ar geometry.The water dimer van der Waals minimum is estimated to be –4.9 kcal mol–1, which is less deep then experimentally derived minimum of –5.4 kcal mol–1, but just within the experimental error limit.

Ab initio calculations of exchange repulsion between two Ar atoms

The first order exchange energy for the Ar-Ar interaction has been calculated using an SCF wavefunction for Ar in a large gaussian basis set. It is shown that in the region of the van der Waals minimum more than 95 per cent of the first order exchange originates from the interaction of M-shell electrons and that three-orbital terms dominate this interaction. The terms of the order S 4 prove to be negligible. Interaction energies from SCF supermolecule calculations are also given.

Perturbation calculations on the variation of hydrogenbond energies with intermolecular distance

In previous perturbation calculations on the hydrogen bond [6] the short-range repulsion was seriously underestimated. It is shown that this can be remedied by choosing a more realistic model system and using exact 3-centre integrals.

Reductive activation and radical formation in a series of substituted benzoquinones: Thermodynamic and quantum chemical studies

Abstract The reduction of the quinone moiety, which is found in many anti-cancer agents, is still a poorly understood process. It is commonly assumed that the reduction of a quinone by the uptake of two electrons and two protons leads to the active hydroquinone form. For a better understanding of these reactions electrochemical data, obtained for a series of substituted benzoquinones, were analyzed. In addition quantum chemical calculations on the STO-3G level were performed to obtain data for the one- and two-electron reduction. From the electrochemical experiments, thermodynamic data can be obtained which show that the unfavourable free energy of electron uptake is overcome by the favourable binding of protons. Both reactions are influenced by the electronic properties of the substituents, as demonstrated by Hammett-type relationships between the free energy of these reactions and the sigma-para character of these substituents. In these relationships the reaction constant of the electron uptake process has an absolute value which is five times higher than that of the proton uptake. Quantum chemical calculations yielded energy values for the one-electron uptake, as expressed by U (LUMO), and for the total reduction process. Most of the results from these calculations are in accord with the thermodynamic study. The calculations also revealed a conformational change to take place upon reduction of NH 2 and N(CH 2 ) 2 substituted benzoquinones, which might be important for chemical and biological activity.