Interaction energies for the water dimer by supermolecular methods and symmetry-adapted perturbation theory: the role of bond functions and convergence of basis subsets

 Using a systematic series of basis sets in supermolecular and symmetry-adapted intermolecular perturbation theory calculations it is examined how interaction energies of various water dimer structures change upon addition and shifting of bond functions. Their addition to augmented double- and triple-zeta basis sets brings the sum of the electron correlation contributions to the second-order interaction energy nearly to convergence, while accurate first-order electrostatic and exchange contributions require better than augmented quadruple-zeta quality. A scheme which combines the different perturbation energy contributions as computed in different basis subsets performs uniformly well for the various dimer structures. It yields a symmetry-adapted perturbation theory value of −21.08 kJ/mol for the energy of interaction of two vibrationally averaged water molecules compared to −21.29 kJ/mol when the full augmented triple-zeta basis set is used throughout. Received: 4 November 1999 / Accepted: 8 February 2000 / Published online: 12 May 2000     

Efficient electronic structure calculations for systems of one-dimensional periodicity with the restricted Hartree–Fock–linear combination of atomic orbitals method implemented in Fourier space

 Formulas are presented for restricted Hartree–Fock (RHF) calculations on systems with periodicity in one dimension using a basis set of contracted spherical Gaussians. Applying Fourier-space and Ewald-type methods, all lattice sums appearing in the formulation have been brought to forms exhibiting accelerated convergence. Calculations have been carried out for infinite chains of Li₂ molecules and a poly(oxymethylene) chain. The methods used here yield results that are far more precise than corresponding direct-space calculations and for the first time show the vanishing of the RHF density of states at the Fermi level for situations of partial band occupancy. Our initial computational implementation was about 5 times slower than the fastest direct-space RHF code, but improvements in special-function evaluations and numerical integrations over the Brillouin zone are shown to remove this disparity in computing speed. Received: 20 August 1999 / Accepted: 17 January 2000 / Published online: 5 June 2000     

Molecular orbital study on the OH stretching frequency of the phenol dimer and its cation

Ab initio calculations were performed to investigate the structure and bonding of the phenol dimer and its cation, especially the OH stretching frequencies. Some stable structures of the phenol dimer and its cation were obtained at the Hartree–Fock level and were found to be in agreement with predictions based on spectroscopic investigations. In these dimers the phenol moieties are bound by a single OH⋯O hydrogen bond. The hydrogen bond is much stronger in the dimer cation than in the neutral dimer. The calculated binding energy of the phenol dimer in the most stable structure was 6.5–9.9 kcal/mol at various levels of calculation, compared with the experimental value of 5 kcal/mol or greater. The binding energy of the phenol dimer cation is more than 3 times (24.1–30.6 kcal/mol) as large as that of the neutral dimer. For the phenol dimer the OH stretching frequency of the proton-accepting phenol (PAP) is 3652 cm⁻¹ and that of the proton-donating phenol (PDP) is 3516 cm⁻¹; these are in agreement with observed values of 3654 and 3530 cm⁻¹, respectively. For the phenol dimer cation the OH stretching frequency of the PAP is 3616–3618 cm⁻¹ in comparison with an observed value of 3620 ± 3 cm⁻¹. That of the PDP in the dimer cation is calculated to be 2434–2447 cm⁻¹, which is 1210–1223 cm⁻¹ lower than that of the bare phenol. The large reduction in the OH stretching frequency of the PDP in the phenol dimer cation is attributed to the formation of a stronger hydrogen bond in the cation than in the neutral dimer. Received: 24 March 2000 / Accepted: 26 April 2000 / Published online: 11 September 2000     

How accurate can molecular dynamics/linear response and Poisson–Boltzmann/solvent accessible surface calculations be for predicting relative binding affinities? Acetylcholinesterase huprine inhibitors as a test case

This study examines the accuracy of molecular dynamics-linear response (MD/LR) and Poisson–Boltzmann/solvent accessible surface (PB/SAS) calculations to predict relative binding affinities. A series of acetylcholinesterase (AChE) huprine inhibitors has been chosen as a test system owing to the availability of free-energy (thermodynamic integration) calculations. The results obtained with the MD/LR approach point out a clear relationship between the experimental affinity and the electrostatic interaction energy alone for a subset of huprines, but the suitability of the MD/LR approach to predict the binding affinity of the whole series of compounds is limited. On the other hand, PB/SAS calculations show a marked dependence on both the computational protocol and the nature of the inhibitor–enzyme complex. Received: 2 August 2000 / Accepted: 8 September 2000 / Published online: 21 December 2000     

Electronic excitation of sulfur-organic compounds – performance of time-dependent density functional theory

 To define the scope and limitations of the time-dependent density functional theory (TDDFT) method, spectral absorption data of a series of about 100 neutral or charged sulfur-organic compounds with up to 24 non-hydrogen atoms and up to four sulfur atoms were calculated in the near-UV, visible and IR regions. Although the theoretical vertical transition energies correspond only approximately to experimental absorption band maxima, the mean absolute deviation was calculated to be 0.21 eV (1600 cm⁻¹). The main absorption features of various compounds with monocoordinated or dicoordinated sulfur atoms are well reproduced. As far as possible TDDFT results were compared with those of semiempirical Zerner's intermediate neglect of differential overlap (ZINDO/S) and of Pariser–Parr–Pople (PPP) calculations. TDDFT also works well in cases where the semiempirical methods fail. Limitations of TDDFT were encountered with calculations of spectral absorptions of dye molecules. The “vinylene shift” of polymethine dyes is not reproduced by TDDFT. Whereas electronic excitation energies delocalized polar and betainic chromophores are reasonably well reproduced, excitation energies of charge-transfer-type and charge-resonance-type transitions of weakly interacting composite chromophores are significantly underestimated. Received: 30 October 2000 / Accepted: 29 November 2000 / Published online: 22 May 2001     

Molecular modeling study of an abasic DNA undecamer duplex: d(GCGTGOGTGCG) · d(CGCACTCACGC)

Molecular mechanics calculations were performed with the JUMNA program on d(GCGTGOGTGCG) · d(CGCACTCACGC) where “O” is a modified abasic site: 3-hydroxy-2-(hydroxymethyl)tetrahydrofuran. From energy minimizations, for intrahelical or extrahelical positions of the unpaired thymine, various structures with different curvatures were obtained. Dynamical properties of this abasic sequence were also investigated through the controlled studies of DNA bending. Poisson-Boltzmann calculations were used to mimic the electrostatic effect of solvent on this sequence. The lowest energy structures show an acceptable agreement with experimental data. Received: 1 June 1998 / Accepted: 17 September 1998 / Published online: 10 December 1998     

Krylov subspace accelerated inexact Newton method for linear and nonlinear equations

A Krylov subspace accelerated inexact Newton (KAIN) method for solving linear and nonlinear equations is described, and its relationship to the popular direct inversion in the iterative subspace method [DIIS; Pulay, P., Chem Phys Lett 1980, 393, 73] is analyzed. The two methods are compared with application to simple test equations and the location of the minimum energy crossing point of potential energy surfaces. KAIN is no more complicated to implement than DIIS, but can accommodate a wider variety of preconditioning and performs substantially better with poor preconditioning. With perfect preconditioning, KAIN is shown to be very similar to DIIS. For these reasons, KAIN is recommended as a replacement for DIIS.     

Theoretical studies on the structure of M+BF−4 ion pairs M = Li+, NH+4: the role of electrostatics and electron correlation

A systematic investigation of the M⁺BF₄ ⁻ (M = Li or NH₄) ion-pair conformers has been carried out using an electrostatic docking model based on the molecular electrostatic potential topography of the free anion. This method provides a guideline for the subsequent ab initio molecular orbital calculations at the Hartree-Fock (HF) and second-order M?ller-Plesset perturbation theory (MP2) levels. It has been demonstrated that the model presented here yields more than 75% of the HF interaction energy when Li⁺ is the cation involved and more than 90% for the case of NH₄ ⁺. Inclusion of MP2 correlation in the HF-optimized geometries leads to stationary point geometries with different numbers of imaginary frequencies and in some places where the energies of two adjacent conformers are very close, the energy rank order is altered. The HF lowest-energy minima for the Li⁺BF₄ ⁻ and NH₄ ⁺BF₄ ⁻ show a bidentate and tridentate coordinating cation, respectively, whereas at the MP2 level, this ordering is reversed. Received: 9 September 1997 / Accepted: 5 November 1997     

Nature and importance of three-body interactions in the (H2O)2HCl trimer

 The nature and importance of nonadditive three-body interactions in the (H₂O)₂HCl cluster have been studied by the supermolecule coupled-cluster method and by symmetry-adapted perturbation theory (SAPT). The convergence of the SAPT expansion was tested by comparison with the results obtained from the supermolecule coupled-cluster calculations including single, double, and noniterative triple excitations [CCSD(T)]. It is shown that the SAPT results reproduce the converged CCSD(T) results within 3% at worst. The SAPT method has been used to analyze the three-body interactions for various geometries of the (H₂O)₂HCl cluster. It is shown that the induction nonadditivity is dominant, but it is partly quenched by the first-order Heitler–London-type exchange and higher-order exchange–induction/deformation terms. This implies that the classical induction term alone is not a reliable approximation to the nonadditive energy and that it will be difficult to approximate the three-body potential for (H₂O)₂HCl by a simple analytical expression. The three-body energy represents as much as 21–27% of the pair CCSD(T) intermolecular energy. Received: 15 September 1999 / Accepted: 3 February 2000 / Published online: 2 May 2000     

Hydration of platinum(II) complexes: a molecular mechanics study using atom-based force-field parameters

 This work is related to the interaction of water with two platinum(II) complexes, [Pt(NH₃)₄]²⁺ (denoted 1) and trans-[Pt(OH)₂(NH₃)₂] (denoted 2). We have considered two approaches of a water molecule to complexes 1 and 2 along the z-axis normal to the platinum(II) coordination plane: approach I, with the water oxygen oriented towards Pt, and approach II, with one water hydrogen directed towards Pt. Calculations have been performed within a molecular mechanics method based upon the interaction potentials proposed earlier by Claverie et al. and subsequently adjusted to results obtained with symmetry – adapted perturbational theory as well as with supermolecule (up to second-order M?ller–Plesset, MP2) methods. We discuss some possible simplifications of the potentials mentioned. The results relative to the hydration of Pt complexes 1 and 2 following approach I or II are discussed and compared to recent (MP2) ab initio energy–distance curves that we have recently determined. The MP2 calculations have shown that besides exchange–repulsion contributions, which are very similar in all hydrated complexes, approach I is mainly governed by electrostatics, whereas for approach II both electrostatic and dispersion contributions are important. Received: 16 September 1999 / Accepted: 3 February 2000 / Published online: 5 June 2000     

Near-degeneracy corrections for second-order perturbation theory: comparison of two approaches

 We compare two approximate perturbation schemes which were developed recently to deal with the (quasi)degeneracy problem in many-body perturbation theory. We conclude that although the two methods were introduced on quite different theoretical grounds, their performances are quite similar, and present an improvement over traditional perturbation theory. Both methods are cheap in computation time, but cannot compete in accuracy with more sophisticated schemes such as complete-active-space perturbation theory or dressed particle theories. Received: 1 August 2000 / Accepted: 2 August 2000 / Published online: 19 January 2001     

Comparison of solvent reaction field representations

 Alternative ways are examined for representing a reaction field to treat the important effects of long-range electrostatic interaction with a solvent in electronic structure calculations on the properties of a solute. Several extant boundary element methods for approximate representation of the solvent reaction field in terms of surface charge distributions are considered, and analogous new methods for approximate representation in terms of surface dipole distributions are introduced. Illustrative computational results are presented on representative small neutral and ionic solutes to evaluate the relative accuracy of various methods. Received: 2 July 2001 / Accepted: 10 September 2001 / Published online: 19 December 2001     

Following the streambed reaction on potential-energy surfaces: a new robust method

A simple procedure with low computational efforts is proposed to follow the reaction path of the potential-energy hypersurface (PES) starting from minima or saddle points. The method uses a modification of the so-called “following the reduced gradient” [Quapp W, Hirsch M, Imig O, Heidrich D (1998) J Comput Chem 19:1087]. The original method connects points where the gradient has a constant direction. In the present article the procedure is replaced by taking iterative varying directions of the gradient controlled by the last tangent of the searched curve. The resulting minimum energy path is that valley floor gradient extremal (GE) which belongs to the smallest (absolute) eigenvalue of the Hessian and, hence, that GE which usually leads along the streambed of a chemical reaction. The new method avoids third derivatives of the PES and obtains the GE of least ascent by second-order calculations only. Nevertheless, we are able to follow the streambed GE uphill or downhill. We can connect a minimum with its saddles if the streambed leads up to a saddle, or we find a turning point or a bifurcation point. The effectiveness and the characteristic properties of the new algorithm are demonstrated by using polynomial test surfaces, an ab initio PES of H₂O, and the analytic potentials of Lennard-Jones (LJ) clusters. By tracing the streambeds we located previously identified saddle points for LJ _N with N=3, 7, 8, and 55. Saddles for LJ _N with N=15, 20, and 30 as presented here are new results. Received: 8 March 2000 / Accepted: 17 July 2000 / Published online: 24 October 2000     

A first principles study of Pd deposition on the TiO2(1 1 0) surface

 The adsorption of isolated Pd atoms on the (1 1 0) surface of rutile TiO₂ was investigated through ab initio embedded-cluster calculations performed at the Hartree–Fock, second-order M?ller–Plesset and Becke's three parameter hybrid method with the Lee–Yang–Parr correlation functional levels. The role played by the magnitude of the surrounding charges used in the embedding procedure was carefully analyzed. The most stable site for adsorption consisted of a fourfold hollow site in which the Pd atom was coordinated to a fivefold Ti atom, two basal oxygens, and a protruding oxygen atom. However, the adsorption energies computed after basis set superposition error corrections seemed to favor a bridge site in which the Pd atom binds two protruding oxygen atoms. A periodic slab calculation using gradient-corrected functionals and plane-wave basis sets confirmed that for full coverage, the hollow site was more stable, although Pd displacement along the fivefold Ti channels was almost free. These results agree with the experimental data obtained from scanning tunneling microscopy. Finally, the adsorption energy computed from the periodic calculations was found to be 1.88 eV. Received: 14 September 1999 / Accepted: 3 February 2000 / Published online: 19 April 2000     

Harmonic analysis and discrete polynomials. From semiclassical angular momentum theory to the hyperquantization algorithm

Orthogonal polynomials of a discrete variable have been widely investigated as fundamental tools of numerical analysis. This work aims to propose the extension of their use to quantum mechanical problems. By exploiting both their connection with coupling and recoupling coefficients of angular momentum theory and their asymptotic relationships (semiclassical limit) with spherical and hyperspherical harmonics, a discretization procedure, the hyperquantization algorithm, has been developed and applied to the study of anisotropic interactions and of reactive scattering. One of the most appealing features of this method turns out to be a drastic reduction of memory requirements and computing time for extensive dynamical calculations. Examples of the application of this technique to stereodirected dynamics via an exact representation for the S matrix as well as to the characterization of molecular beam polarization are also illustrated. Received: 17 September 1999 / Accepted: 3 February 2000 / Published online: 5 June 2000     

A reexamination of virial coefficients of the Lennard-Jones fluid

The fourth-order virial coefficients have been calculated exactly to five decimal places for pure fluids of the Lennard-Jones potential at many points in the phase diagram. The calculations were performed through direct evaluation of the integrals, or diagrams, which make up the density expansion of the radial distribution function: included were the standard fast Fourier transform method of evaluating the simply connected diagrams and the evaluation of the bridge diagram for the fourth order in density by expansion in Legendre polynomials. The polynomial-order dependence of the bridge diagram calculation and the range dependence of the simply connected diagrams of the fourth order are found to have more significance than was thought from previous studies, especially in the low-temperature range. This result was confirmed by direct evaluation of the diagrams which construct the virial coefficients, as given by Rowlinson, Barker, and coworkers. This calculation confirmed that numerical convergence has not been achieved at the precision levels previously reported in the literature. These differences, though minor at higher temperatures, can be seen to be more significant at the lower temperature ranges. Received: 31 July 2000 / Accepted: 18 September 2000 / Published online: 21 December 2000     

Quasirelativistic valence ab initio calculation of the potential-energy curves for Cd–rare gas atom pairs

The results of large-scale valence ab initio calculations of the potential-energy curves for the ground states and several excited states of Cd–rare gas (RG) van der Waals molecules are reported. In the calculations, Cd²⁰⁺ and RG⁸⁺ cores are simulated by energy-consistent pseudopotentials, which also account for scalar-relativistic effects and spin-orbit interaction within the valence shell. The potential energies of the Cd–RG species in the ΛS coupling scheme have been evaluated by means of ab initio complete-active-space multiconfiguration self-consistent-field (CASSCF)/CAS multireference second-order perturbation theory (CASPT2) calculations with a total 28 valence electrons, but the spin-orbit matrix has been computed in a reduced configuration interaction space restricted to the CASSCF level. Finally, the Ω potential curves are obtained by diagonalization of the modified spin-orbit matrix (its diagonal elements before diagonalization substituted by the corresponding CASPT2 eigenenergies). The calculated potential curves, especially the spectroscopic parameters derived for the ground states and several excited states of the Cd–RG species are presented and discussed in the context of available experimental data. The theoretical results exhibit very good agreement with experiment. Received: 20 April 2000 / Accepted: 1 September 2000 / Published online: 21 December 2000     

Theoretical study of the role of low-barrier hydrogen bonds in enzyme catalysis: a model of proton transfer in serine protease

 A model of low-barrier hydrogen bonds (LBHBs) in enzymes has been studied by ab initio quantum mechanical calculations including the self-consistent reaction field solvent model. The hydrogen-bond strengths and the deprotonation energies for the hydrogen-bonded and non-hydrogen-bonded cis-urocanic acid were calculated at the HF/6-31 + G(d,p) level at various dielectric constants. The same calculations were performed for the α,β-dihydrourocanic acid to model the catalytic dyad of serine protease. The deprotonation energy of N^ɛ2 in α,β-dihydrourocanic acid is increased by formation of LBHBs and depends very much on the dielectric constant. This study suggests that the formation of LBHBs increases the basicity of the dyad, and the polarity change near the reaction center in the active site could help the proton abstraction from Ser 195 and the donation to the leaving group. Both the LBHBs and the environment can play crucial roles in the enzyme catalysis. Received: 8 March 2000 / Accepted: 3 January 2001 / Published online: 3 May 2001