Showing papers in "Theoretical Chemistry Accounts in 1997"

Auxiliary basis sets for main row atoms and transition metals and their use to approximate Coulomb potentials

Abstract: We present auxilliary basis sets for the atoms H to At – excluding the Lanthanides – optimized for an efficient treatment of molecular electronic Coulomb interactions. For atoms beyond Kr our approach is based on effective core potentials to describe core electrons. The approximate representation of the electron density in terms of the auxilliary basis has virtually no effect on computed structures and affects the energy by less than 10−4 a.u. per atom. Efficiency is demonstrated in applications for molecules with up to 300 atoms and 2500 basis functions.

RI-MP2: first derivatives and global consistency

Abstract: The evaluation of RI-MP2 first derivatives with respect to nuclear coordinates or with respect to an external electric field is described. The prefix RI indicates the use of an approximate resolution of identity in the Hilbert space of interacting charge distributions (Coulomb metric), i.e., the use of an auxiliary basis set to approximate charge distributions. The RI technique is applied to first derivatives of the MP2 correlation energy expression while the (restricted) Hartree-Fock reference is treated in the usual way. Computational savings by a factor of 10 over conventional approaches are demonstrated in an application to porphyrin. It is shown that the RI approximation to MP2 derivatives does not entail any significant loss in accuracy. Finally, the relative energetic stabilities of a representative sample of closed-shell molecules built from first and second row elements have been investigated by the RI-MP2 approach, and thus it is tested whether such properties that refer to potential energy hypersurfaces in a more global way can be described with similar consistency to the more locally defined derivatives.

The impact of the resolution of the identity approximate integral method on modern ab initio algorithm development

Abstract: The computation of the two-electron four-center integrals over gaussian basis functions is a significant component of the overall work of many ab initio methods used today. Improvements in the computational efficiency of the base algorithms have provided significant impact. Somewhat overlooked are methods that provide approximations to these integrals and their implementation in application software. A partial review of approximate integral techniques focused on the resolution of the identity (RI) four-center, two-electron integral approximation is given. The past and current uses of the RI algorithms are presented along with possibilities for further exploitation of the technology.

Approximate molecular relativistic Dirac-Coulomb calculations using a simple Coulombic correction

Abstract: A simple point-charge model is used to correct molecular four-component Dirac-Coulomb calculations which neglect two-electron integrals over the small components of the wave function. The calculated valence properties show no degeneration relative to the full calculation, while a speed-up factor of 3 is obtained.

The Beijing four-component density functional program package (BDF) and its application to EuO, EuS, YbO and YbS

Abstract: A four-component density functional program package (Beijing Density Functional), suitable for the calculation of total-energy-related chemical properties of systems containing heavy atoms, was developed. The code is based on modern sophisticated exchange-correlation functionals and was applied to calculate the spectroscopic constants of the lanthanide diatomic molecules of EuO, EuS, YbO and YbS. It is suggested that the experimental bond lengths for EuS and YbS, derived from empirical interpolations, need to be revised. Relativistic effects on the electronic structure are discussed and compared with results from previous work. The involvement of the lanthanide valence orbitals in chemical bonding is investigated with a newly developed population and bonding analysis approach.

Benchmark calculations with correlated molecular wave functions XII. Core correlation effects on the homonuclear diatomic molecules B2-F2

Abstract: Using systematic sequences of the newly developed correlation consistent core-valence basis sets from cc-pCVDZ through cc-pCV6Z, the spectroscopic constants of the homonuclear diatomic molecules containing first row atoms, B–F, are calculated both with and without inclusion of 1s correlation. Internally contracted multireference configuration interaction (IC-MRCI) and singles and doubles coupled cluster (CCSD) theory with a perturbational estimate of connected triple excitations, CCSD(T), have been investigated. By exploiting the convergence of the correlation consistent basis sets, complete basis set (CBS) limits have been estimated for total energies, dissociation energies, equilibrium geometries, and harmonic frequencies. Based on the estimated CBS limits the effects of 1s correlation on D e (kcal/mol), r e (A), and ω e (cm−1) are: +1.1, −0.0070, +10 for B2; +1.5, −0.0040, +13 for C2; +0.9, −0.0020, +9 for N2; +0.3, −0.0020, +6 for O2; and −0.1, −0.0015, +1 for F2.

A systematic ab initio study of the water dimer in hierarchies of basis sets and correlation models

Abstract: A systematic, high-level ab initio investigation of the water dimer has been performed. The oxygen-oxygen bond distance has been estimated to be around 2.90 A, about 0.05 A shorter than the experimentally estimated distance, challenging the accuracy of the latter. The interaction energy has been obtained at −5.0±0.1 kcal/mol, which compares favourably with the experimentally estimated value of −5.4±0.7 kcal/mol. The importance of employing basis sets that include diffuse functions in correlated calculations on hydrogen-bonded systems is confirmed. In correlated calculations on the water dimer and the hydrogen fluoride dimer, the counterpoise-corrected interaction energies converge considerably slower towards the basis set limit than do the uncorrected energies, provided that the correlation-consistent basis sets are augmented with diffuse functions.

Direct SCF direct static-exchange calculations of electronic spectra

Abstract: Applications of the direct SCF direct static-exchange method are reviewed for three different types of systems (free molecules, polymers, and surface adsorbates) and for six types of spectroscopy (X-ray absorption-, -emission-, and -shake-up spectroscopy, ultraviolet photoelectron emission, X-ray Raman and circular dichroism spectroscopy.

Determination of diabatic states through enforcement of configurational uniformity

Abstract: . An electronic structure-based construction of diabatic states from adiabatic states is formulated that is applicable when individual diabatic states contain several dominant configurations. It is accomplished by maximizing the electronic uniformity of the diabatic states with respect to their dominant configurations throughout the entire nuclear coordinate region. The configurations are generated from unambiguously defined diabatization-adapted molecular orbitals. The orthogonal transformation from adiabatic to diabatic states is deduced by an intrinsic analysis of the adiabatic CI coefficients, without calculating matrix elements of additional, derivative or non-derivative operators. The practicality of the method is demonstrated by applying it to the conical intersection region of the 11 A 1 and 21 A 1 states of ozone.

Approximate second order method for orbital optimization of SCF and MCSCF wavefunctions

Abstract: A quasi-Newton method involving a diagonal guess orbital hessian with iterative updates has been proposed recently by Almlof for the optimization of closed shell self-consistent field (SCF) wavefunctions. The technique is extended in the present work to more general wavefunctions, ranging from open shell SCF through multiconfigurational SCF. A number of examples are presented to show that convergence for closed and open shell SCF rivals conventional direct inversion in the iterative subspace (DIIS). For multiconfigurational SCF wavefunctions, the method presented here requires more iterations than an exact second order program, but since each iteration is substantially faster, leads to a more efficient overall program.

A universal model for the quantum mechanical calculation of free energies of solvation in non-aqueous solvents

Abstract: The SM5.4 quantum mechanical solvation model has been extended to calculate free energies of solvation in virtually any organic solvent. Electrostatics and solute-solvent polarization are included self-consistently by the generalized Born equation with class IV charges, and first-solvation-shell effects are modeled in terms of solvent-accessible surface areas that depend on solute geometries and four solvent descriptors. The inclusion of solvent properties in the first-solvation-shell term provides a model that predicts accurate solvation free energies in any solvent for which those properties are known. The model was developed using 1786 experimentally measured solvation free energies for 206 solutes in one or more of 90 solvents. Parameters have been obtained for solutes containing H, C, N, O, F, S, Cl, Br, and I, and the solutes used for parameterization span a wide range of organic functional groups. Solvents used in the parameterization contain H, C, N, O, F, P, S, Cl, Br, and I and include the most common organic solvents. Two general parameterizations are presented here, one for use with the AM1 Hamiltonian (SM5.4/AM1) and one for use with the PM3 Hamiltonian (SM5.4/PM3). In each case, one parameter is specially re-optimized for benzene and toluene to reduce systematic errors for these solvents. Chloroform is also treated with special parameters. The final mean unsigned error for both the SM5.4/AM1 and SM5.4/PM3 parameterizations is less than 0.5kcalmol−1 over the entire data set of 1786 free energies of solvation in 90 organic solvents.

Variational transition state theory without the minimum-energy path

Abstract: In this paper we propose a method for carrying out variational transition state theory calculations without first obtaining a converged minimum-energy path (MEP). We illustrate the method in two ways, first of all by employing an unconverged MEP and secondly by using a dynamically optimized distinguished reaction path. Preliminary tests of the algorithm for the reactions OH+H2→H2O+H and C2H5→C2H4+H are very encouraging.

Direct relativistic MP2: properties of ground state CuF, AgF and AuF

Abstract: A computer program for the calculation of the MP2 energy correction for a Kramers-restricted Dirac-Hartree-Fock four component wave-function is presented. In the spirit of the integral-driven direct SCF scheme the algorithm has been developed as direct MP2, calculating integrals as they are needed and avoiding the integral storage bottle-neck of conventional MP2. Relativistic MP2 is applied to ground state (1Σ+) CuF, AgF and AuF.

Kinetic partitioning mechanism as a unifying theme in the folding of biomolecules

Abstract: We describe a unified approach to describe the kinetics of protein and RNA folding. The underlying conceptual basis for this framework relies on the notion that biomolecules are topologically frustrated due to their polymeric nature and due to the presence of conflicting energies. As a result, the free energy surface (FES) has, in addition to the native basin of attraction (NBA), several competing basins of attraction. A rough FES results in direct and indirect pathways to the NBA, i.e., a kinetic partitioning mechanism (KPM). The KPM leads to a foldability principle according to which fast folding sequences are characterized by the folding transition temperature T F being close to the collapse transition temperature T θ, at which a transition from the random coil to the compact structure takes place. Biomolecules with T θ ≈ T F , such as small proteins and tRNAs, are expected to fold rapidly with two-state kinetics. Estimates for the multiple time scales in KPM are also given. We show that experiments on proteins and RNA can be understood semi-quantitatively in terms of the KPM.

Multiple basis sets in calculations of triples corrections in coupled-cluster theory

Abstract: Multiple basis sets are used in calculations of perturbational corrections for triples replacements in the framework of single-reference coupled-cluster theory. We investigate a computational procedure, where the triples correction is calculated from a reduced space of virtual orbitals, while the full space is employed for the coupled-cluster singles-and-doubles model. The reduced space is either constructed from a prescribed unitary transformation of the virtual orbitals (for example into natural orbitals) with subsequent truncation, or from a reduced set of atomic basis functions. After the selection of a reduced space of virtual orbitals, the singles and doubles amplitudes obtained from a calculation in the full space are projected onto the reduced space, the remaining set of virtual orbitals is brought into canonical form by diagonalizing the representation of the Fock operator in the reduced space, and the triples corrections are evaluated as usual. The case studies include the determination of the spectroscopic constants of N2, F2, and CO, the geometry of O3, the electric dipole moment of CO, the static dipole polarizability of F−, and the Ne⋯Ne interatomic potential.

Kohn-Sham potentials corresponding to Slater and Gaussian basis set densities.

Abstract: A new method based on linear response theory is proposed for the determination of the Kohn-Sham potential corresponding to a given electron density. The method is very precise and affords a comparison between Kohn-Sham potentials calculated from correlated reference densities expressed in Slater-(STO) and Gaussian-type orbitals (GTO). In the latter case the KS potential exhibits large oscillations that are not present in the exact potential. These oscillations are related to similar oscillations in the local error function δ i (r)=(−ɛ i )ϕ i (r) when SCF orbitals (either Kohn-Sham or Hartree-Fock) are expressed in terms of Gaussian basis functions. Even when using very large Gaussian basis sets, the oscillations are such that extreme care has to be exercised in order to distinguish genuine characteristics of the KS potential, such as intershell peaks in atoms, from the spurious oscillations. For a density expressed in GTOs, the Laplacian of the density will exhibit similar spurious oscillations. A previously proposed iterative local updating method for generating the Kohn-Sham potential is evaluated by comparison with the present accurate scheme. For a density expressed in GTOs, it is found to yield a smooth “average” potential after a limited number of cycles. The oscillations that are peculiar to the GTO density are constructed in a slow process requiring very many cycles.

A simple correction to final state energies of doublet radicals described by equation-of-motion coupled cluster theory in the singles and doubles approximation (Erratum)

Abstract: A computationally inexpensive energy correction is suggested for radicals described by the equation-of-motion coupled cluster method for ionized states in the singles and doubles approximation (EOMIP-CCSD). The approach is primarily intended for doublet states that are qualitatively described by Koopmans' approximation. Following a strategy similar to those used in multireference coupled cluster theory, the proposed correction accounts for all correlation effects through third order in perturbation theory and also includes selected contributions to higher-order energies. As an initial test of the numerical performance of the method, total energies and energy splittings are calculated for some small prototype radicals.

Corannulene-based fullerene fragments C20H10-C50H10: when does a buckybowl become a buckytube?

Abstract: An ab initio study of the structural and physical properties of fullerene fragments based on corannulene shows a distinct defining point between bowl and tube-like character.

Contracted polarization functions for the atoms helium through neon

Abstract: Contracted Gaussian-type function sets are proposed for polarization functions of the atoms helium through neon, with the exception of lithium. A segmented contraction scheme is used for its compactness and computational efficiency. The contraction coefficients and orbital exponents are fully optimized to minimize the difference from accurate atomic natural orbitals. The present polarization functions yield more than 99% of atomic correlation energies predicted by accurate natural orbitals of the same size.

Solvent effects on the nπ* transition of pyrimidine in aqueous solution

Abstract: A hybrid quantum mechanical and molecular mechanical potential is used in Monte Carlo simulations to examine the solvent effects on the electronic excitation energy for the n→π* transition of pyrimidine in aqueous solution. In the present study, the pyrimidine molecule is described by the semi-empirical AM1 model, while the solvent molecules are treated classically. Two sets of calculations are performed: the first involves the use of the pairwise three-point charge TIP3P model for water, and the second computation employs a polarizable many-body potential for the solvent. The latter calculation takes into account the effect of solvent polarization following the solute electronic excitation, and makes a correction to the energies determined using pairwise potentials, which neglects such fast polarization effects and overestimates the solute-solvent interactions on the Franck-Condon excited states. Our simulation studies of pyrimidine in water indicate that the solvent charge redistribution following the solute electronic excitation makes modest corrections (about −130␣cm−1) to the energy predicted by using pairwise potentials. Specific hydrogen bonding interactions between pyrimidine and water are important for the prediction of solvatochromic shifts for pyrimidine. The computed n→π* blue shift is 2275±110 cm−1, which may be compared with the experimental value (2700 cm−1) from isooctane to water.

A theoretical study of the N8 cubane to N8 pentalene isomerization reaction

Abstract: The isomerization reaction of cubic N8 to the planar bicyclic structure analogous to pentalene has been investigated using multiconfigurational self-consistent field and second-order perturbation theory (CASPT2). Comparative calculations using density functional theory have also been performed. Five local minima on the energy surface have been found, and the transition states between each two consecutive minima have been determined. The results show that all steps in the isomerization process, except one, can proceed via a set of transition states with moderately high energy barriers (10–20 kcal/mol).

The inner-hydrogen migration in free base porphyrin

Abstract: We present the results of a comprehensive study on the inner-hydrogen migration in free base porphyrin, using density functional theory with the hybrid B3-LYP exchange-correlation functional, and both the 6-31G(d ) and a triple-zeta double-polarization (TZ2P) basis set. The latter computations, involving 726 contracted functions, are the largest calculations on this system to date. Full geometry optimization was carried out for the cis and trans minima, the transition state for trans-cis isomerization, and the symmetric stationary point for the synchronous trans-trans isomerization. All stationary points were characterized by vibrational analysis. Our results strongly support the conclusion, reached by earlier workers, that trans-trans hydrogen transfer occurs in a two-step process via a cis intermediate. With the TZ2P basis and including zero-point effects for the -h 2 isotopomer, the trans-cis barrier height is 13.1 kcal/mol, the cis-trans energy difference is 8.1 kcal/mol and the reverse cis-trans barrier height is 5.0 kcal/mol. The trans-cis barrier height agrees well with the value of Braun et al. (J Am Chem Soc (1996) 118: 7231) obtained from NMR line shapes and a modified Bell tunneling model, but our cis-trans energy difference is higher, and the reverse barrier is lower, than the values of Braun et al. Tunneling precludes the existence of -h 2 cis-porphyrin as an observable species, but the -d 2 and, especially, -t 2 isotopomers might be observable at low temperatures if the reverse barrier is higher than our calculated value. We predict the theoretical vibrational spectrum of cis-porphyrin and suggest that IR active modes at 566 cm−1 and 2333 cm−1 in the -d 2 isotopomer may be used to detect the presence of the cis intermediate.

Expectation values of operators in approximate two-component relativistic theories

Abstract: Two methods for the evaluation of expectation values with approximate two-component relativistic functions are analysed. The first of them is based on the change of picture for the operator whose expectation value is to be calculated and associated with approximations leading to the given two-component relativistic wave function. This method, though hardly used in numerical calculations, gives the expectation values that directly reflect the accuracy of the wave function used for their calculation. The second method, most commonly used in calculations, neglects the picture change and is shown always to introduce an error of the order of α2, where α is the fine structure constant. This error is present independently of the accuracy of the approximate two-component wave function. The perturbation formalism developed in this paper is illustrated by calculations of relativistic corrections to the expectation values of r−1 for arbitrary states of hydrogenic ions.

Multireference perturbation CI I. Extrapolation procedures with CAS or selected zero-order spaces

Abstract: We discuss the “three class” approximation to full multireference perturbation CI, which greatly reduces the computational effort by restricting the summation of diagrams to determinants belonging to a subspace of the zero-order space. In the framework of the CIPSI algorithm, we propose a new extrapolation procedure allowing recovery of the full “two class” results. The new procedure is applied to complete active spaces (CAS) and to individually selected zero-order spaces. Comparison with a full two class calculation on a CAS shows a reduction of computer time of one or two orders of magnitude in the tests presented here, with an accuracy in the order of 0.1 kcal/mol. Our procedure can thus compete with the CASPT2 algorithm, specifically conceived to deal with CAS. In the case of selected zero-order spaces, the speed-up is less dramatic but the method still retains its advantages.

Hydrogen transfer in the presence of amino acid radicals

Abstract: Quantum chemical model studies of hydrogen transfer between amino acids in the presence of radicals have been performed using the density functional theory method B3LYP. These studies were made to investigate alternative mechanisms to the conventional electron transfer-proton transfer mechanisms. The model reactions studied are such that the net result of the reaction is a transfer of one neutral hydrogen atom. Simple models are used for the amino acids. Three different mechanisms for hydrogen transfer were found. In the first of these, a transition state with a protonated intermediate residue is found, in the second, the proton and electron take different paths and in the third, a neutral hydrogen atom can be identified along the reaction pathway. A key feature of these mechanisms is that charge separation is always kept small in contrast to the previous electron transfer-proton transfer mechanisms. It is therefore proposed that the processes normally considered as electron transfer in the biochemical literature could in fact be better explained as hydrogen atom transfer, at least in cases where a suitable hydrogen bonded chain pathway is present in the protein. The presence of such chains in principle allows the protein to define the path of net hydrogen transfer. Another important conclusion is that standard quantum chemical methods can be used to treat these mechanisms for hydrogen transfer, allowing for an accurate representation of the geometric changes during the reactions.

Solvent effects on tautomerism equilibria in heterocycles

Abstract: . High-level ab initio quantum mechanical methods have been used to analyze the tautomeric preferences in the gas phase and in aqueous solution of three important five-member heterocycles: 4-(5-)methylimidazole, 5-hydroxyisoxazole, and 3-hydroxypyrazole. Solvent effects have been introduced by means of self-consistent reaction field (SCRF) calculations at the ab initio level using our parametrized version of the polarizable continuum model developed by Miertus, Scrocco and Tomasi (MST), including geometry relaxation upon solvation. The extent to which the MST model, and SCRF methods in general, are suitable for the study of processes of this type is discussed.

Multireference perturbation CI II. Selection of the zero-order space

Abstract: In this paper, the second of a series devoted to multi-reference perturbation CI, we tackle the problem of the appropriate selection of the zero-order space in CIPSI calculations. We propose a new selection procedure, explicitly devised in order to obtain a balanced description for different electronic states and nuclear geometries. To this aim, we define numerically the quality of the zero-order space by means of a suitable parameter σ, which is the square norm of the perturbative correction of the wavefunction. The zero-order space is expanded stepwise so as to obtain the same target σ for all states and geometries. This strategy is applied to the calculation of dissociation, activation and transition energies. It yields a much better convergence of perturbative and zero-order results, when compared with the selection procedure previously used.

Molecular integrals over Gaussian-type geminal basis functions

Abstract: We present formulas for the evaluation of molecular integrals over basis functions with an explicit Gaussian dependence on interelectronic coordinates. These formulas use expansions in Hermite Gaussian functions and represent an extension to the work of McMurchie and Davidson to two-electron basis functions. Integrals that depend on the coordinates of up to four electrons are discussed explicitly. A key feature of this approach is that it allows full exploitation of the shell structure of the orbital part of the basis.

A determinantal approach to spin-orbit configuration interaction

Abstract: A general configuration interaction (CI) algorithm incorporating one- and two-electron spin-orbit operators is presented. The algorithm is determinant based and enables the use of highly vectorized non-relativistic algorithms in the most operation-intensive part. Excitations between α and β spin orbitals are avoided in the time consuming parts by performing separate S + and S − operations. The relativistic CI expansions are often very large, so the algorithms require only the presence of segments of vectors in memory. Double-group symmetry is fully accounted for and time-reversal symmetry is exploited for both even and odd numbers of electrons.

Relativistic effects in nuclear quadrupole coupling

Abstract: Relativistic effects strongly influence the nuclear quadrupole coupling of atoms, molecules or solids. As first shown by Casimir in 1936, in the atomic or single-centre case, for the two states j=l±s, three radial electric-field-gradient (EFG) integrals, R++,R+−, and R, must be introduced. The relativistic correction factors, defined for operator \(\) as $$$$