Showing papers in "Journal of Chemical Physics in 2001"

A long-range correction scheme for generalized-gradient-approximation exchange functionals

Abstract: We propose a new long-range correction scheme that combines generalized-gradient-approximation (GGA) exchange functionals in density-functional theory (DFT) with the ab initio Hartree–Fock exchange integral by using the standard error function. To develop this scheme, we suggest a new technique that constructs an approximate first-order density matrix that corresponds to a GGA exchange functional. The calculated results of the long-range correction scheme are found to support a previous argument that the lack of the long-range interactions in conventional exchange functionals may be responsible for the underestimation of 4s−3d interconfigurational energies of the first-row transition metals and for the overestimation of the longitudinal polarizabilities of π-conjugated polyenes in DFT calculations.

Approximate accelerated stochastic simulation of chemically reacting systems

Abstract: The stochastic simulation algorithm (SSA) is an essentially exact procedure for numerically simulating the time evolution of a well-stirred chemically reacting system. Despite recent major improvements in the efficiency of the SSA, its drawback remains the great amount of computer time that is often required to simulate a desired amount of system time. Presented here is the “τ-leap” method, an approximate procedure that in some circumstances can produce significant gains in simulation speed with acceptable losses in accuracy. Some primitive strategies for control parameter selection and error mitigation for the τ-leap method are described, and simulation results for two simple model systems are exhibited. With further refinement, the τ-leap method should provide a viable way of segueing from the exact SSA to the approximate chemical Langevin equation, and thence to the conventional deterministic reaction rate equation, as the system size becomes larger.

Time-dependent density functional theory for molecules in liquid solutions

Abstract: A procedure based on the polarizable continuum model (PCM) has been applied to reproduce solvent effects on electronic spectra in connection with the time-dependent density functional theory (TD-DFT). To account for solute-solvent interactions, a suitable operator has been defined, which depends on the solute electronic density and can be used to modify the TD-DFT equations for the calculation of molecular polarizabilities and of electronic transition energies. The solute-solvent operator has been derived from a PCM approach depending on solute electrostatic potential: Recently, it has been shown that such an approach also provides an excellent treatment of the solute electronic charge lying far from the nuclei, being particularly reliable for this kind of applications. The method has been tested for formaldehyde in water and in diethyl-ether, and then applied to the calculation of solvent effects on the n→π* transition of diazabenzenes in different solvents. The computed transition energies are in fairly...

Gaussian basis sets for use in correlated molecular calculations. X. The atoms aluminum through argon revisited

Abstract: For molecules containing second row atoms, unacceptable errors have been found in extrapolating dissociation energies calculated with the standard correlation consistent basis sets to the complete basis set limit. By carefully comparing the convergence behavior of De(O2) and De(SO), we show that the cause of these errors is a result of two inter-related problems: near duplication of the exponents in two of the d sets and a lack of high-exponent functions in the early members of the sets. Similar problems exist for the f sets (and probably in higher angular momentum sets), but have only a minor effect on the calculated dissociation energies. A number of approaches to address the problems in the d sets were investigated. Well behaved convergence was obtained by augmenting the (1d) and (2d) sets with a high-exponent function and by replacing the (3d) set by the (4d) set and the (4d) set by the (5d) set and so on. To ensure satisfactory coverage of both the L and M shell regions, the exponents of the new d se...

Introduction of n-electron valence states for multireference perturbation theory

Abstract: The present work presents three second-order perturbative developments from a complete active space (CAS) zero-order wave function, which are strictly additive with respect to molecular dissociation and intruder state free. They differ by the degree of contraction of the outer-space perturbers. Two types of zero-order Hamiltonians are proposed, both are bielectronic, incorporating the interactions between electrons in the active orbitals, therefore introducing a rational balance between the zero-order wave function and the outer-space. The use of Dyall’s Hamiltonian, which puts the active electrons in a fixed core field, and of a partially contracted formalism seems a promising compromise. The formalism is generalizable to multireference spaces which are parts of a CAS. A few test applications of the simplest variant developed in this paper illustrate its potentialities.

Theory of rubber friction and contact mechanics

Abstract: When rubber slides on a hard, rough substrate, the surface asperities of the substrate exert oscillating forces on the rubber surface leading to energy “dissipation” via the internal friction of the rubber. I present a discussion of how the resulting friction force depends on the nature of the substrate surface roughness and on the sliding velocity. I consider in detail the case when the substrate surface has a self affine fractal structure. I also present a theory for the area of real contact, both for stationary and sliding bodies, with elastic or elastoplastic properties. The theoretical results are in good agreement with experimental observation.

Correlation consistent valence basis sets for use with the Stuttgart–Dresden–Bonn relativistic effective core potentials: The atoms Ga–Kr and In–Xe

Abstract: We propose large-core correlation-consistent (cc) pseudopotential basis sets for the heavy p-block elements Ga–Kr and In–Xe. The basis sets are of cc-pVTZ and cc-pVQZ quality, and have been optimized for use with the large-core (valence-electrons only) Stuttgart–Dresden–Bonn (SDB) relativistic pseudopotentials. Validation calculations on a variety of third-row and fourth-row diatomics suggest them to be comparable in quality to the all-electron cc-pVTZ and cc-pVQZ basis sets for lighter elements. Especially the SDB-cc-pVQZ basis set in conjunction with a core polarization potential (CPP) yields excellent agreement with experiment for compounds of the later heavy p-block elements. For accurate calculations on Ga (and, to a lesser extent, Ge) compounds, explicit treatment of 13 valence electrons appears to be desirable, while it seems inevitable for In compounds. For Ga and Ge, we propose correlation consistent basis sets extended for (3d) correlation. For accurate calculations on organometallic complexes o...

Valence basis sets for relativistic energy-consistent small-core actinide pseudopotentials

Abstract: Gaussian (14s13p10d8f6g)/[6s6p5d4f3g] atomic natural orbital valence basis sets have been derived for relativistic energy-consistent small-core lanthanide pseudopotentials of the Stuttgart–Bonn variety. The existing set of lanthanide pseudopotentials has been supplemented by corresponding potentials for lanthanum and lutetium in order to arrive at a set analogous to the one available for the actinides. Multiconfiguration self-consistent field and subsequent multireference averaged coupled-pair functional calculations are presented for the first to fourth ionization potentials of all lanthanide elements. Molecular calibration studies using the coupled-cluster singles, doubles, and perturbative triples approach are reported for the monohydrides, monoxides, and monofluorides of lanthanum and lutetium.

Hydrogen bonding and stacking interactions of nucleic acid base pairs: A density-functional-theory based treatment

Abstract: We extend an approximate density functional theory (DFT) method for the description of long-range dispersive interactions which are normally neglected by construction, irrespective of the correlation function applied. An empirical formula, consisting of an R−6 term is introduced, which is appropriately damped for short distances; the corresponding C6 coefficient, which is calculated from experimental atomic polarizabilities, can be consistently added to the total energy expression of the method. We apply this approximate DFT plus dispersion energy method to describe the hydrogen bonding and stacking interactions of nucleic acid base pairs. Comparison to MP2/6-31G*(0.25) results shows that the method is capable of reproducing hydrogen bonding as well as the vertical and twist dependence of the interaction energy very accurately.

Calculating free energies using average force

Abstract: A new, general formula that connects the derivatives of the free energy along the selected, generalized coordinates of the system with the instantaneous force acting on these coordinates is derived. The instantaneous force is defined as the force acting on the coordinate of interest so that when it is subtracted from the equations of motion the acceleration along this coordinate is zero. The formula applies to simulations in which the selected coordinates are either unconstrained or constrained to fixed values. It is shown that in the latter case the formula reduces to the expression previously derived by den Otter and Briels. If simulations are carried out without constraining the coordinates of interest, the formula leads to a new method for calculating the free energy changes along these coordinates. This method is tested in two examples - rotation around the C-C bond of 1,2-dichloroethane immersed in water and transfer of fluoromethane across the water-hexane interface. The calculated free energies are compared with those obtained by two commonly used methods. One of them relies on determining the probability density function of finding the system at different values of the selected coordinate and the other requires calculating the average force at discrete locations along this coordinate in a series of constrained simulations. The free energies calculated by these three methods are in excellent agreement. The relative advantages of each method are discussed.

Parallel Douglas-Kroll Energy and Gradients in NWChem. Estimating Scalar Relativistic Effects Using Douglas-Kroll Contracted Basis Sets.

Abstract: A parallel implementation of the spin-free one-electron Douglas–Kroll–Hess (DKH) Hamiltonian in NWChem is discussed. An efficient and accurate method to calculate DKH gradients is introduced. It is shown that the use of a standard (nonrelativistic) contracted basis set can produce erroneous results for elements beyond the first row elements. The generation of DKH contracted cc-pVXZ(X=D,T,Q,5) basis sets for H, He, B–Ne, Al–Ar, and Ga–Br is discussed. The effect of DKH at the Hartree–Fock level on the bond distances, vibrational frequencies, and total dissociation energies for CF4, SiH4, SiF4, and Br2CO is discussed. It is suggested that the predominant effect of the scalar relativistic correction on the total dissociation energy can be calculated at the Hartree–Fock level if an adequate basis set is used.

The charge of glass and silica surfaces

Abstract: We present a method of calculating the electric charge density of glass and silica surfaces in contact with aqueous electrolytes for two cases of practical relevance that are not amenable to standard techniques: surfaces of low specific area at low ionic strength and surfaces interacting strongly with a second anionic surface.

Langevin stabilization of molecular dynamics

Abstract: In this paper we show the possibility of using very mild stochastic damping to stabilize long time step integrators for Newtonian molecular dynamics. More specifically, stable and accurate integrations are obtained for damping coefficients that are only a few percent of the natural decay rate of processes of interest, such as the velocity autocorrelation function. Two new multiple time stepping integrators, Langevin Molly (LM) and Brunger–Brooks–Karplus–Molly (BBK–M), are introduced in this paper. Both use the mollified impulse method for the Newtonian term. LM uses a discretization of the Langevin equation that is exact for the constant force, and BBK–M uses the popular Brunger–Brooks–Karplus integrator (BBK). These integrators, along with an extrapolative method called LN, are evaluated across a wide range of damping coefficient values. When large damping coefficients are used, as one would for the implicit modeling of solvent molecules, the method LN is superior, with LM closely following. However, with mild damping of 0.2 ps−1, LM produces the best results, allowing long time steps of 14 fs in simulations containing explicitly modeled flexible water. With BBK–M and the same damping coefficient, time steps of 12 fs are possible for the same system. Similar results are obtained for a solvated protein–DNA simulation of estrogen receptor ER with estrogen response element ERE. A parallel version of BBK–M runs nearly three times faster than the Verlet-I/r-RESPA (reversible reference system propagator algorithm) when using the largest stable time step on each one, and it also parallelizes well. The computation of diffusion coefficients for flexible water and ER/ERE shows that when mild damping of up to 0.2 ps−1 is used the dynamics are not significantly distorted.

A new parametrization of exchange–correlation generalized gradient approximation functionals

Abstract: A new “HCTH” generalized gradient approximation (GGA) functional is presented. Its 15 parameters have been refined against data from a training set containing 407 atomic and molecular systems. We believe that the much enhanced training set means that the new functional HCTH/407 has a much greater universality than previous GGA functionals. Statistical data is presented for the 407 set for the new functional, as well as other functionals.

Interaction energies of van der Waals and hydrogen bonded systems calculated using density functional theory: Assessing the PW91 model

Abstract: The performance of density functional theory using the Perdew and Wang’s exchange and correlation functionals (PW91) functional for the prediction of intermolecular interactionenergies is evaluated based on calculations on the neon, argon, methane, ethylene, and benzene dimers, as well as on 12 hydrogen bonded complexes (water, methanol, formic acid, hydrogen fluoride, ammonia, formamide dimers and water–methanol, water–dimethyl ether, water–formaldehyde, hydrogen cyanide–hydrogen fluoride, water–ammonia, water–formamide complexes). The results were compared with those obtained from Becke’s exchange and Lee, Yang, and Parr’s correlation functionals (BLYP), Becke’s 3 parameter functional combined with Lee, Yang, and Parr’s correlation functional (B3LYP), second order Mo/ller–Plesset perturbation (MP2), and coupled cluster calculations with single and double substitutions and with non-iterative triple corrections [CCSD(T)] calculations. The calculated interactionenergies show that the PW91 functional performs much better than the BLYP or B3LYP functionals. The error in the computed binding energies of the hydrogen bonded complexes is 20% in the worst case. The most demanding cases are the systems with large dispersion contributions to the binding energy, such as the benzene dimer. In contrast to the BLYP and B3LYP functionals which fail to account for dispersion, the PW91 functional at least partly recovers the attraction. The basis set dependence of the PW91 functionals is relatively small in contrast to the MP2 and CCSD(T) methods. Despite its occasional difficulties with dispersion interaction, the PW91 functional may be a viable alternative to the ab initio methods, certainly in situations where large complexes are being studied.

Higher excitations in coupled-cluster theory

Abstract: The viability of treating higher excitations in coupled-cluster theory is discussed. An algorithm is presented for solving coupled-cluster (CC) equations which can handle any excitation. Our method combines the formalism of diagrammatic many-body perturbation theory and string-based configuration interaction (CI). CC equations are explicitly put down in terms of antisymmetrized diagrams and a general method is proposed for the factorization of the corresponding algebraic expressions. Contractions between cluster amplitudes and intermediates are evaluated by a string-based algorithm. In contrast to our previous developments [J. Chem. Phys. 113, 1359 (2000)] the operation count of this new method scales roughly as the (2n+2)nd power of the basis set size where n is the highest excitation in the cluster operator. As a by-product we get a completely new CI formalism which is effective for solving both truncated and full CI problems. Generalization for approximate CC models as well as multireference cases is also discussed.

Towards extending the applicability of density functional theory to weakly bound systems

Abstract: While the attempts currently in progress in several groups for the rigorous inclusion of dispersion interactions in density functional theory (DFT) calculations mature and evolve into practical methodology, we contribute to the debate on the applicability of current functionals to the calculation of weak interaction with a systematic investigation of a few, typical, weakly bound systems. We have used both pure DFT and a hybrid approach in which the total interaction energy is partitioned into two parts: (a) the dispersion energy which, in a first approximation is the contribution due to intermonomer correlations and (b) all other interactions. The first component is accurately obtained at all distances of interest by means of a well-known damped multipolar expansion of the dispersion energy while for the second component different approximations will be evaluated. The need to avoid double counting a fraction of the correlation energy when using the hybrid approach and the choice of the appropriate functio...

Low-order scaling local electron correlation methods. IV. Linear scaling local coupled-cluster (LCCSD)

Abstract: A new implementation of local coupled-cluster theory with single and double excitations (LCCSD) is presented for which asymptotically all computational resources (CPU, memory, and disk) scale only linearly with the molecular size. This is achieved by: (i) restricting the correlation space for each electron pair to domains that are independent of molecular size; (ii) classifying the pairs according to a distance criterion and treating only strong pairs at the highest level; (iii) using efficient prescreening algorithms in the integral transformation and other integral-direct procedures; and (iv) neglect of small couplings of electron pairs that are far apart from each other. The errors caused by the various approximations are negligible. LCCSD calculations on molecules including up to 300 correlated electrons and over 1000 basis functions in C1 symmetry are reported, all carried out on a workstation.

Polarization consistent basis sets: Principles

Abstract: and CH4 molecules is analyzed using optimized basis functions. Based on these analysis a sequence of polarization consistent basis sets are proposed which should be suitable for systematically improving Hartree‐Fock and density functional energies. Analogous to the correlation consistent basis sets designed for correlation energies, higher angular momentum functions are included based on their energetical importance. In contrast to the correlation consistent basis sets, however, the importance of higher angular momentum functions decreases approximately geometric, rather than arithmetic. It is shown that it is possible to design a systematic sequence of basis sets for which results converge monotonic to the Hartree‐Fock limit. The primitive basis sets can be contracted by a general contraction scheme. It is found that polarization consistent basis sets provide a faster convergence than the correlation consistent basis sets. Results obtained with polarization consistent basis sets can be further improved by extrapolation. © 2001 American Institute of Physics. @DOI: 10.1063/1.1413524#

Electronic structure and bonding in metal phthalocyanines, Metal=Fe, Co, Ni, Cu, Zn, Mg

Abstract: Electronic structure and bonding in metal phthalocyanines (Metal=Fe, Co, Ni, Cu, Zn, Mg) is investigated in detail using a density functional method. The metal atoms are strongly bound to the phthalocyanine ring in each case, by as much as 10 eV. The calculated orbital energy levels and relative total energies of these D4h structures indicate that Fe and Co phthalocyanines have 3A2g and 2Eg ground states, respectively, but that these states are changed upon interaction with strong-field axial ligands. The valence electronic structures of Fe and Co phthalocyanines differ significantly from those of the others. The HOMOs in Fe, Co, and Cu phthalocyanine are metal 3d-like, whereas in Ni and Zn phthalocyanines, the HOMO is localized on the phthalocyanine ring. The first ionization removes an electron from the phthalocyanine a1u orbital in all cases, with very little sensitivity of the ionization energy to the identity of the metal. Whereas the first reduction in Fe and Co phthalocyanine occurs at the metal, i...

Prediction of electron paramagnetic resonance g values using coupled perturbed Hartree–Fock and Kohn–Sham theory

Abstract: A method for calculating the EPR g-tensor based on coupled perturbed Hartree–Fock (HF) and density functional theory (DFT) is presented. The one-electron molecular orbitals of a spin- unrestricted Slater determinant are calculated up to first order in the applied magnetic field. The g-tensor is evaluated as a mixed second derivative property with respect to the applied field and the electron magnetic moment. Thus, spin-polarization and spin–orbit coupling are simultaneously included in the calculation. The treatment focuses on orbitally nondegenerate molecules but is valid for a general ground state spin S and, for the first time, it is possible to include hybrid density functionals in the treatment. The relativistic mass and diamagnetic gauge corrections are also considered. An implementation of the theory is described. Extensive numerical calculations for a series of small molecules are reported with the Hartree–Fock (HF) method, the local density approximation (LSD), the generalized gradient approximation (GGA) and hybrid density functionals such as B3LYP and PBE0 and large Gaussian basis sets. Detailed comparison with available ab initio and DFT calculations are made. The results indicate that the hybrid functionals offer little or no improvement over the GGA functionals for small radicals made of light atoms. For transition metal complexes the situation is different. The hybrid functionals give, on average, better results than the GGA functionals but significant disagreement between theoretical and experimental g-shifts still remain. Overall, the results indicate that the present method is among the most accurate so far developed models for the prediction of g values.

``On''/``off'' fluorescence intermittency of single semiconductor quantum dots

Abstract: Single molecule confocal microscopy is used to investigate the detailed kinetics of fluorescence intermittency in colloidal II–VI (CdSe) semiconductor quantum dots. Two distinct modes of behavior are observed corresponding to (i) sustained “on” episodes (τon) of rapid laser absorption/fluorescence cycling, followed by (ii) sustained “off” episodes (τoff) where essentially no light is emitted despite continuous laser excitation. Both on-time and off-time probability densities follow an inverse power law, P(τon/off)∝1/τon/offm, over more than seven decades in probability density and five decades in time. Such inverse power law behavior is an unambiguous signature of highly distributed kinetics with rates varying over 105-fold, in contrast with models for switching between “on” and “off” configurations of the system via single rate constant processes. The unprecedented dynamic range of the current data permits several kinetic models of fluorescence intermittency to be evaluated at the single molecule level a...

Ab initio molecular dynamics: Propagating the density matrix with Gaussian orbitals

Abstract: We propose and implement an alternative approach to the original Car–Parrinello method where the density matrix elements (instead of the molecular orbitals) are propagated together with the nuclear degrees of freedom. Our new approach has the advantage of leading to an O(N) computational scheme in the large system limit. Our implementation is based on atom-centered Gaussian orbitals, which are especially suited to deal effectively with general molecular systems. The methodology is illustrated by applications to the three-body dissociation of triazine and to the dynamics of a cluster of a chloride ion with 25 water molecules.

On the calculation of entropy from covariance matrices of the atomic fluctuations

Abstract: An ad hoc method for calculating the entropy of a biomolecular system from the covariance matrix of the atomic fluctuations is analyzed. It is shown that its essential assumption can be eliminated by a quasiharmonic analysis. The computer time required for use of the latter is of the same order as that of the former.

Hybrid exchange-correlation functional determined from thermochemical data and ab initio potentials

Abstract: Multiplicative potentials, appropriate for adding to the non-multiplicative fractional orbital exchange term in the Kohn–Sham equations, are determined from correlated ab initio electron densities. The potentials are examined graphically and are used in conjunction with conventional thermochemical data to determine a new hybrid exchange-correlation functional, denoted B97-2. Calculations using B97-2 are compared with those from (a) the B97-1 functional [J. Chem. Phys. 109, 6264 (1998)], which has the same functional form and fraction of orbital exchange, but was fitted to just thermochemical data; and (b) the widely used B3LYP functional [J. Chem. Phys. 98, 5648 (1993)]. B97-2 atomization energies are close to those from B97-1; total electronic energies and ionization potentials are less accurate, but remain an improvement over B3LYP. Molecular structures from all three functionals are comparable. Static isotropic polarizabilities improve from B3LYP to B97-1 to B97-2; the B97-2 functional underestimates experimental values, which is consistent with the neglect of zero-point vibrational corrections. NMR shielding constants—determined as the conventional second derivative of the electronic energy—improve from B3LYP to B97-1 to B97-2. Shieldings determined directly from these DFT electron densities using the recently proposed MKS approach [Chem. Phys. Lett. 337, 341 (2001)] are two to three times more accurate than the conventional shieldings, and exhibit an analogous improvement across the three functionals. Classical reaction barriers for sixteen chemical reactions improve significantly from B3LYP to B97-1 to B97-2. The introduction of multiplicative potentials into semi-empirical hybrid functional development therefore appears beneficial.

A practical method for the use of curvilinear coordinates in calculations of normal-mode-projected displacements and Duschinsky rotation matrices for large molecules

Abstract: While use of curvilinear coordinates such as bond lengths and bond angles is common in accurate spectroscopic and/or scattering calculations for triatomic and other small molecules, their use for large molecules is uncommon and restricted. For large molecules, normal-mode analysis is feasible but gives sensible results only if the dynamical or spectroscopic process being considered involves changes in angular coordinates, including ring deformations, which are so small that the motion can be approximated by its tangential component. We describe an approximate method by which curvilinear normal-mode-projected displacements and hence Franck–Condon factors, reorganization energies, and vibronic coupling constants, as well as Duschinsky (Dushinsky, Duschinskii) rotation matrices, can be evaluated for large systems. Three illustrative examples are provided: (i) to understand the nature of the first excited state of water, illustrating properties of large-amplitude bending motions; (ii) to understand the nature of the “boat” relaxation of the first excited state of pyridine, illustrating properties of large-amplitude torsional motions; and (iii) to understand the coupling of vibrational modes to the oxidation of bacteriochlorophyll-a, a paradigm with many applications to both chemical and biological electron transfer, illustrating properties of macrocyclic deformations. The method is interfaced to a wide variety of computational chemistry computer programs.

Gaussian-3X (G3X) theory : use of improved geometries, zero-point energies, and Hartree-Fock basis sets.

Abstract: A modification of G3 theory incorporating three changes is presented. The three new features include: (1) B3LYP/6-31G(2df,p) geometry; (2) B3LYP/6-31G(2df,p) zero-point energy; and (3) addition of a g polarization function to the G3Large basis set for second-row atoms at the Hartree–Fock level. Extension of G3 theory in this manner, referred to as G3X, is found to give significantly better agreement with experiment for the G3/99 test set of 376 reaction energies. Overall the mean absolute deviation from experiment decreases from 1.07 kcal/mol (G3) to 0.95 kcal/mol (G3X). The largest improvement occurs for nonhydrogens. In this subset of energies the mean absolute deviation from experiment decreases from 2.11 to 1.49 kcal/mol. The increased accuracy is due to both the use of new geometries and the larger Hartree–Fock basis set. In addition, five other G3 methods are modified to incorporate these new features. Two of these are based on reduced orders of perturbation theory, G3X(MP3) and G3X(MP2), and have m...

Charge transfer and “band lineup” in molecular electronic devices: A chemical and numerical interpretation

Abstract: We present first-principles based calculation of charge transfer and “band lineup” in molecular electronic devices using as an example the device formed by a phenyldithiolate molecule bridging two gold electrodes and local-spin-density-functional theory with a Gaussian-type orbital basis. We show that significant charge transfer from the metal to the molecule occurs, reflecting the partially ionic character of the sulfur–gold bond and localized in the interfacial region. Such charge transfer increases the electrostatic potential in the molecule which changes the molecular energy level structures. The interaction between the molecular orbitals under the self-consistent potential and the surface metal states determines the lineup of molecular levels relative to the metal Fermi level. We also discuss the implications of our work on device engineering at the molecular scale.

Assessment of W1 and W2 theories for the computation of electron affinities, ionization potentials, heats of formation, and proton affinities

Abstract: The performance of two recent ab initio computational thermochemistry schemes, W1 and W2 theory [J. M. L. Martin and G. de Oliveira, J. Chem. Phys. 111, 1843 (1999)], is assessed for an enlarged sample of thermochemical data consisting of the ionization potentials and electron affinities in the G2-1 and G2-2 sets, as well as the heats of formation in the G2-1 and a subset of the G2-2 set. We find W1 theory to be several times more accurate for ionization potentials and electron affinities than commonly used (and less expensive) computational thermochemistry schemes such as G2, G3, and CBS-QB3: W2 theory represents a slight improvement for electron affinities but no significant one for ionization potentials. The use of a two-point A+B/L5 rather than a three-point A+B/CL extrapolation for the self-consistent field (SCF) component greatly enhances the numerical stability of the W1 method for systems with slow basis set convergence. Inclusion of first-order spin–orbit coupling is essential for accurate ioniza...

On the density matrix based approach to time-dependent density functional response theory

Abstract: The formulation of time-dependent Kohn–Sham (TDKS) response theory based on the noninteracting one-particle density matrix is reanalyzed in detail. A transparent derivation starting from a von-Neumann-type equation of motion for the TDKS one-particle density matrix is presented. The resulting scheme has a simple structure and leads to compact expressions for frequency-dependent response properties. A systematic treatment of excited states is inferred from a pole analysis of the frequency-dependent density matrix response. A variational principle for excitation energies is established. Excited state properties are straightforward by analytical derivative techniques. The theory provides a particularly suitable starting point for linear scaling implementations. Magneto-optic properties such as rotatory strengths and the rotatory dispersion are accessible from the TDKS current-density response. The formalism is gauge-invariant. Various new sum rules within the adiabatic approximation (AA) are derived. It is shown that there is no “assignment problem” for excited states in the density matrix based formulation; the common density based approach is included as a special case. Merits and limitations of the AA are discussed.