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It is demonstrated that a set of local orthonormal Hartree-Fock (HF) molecular orbitals can be obtained for both the occupied and virtual orbital spaces by minimizing powers of the orbital variance using the trust-region algorithm. For a power exponent equal to one, the Boys localization function is obtained. For increasing power exponents, the penalty for delocalized orbitals is increased and smaller maximum orbital spreads are encountered. Calculations on superbenzene, C60, and a fragment of the titin protein show that for a power exponent equal to one, delocalized outlier orbitals may be encountered. These disappear when the exponent is larger than one. For a small penalty, the occupied orbitals are more local than the virtual ones. When the penalty is increased, the locality of the occupied and virtual orbitals becomes similar. In fact, when increasing the cardinal number for Dunning's correlation consistent basis sets, it is seen that for larger penalties, the virtual orbitals become more local than the occupied ones. We also show that the local virtual HF orbitals are significantly more local than the redundant projected atomic orbitals, which often have been used to span the virtual orbital space in local correlated wave function calculations. Our local molecular orbitals thus appear to be a good candidate for local correlation methods. [ABSTRACT FROM AUTHOR]

Coupled cluster calculations can be carried out for large molecular systems via a set of calculations that use small orbital fragments of the full molecular orbital space. The error in the correlation energy of the full molecular system is controlled by the precision in the small fragment calculations. The determination of the orbital spaces for the small orbital fragments is black box in the sense that it does not depend on any user—provided molecular fragmentation, rather orbital spaces are carefully selected and extended during the calculation to give fragment energies of a specified precision. The computational method scales linearly with the size of the molecular system and is massively parallel. [ABSTRACT FROM AUTHOR]

A new strategy is introduced for obtaining localized orthonormal Hartree–Fock (HF) orbitals where the underlying principle is to minimize the size of the transformation matrix from the atomic orbital basis to the HF optimized orbital basis. The new strategy gives both localized occupied and localized virtual orbital spaces. The locality of the occupied orbital space is similar to one obtained using standard localization schemes. For the virtual space, standard localization schemes fail to give local orbitals while the new strategy gives a virtual space which has a locality similar to the one of a Löwdin orthonormalization of the atomic orbital basis. Since Löwdin orthonormalization gives the most local orthonormal basis functions in the sense that they have the largest similarity with the local atomic basis functions, the new strategy thus allows the orthonormal basis to become optimized without introducing significant delocalization. [ABSTRACT FROM AUTHOR]

We present a novel method for the optimization of Hartree–Fock and Kohn–Sham energies that does not suffer from the flaws of the conventionally used two-step Roothaan–Hall (RH) with direct inversion in iterative subspace (DIIS) acceleration scheme, improving the reliability of the optimization while reducing its cost. The key to its success is the replacement of the two separate steps of each RH/DIIS iteration by a single concerted step that fully exploits the Hessian information available from the previous iterations. It is a trust-region based method and therefore by design converges to an energy minimum. Numerical examples are given to illustrate that the algorithm is robust and cost efficient, converging smoothly to a minimum also in cases when the RH/DIIS algorithm fails to converge or when it converges to a saddle point rather than to a minimum. The algorithm is based on matrix multiplications and becomes linearly scaling for sufficiently large systems. [ABSTRACT FROM AUTHOR]

Corrections to articles in the previous issues are presented including "Density-functional and electron correlated study of five linear birefringences--Kerr, Cotton-Mouton, Buckinghma, Jones and magnetoelectric--in gaseous benzene" that was published in 2004, "Density-functional study of electric and magnetic properties of hexafluorobenzene in the vapor phase," that was published in 2005, and "A computational study of some electric and magnetic properties of gaseous BF and BCI," that was published in 2005.

A linear-scaling implementation of Hartree-Fock and Kohn-Sham self-consistent field theories for the calculation of frequency-dependent molecular response properties and excitation energies is presented, based on a nonredundant exponential parametrization of the one-electron density matrix in the atomic-orbital basis, avoiding the use of canonical orbitals. The response equations are solved iteratively, by an atomic-orbital subspace method equivalent to that of molecular-orbital theory. Important features of the subspace method are the use of paired trial vectors (to preserve the algebraic structure of the response equations), a nondiagonal preconditioner (for rapid convergence), and the generation of good initial guesses (for robust solution). As a result, the performance of the iterative method is the same as in canonical molecular-orbital theory, with five to ten iterations needed for convergence. As in traditional direct Hartree-Fock and Kohn-Sham theories, the calculations are dominated by the construction of the effective Fock/Kohn-Sham matrix, once in each iteration. Linear complexity is achieved by using sparse-matrix algebra, as illustrated in calculations of excitation energies and frequency-dependent polarizabilities of polyalanine peptides containing up to 1400 atoms. [ABSTRACT FROM AUTHOR]

We present a robust linear-scaling algorithm to compute the symmetric square-root or Löwdin decomposition of the atomic-orbital overlap matrix. The method is based on Newton-Schulz iterations with a new approach to starting matrices. Calculations on 12 chemically and structurally diverse molecules demonstrate the efficiency and reliability of the method. Furthermore, the calculations show that linear scaling is achieved. [ABSTRACT FROM AUTHOR]

A linear-scaling implementation of Hartree-Fock and Kohn-Sham self-consistent field (SCF) theories is presented and illustrated with applications to molecules consisting of more than 1000 atoms. The diagonalization bottleneck of traditional SCF methods is avoided by carrying out a minimization of the Roothaan-Hall (RH) energy function and solving the Newton equations using the preconditioned conjugate-gradient (PCG) method. For rapid PCG convergence, the Löwdin orthogonal atomic orbital basis is used. The resulting linear-scaling trust-region Roothaan-Hall (LS-TRRH) method works by the introduction of a level-shift parameter in the RH Newton equations. A great advantage of the LS-TRRH method is that the optimal level shift can be determined at no extra cost, ensuring fast and robust convergence of both the SCF iterations and the level-shifted Newton equations. For density averaging, the authors use the trust-region density-subspace minimization (TRDSM) method, which, unlike the traditional direct inversion in the iterative subspace (DIIS) scheme, is firmly based on the principle of energy minimization. When combined with a linear-scaling evaluation of the Fock/Kohn-Sham matrix (including a boxed fitting of the electron density), LS-TRRH and TRDSM methods constitute the linear-scaling trust-region SCF (LS-TRSCF) method. The LS-TRSCF method compares favorably with the traditional SCF/DIIS scheme, converging smoothly and reliably in cases where the latter method fails. In one case where the LS-TRSCF method converges smoothly to a minimum, the SCF/DIIS method converges to a saddle point. [ABSTRACT FROM AUTHOR]

The magnetic-field-induced axial birefringence (magnetochirality) of five closed-shell chiral molecules (three substituted oxiranes, carvone, and limonene) is studied at the density functional theory level using Becke’s 3-parameter Lee-Yang-Parr functional and frequency-dependent quadratic response theory. The influence of the environment and the conformational distribution on the property is also studied. The environment effects are described by the polarizable continuum model in its integral-equation formulation. The effect of the conformational distribution is investigated by performing calculations on several conformers—for carvone and limonene—followed by Boltzmann averaging. The calculated values for the magnetochiral birefringence are compared to previous ab initio results and experimental data where available. The refined model presented here brings the ab initio values closer to experiment. Still, disagreements remain in some cases and it appears difficult to resolve these discrepancies. [ABSTRACT FROM AUTHOR]

The origin dependence of the expression of two-photon circular dichroism in the length formulation employed by the authors in a recent computational study [B. Jansík et al., Chem. Phys. Lett. 414, 461 (2005)] is discussed in detail, and some inherently origin invariant alternative formulations are introduced. Extensive computational tests on a small reference chiral system, namely, a chiral form of H2O2, are performed at the density functional theory (DFT)/B3LYP level of theory with large diffuse correlation consistent basis sets. The results indicate that the velocity formulation originally proposed by Tinoco, Jr. [J. Chem. Phys. 62, 1006 (1975)] provides the most convenient approach for an origin invariant calculation of two-photon circular dichroism. [ABSTRACT FROM AUTHOR]

The nonlinear changes induced in the refractive index and in the optical rotatory dispersion when radiation interacts with a chiral system are studied computationally. The molecular parameters describing these effects are determined for methyloxirane, employing Hartree-Fock and density functional frequency dependent analytical response theory, the latter with the use of Becke three-parameter Lee-Yang-Parr functional. Their contribution to several circular and axial birefringences, which could be observed in pump-and-probe experiments for various combinations of polarization status and propagation direction of the two beams, is ascertained. [ABSTRACT FROM AUTHOR]

A series of electric and magnetic properties of hexafluorobenzene have been calculated, including the electric dipole polarizability, magnetizability, electric quadrupole moment, and nonlinear mixed electric dipole-magnetic dipole-electric quadrupole hyperpolarizabilities needed to obtain estimates of the Kerr, Cotton-Mouton, Buckingham, Jones, and magnetoelectric birefringences in the vapor phase. Time-dependent density-functional theory was employed for the calculation of linear-, quadratic, and cubic response functions. A number of density functionals have been considered, along with Sadlej’s triple-ζ basis set and the augmented correlation-consistent polarized valence double zeta and augmented correlation-consistent polarized valence triple zeta basis sets. Comparisons have been made with experiment where possible. The analysis of results allows for an assessment of the capability of time-dependent density-functional theory for high-order electromagnetic properties of an electron-rich system such as hexafluorobenzene. [ABSTRACT FROM AUTHOR]

We present the results of an extended study of five birefringences—Kerr, Cotton–Mouton, Buckingham, Jones, and Magnetoelectric—on benzene in the gas phase. The relevant molecular quantities—first-order properties, linear, quadratic, and cubic response functions—are computed employing the density-functional theory (DFT) response theory, with a choice of functionals. In some cases, different functionals are employed for the wave-function computational step and for the subsequent analytical response calculation to determine the combination yielding at the same time the optimal energy and energy derivative results. Augmented correlation consistent basis sets of double and triple zeta quality are used. The DFT results are compared to those obtained at the Hartree–Fock level and in some cases within a coupled cluster singles and doubles electronic structure model. The study tries to assess the ability of the DFT response theory to describe a wide range of properties in a system of rather large size and high complexity. The relative strength of the five birefringences for plausible experimental conditions is determined and, when possible, comparison is made with the results of the measurements.© 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Using coupled cluster singles and doubles linear response theory and the d-aug-cc-pVTZ basis set extended with a 3s3p2d1f1g set of midbond functions, the interaction induced electric dipole polarisability surface of the CO-Ar van der Waals complex is computed. Combining this surface with accurate intermolecular potential energy and electric dipole surfaces, the pressure and dielectric second virial coefficients of the complex are calculated by a classical statistical approach. Excellent agreement with experimental results (to within the experimental error bars) is obtained for the pressure second virial coefficient over a range of temperatures. No previous experimental or theoretical investigations have been carried out for the dielectric second virial coefficient, Bε(T), which is estimated to be about 1.9 cm6 mol- 1 at room temperature. This value results from a balance of terms due to the interaction induced electric dipole polarisability (predominant at high temperatures) and orientational electric dipole contributions. [ABSTRACT FROM AUTHOR]

Dalton is a powerful general-purpose program system for the study of molecular electronic structure at the Hartree-Fock, Kohn-Sham, multiconfigurational self-consistent-field, Møller-Plesset, configuration-interaction, and coupled-cluster levels of theory. Apart from the total energy, a wide variety of molecular properties may be calculated using these electronic-structure models. Molecular gradients and Hessians are available for geometry optimizations, molecular dynamics, and vibrational studies, whereas magnetic resonance and optical activity can be studied in a gauge-origin-invariant manner. Frequency-dependent molecular properties can be calculated using linear, quadratic, and cubic response theory. A large number of singlet and triplet perturbation operators are available for the study of one-, two-, and three-photon processes. Environmental effects may be included using various dielectric-medium and quantum-mechanics/molecular-mechanics models. Large molecules may be studied using linear-scaling and massively parallel algorithms. Dalton is distributed at no cost from http://www.daltonprogram.org for a number of UNIX platforms.

Kohn-Sham density-functional calculations are used in many branches of science to obtain information about the electronic structure of molecular systems and materials. Conventional algorithms for minimization of the Kohn-Sham energy have certain deficiencies, however, that may cause divergence or, worse, convergence to unphysical saddle points. We here present a three-level hierarchical minimization strategy which is both more efficient and robust than the conventional algorithms and which does not suffer from the flaws of these algorithms. Using the three-level minimization strategy, the molecular density is built up in a hierarchical fashion in accordance with chemical insight: First, the molecular density is composed by a superposition of atomic densities; next, bonds are formed by performing a simple valence-shell optimization; finally, the molecular description is refined by an optimization in the full molecular basis. Importantly, the density matrix generated at each of the two lower levels in this hierarchy is transferred to the next without loss of information. Examples demonstrate the efficacy and robustness of the proposed scheme.

A computational study of the Faraday B term of magnetic circular dichroism at the coupled cluster singles and doubles level is presented for pyridine, pyrazine, pyrimidine, and phosphabenzene. Gauge-origin independence is obtained by expressing the B term as a total derivative of the one-photon dipole transition strength and using London orbitals. The high quality of the coupled cluster singles and doubles (CCSD) B terms makes these useful for the assignment of experimental spectra. Previous assignments of the experimental spectra based on the qualitative perimeter model are confirmed by the CCSD results for the three azines, while a reassignment is proposed for phosphabenzene. For non-overlapping bands, the B terms calculated at the equilibrium geometries are in good agreement with the experimental values. For overlapping bands, large deviations occur. Attributing a line width to the calculated equilibrium B terms leads to a large cancellation of positive and negative contributions. This cancellation may result in a large displacement of the band center maximum, leading to a large uncertainty in the assignments of "vertical experimental excitation energies" (pyridine). Bands may also completely vanish due to such cancellation (phosphabenzene). Explicit consideration of the cancellation yields simulated theoretical spectra that are in good agreement with experiment once the theoretical spectra are parallel displaced. A major contribution for this parallel displacement is the shift in the excitation energies due to correlation beyond CCSD, as seen when comparing vertical CCSD and CC3 equilibrium-geometry excitation energies.