Hard-surface effects in polymer self-consistent field calculations

We have investigated several effects due to the confinement of polymer melts by impenetrable (hard) surfaces in the self-consistent field calculations. To adequately represent such confinement, the total (normalized) polymer segmental density (volume fraction) is usually constrained to an imposed profile that continuously decreases from 1 in the interior of confined melts to 0 at the surfaces over a short distance. The choice of this profile strongly influences the numerical performance of the self-consistent field calculations. In addition, for diblock copolymers A-B the hard-surface confinement has both energetic and entropic effects: On one hand, the decrease of polymer density from 1 reduces A-B repulsion and favors morphologies with more A-B interfaces near the surfaces. On the other hand, the enrichment of chain ends and depletion of middle segments near the surfaces favor parallel morphologies where chains orient mainly perpendicular to the surfaces. These two effects are comparable in magnitude, and for asymmetric diblock copolymers result in an entropic preference of a neutral surface for the shorter block as proposed previously [Q. Wang et al., Macromolecules 34, 3458 (2001)]. The hard-surface effects are weak in practice and thus manifested only when the surfaces are nearly neutral.     

Approaches to large-scale parallel self-consistent field calculations

The availability of massively parallel computers with high computation rates but limited memory and input/output bandwidth prompts the reevaluation of appropriate solution schemes for the self-consistent field (SCF) equations. Several algorithms are considered which exhibit between linear and quadratic convergence using various approximations to the orbital Hessian. A prototype is developed to understand the computational expense of each approach. The optimal choice is found to be a conjugate–gradient method preconditioned with a level-shifted approximation to the orbital Hessian. This is a compromise between efficiency, stability, and low memory usage. Sample benchmarks on two parallel supercomputers are also reported. © 1995 John Wiley & Sons, Inc.     

Globally convergent trust-region methods for self-consistent field electronic structure calculations

As far as more complex systems are being accessible for quantum chemical calculations, the reliability of the algorithms used becomes increasingly important. Trust-region strategies comprise a large family of optimization algorithms that incorporates both robustness and applicability for a great variety of problems. The objective of this work is to provide a basic algorithm and an adequate theoretical framework for the application of globally convergent trust-region methods to electronic structure calculations. Closed shell restricted Hartree-Fock calculations are addressed as finite-dimensional nonlinear programming problems with weighted orthogonality constraints. A Levenberg-Marquardt-like modification of a trust-region algorithm for constrained optimization is developed for solving this problem. It is proved that this algorithm is globally convergent. The subproblems that ensure global convergence are easy-to-compute projections and are dependent only on the structure of the constraints, thus being extendable to other problems. Numerical experiments are presented, which confirm the theoretical predictions. The structure of the algorithm is such that accelerations can be easily associated without affecting the convergence properties.     

Convergence optimization of restricted open-shell self-consistent field calculations

Different self-consistent field (SCF) iteration schemes for open-shell systems are discussed. After a brief summary of the well-known level shifting and damping procedure, we describe the quadratically convergent SCF (QCSCF) approach based on the gradient and the Hessian matrix in a space of orbital rotation parameters. An analytical expression for the latter is derived for the general many-shell case. Starting from the expression for the energy change obtained by the QCSCF method, we then present a simplified direct procedure avoiding matrix diagonalization but also the difficulties of the QCSCF method in handling the Hessian matrix. Numerical calculations on some open-shell systems involving transition-metal complexes show that this method leads to rapid and reliable convergence of the iteration process in cases where the usual SCF procedure of iterative diagonalization tends to diverge. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 62: 617–637, 1997     

Molecular-orbital self-consistent field calculations of quinoline and its derivatives

The electronic spectra of the thiol, anionic, protonated, and mesoionic forms of 8-mercaptoquinoline and the mesoionic form of 5-mercaptoquinoline and the 5-mercapto-N-methylquinolinium ion were calculated within the CNDO (complete neglect of differential overlap) approximation. The inclusion of the d orbitals of the sulfur atom in the AO basis has virtually no effect on the energies of the electron transitions of these compounds.See [4] for communication I.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 11, pp. 1530–1534, November, 1978.     

Pre-processing two-electron integrals for efficient utilization in many-electron self-consistent field calculations

A procedure for pre-processing a random list of two-electron integrals is described. Construction of Fock-matrices with the resulting PK-file is shown to be three times faster than use of a file containing the random two-electron integrals, indices, and a branching code.     

Basis set modeling for molecular calculations using effective core potential

A new approach for developing of basis sets to be used along with effective core potential is systematically studied. The behavior of the LCAO coefficients versus the ln(α) of the respective primitives can provide simple guidelines to establish the range over which the basis set should be developed or modified, especially when using effective core potential. Double-zeta basis sets were modeled for SBK pseudopotential from all-electron basis sets for a series of compounds containing elements of the second period of the periodic table. Application of the modeled basis sets at the Hartree–Fock and MP2 levels of theory shows that the new method provides molecular properties as accurate as those calculated by all-electron calculations. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1918–1929, 1997     

Perturbative correction for the basis set incompleteness error of complete-active-space self-consistent field

To reduce the basis set incompleteness of the complete-active-space self-consistent field (CASSCF) wave function and energy we develop a second-order perturbation correction due to single excitations to complete set of unoccupied states. Other than the one- and two-electron integrals, only one- and two-particle reduced density matrices are required to compute the correction, denoted as [2](S). Benchmark calculations on prototypical ground-state bond-breaking problems show that only the aug-cc-pVXZ basis is needed with the [2](S) correction to match the accuracy of CASSCF energies of the aug-cc-pV(X+1)Z quality.     

Fast vibrational self-consistent field calculations through a reduced mode-mode coupling scheme

We present a new methodology to perform fast correlation-corrected vibrational self-consistent field (CC-VSCF) calculations using ab initio potential energy points calculated on the fly. Our method is based on the replacement of all-electron basis sets with a pseudo-potential basis for heavy atoms, and on an efficient reduction of the number of pair-coupling elements used in the CC-VSCF procedure. The method is applied to several test systems: H2O, NH3, and CH4, where it proves to be efficient, providing a speedup factor of 2 compared to a standard CC-VSCF calculation. We also apply our technique to the simulation of the vibrational spectrum of ethane and show that very accurate results can be obtained with a substantial speedup for this system.     

Non self-consistent field theory — A new approach in quantum mechanical calculations

An R ^o-independent electronic repulsion matrix is constructed, replacing the R ^o-dependent Hamiltonian matrix (R ^o is the density matrix). A non-SCF theory is developed to solve the eigenequation without using an iterative procedure. Three methods are proposed to solve for the eigenvectors and eigenvalues. Illustrative calculations are reported comparing the non-SCF and SCF theories. The calculated results are as expected: the ground state energies are nearly unchanged while the orbital energies are nearer to the experimental results. Other physical properties and spectral quantities are also compared. It is found that the ZDO assumption is applicable in the non-SCF theory if it is applicable in SCF theory.

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Zusammenfassung Eine R ^o-unabhängige Elektronenabstoßungsmatrix wird eingeführt, die die R ^o-abhängige Hamiltonmatrix ersetzt (R ^o ist die Dichtematrix). Zur Lösung der Eigenwertgleichung ohne iterative Prozeduren wird eine sog. Nicht-SCF-Theorie aufgestellt. An Beispielen werden die Ergebnisse von SCF- und Nicht-SCF-Rechnungen verglichen; dabei erweisen sich die Energien des Grundzustandes als nahezu unverändert, während die Energien der Orbitale näher bei den experimentellen Werten liegen. Die zero-differential-overlap-Näherung ist immer dann in der neuen Theorie anwendbar, wenn sie in der SCF-Theorie anwendbar ist.

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Résumé Une matrice de répulsion électronique indépendante de R ^o est construite, remplaçant la matrice hamiltonienne dépendant de R ^o (R ^o matrice de densité). Une théorie non SCF est développée afin de résoudre l'équation aux valeurs propres sans itérations. Trois méthodes de résolution du problème aux valeurs propres sont proposées. Des calculs illustrent la comparaison entre les théories SCF et non SCF. Les résultats des calculs sont comme prévus: l'énergie de l'état fondamental varie peu alors que les énergies orbitales sont plus proches des résultats expérimentaux. D'autres propriétés physiques ainsi que des grandeurs spectrales sont comparées. On trouve que l'approximation du recouvrement différentiel nul est applicable dans la théorie non SCF si elle est applicable dans la théorie SCF.

     

Basis set convergence of explicitly correlated double-hybrid density functional theory calculations

The basis set convergence of explicitly correlated double-hybrid density functional theory (DFT) is investigated using the B2GP-PLYP functional. As reference values, we use basis set limit B2GP-PLYP-F12 reaction energies extrapolated from the aug(')-cc-pV(Q+d)Z and aug(')-cc-pV(5+d)Z basis sets. Explicitly correlated double-hybrid DFT calculations converge significantly faster to the basis set limit than conventional calculations done with basis sets saturated up to the same angular momentum (typically, one "gains" one angular momentum in the explicitly correlated calculations). In explicitly correlated F12 calculations the VnZ-F12 basis sets converge faster than the orbital A(')VnZ basis sets. Furthermore, basis set convergence of the MP2-F12 component is apparently faster than that of the underlying Kohn-Sham calculation. Therefore, the most cost-effective approach consists of combining the MP2-F12 correlation energy from a comparatively small basis set such as VDZ-F12 with a DFT energy from a larger basis set such as aug(')-cc-pV(T+d)Z.     

Basis set dependence of phosphate frequencies in density functional theory calculations

The addition of extravalence, polarization and diffuse functions, were studied in order to conclude how they affect the P? O stretching frequencies of several biological relevant phosphate molecules. The results show that the polarization and the diffuse functions have opposite effects on the frequencies: the polarization functions downshift while the diffuse functions upshift the frequencies. The effect of the valence functions was more difficult to interpret. The effect of the conductor‐like screening model (CPCM)‐continuum model was also studied. The results show that the CPCM‐continuum model has a substantial effect on the frequencies for these small molecules. The continuum model's efficiency is mainly due to its effect on the geometries and not on the frequencies. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Highly accurate relativistic universal Gaussian basis set for Dirac–Fock–Breit calculations

Ion mobilities of H₂O⁺ drifting in helium are calculated and compared with experiment. These calculations employ global potential energy surfaces of the H₂O⁺–He complex, which in the present case were calculated ab initio at the unrestricted MP2 level of theory using a basis set of aug‐cc‐pVTZ quality, and treating the ion as a rigid body. Details are presented of the general characteristics of both the ground and first‐excited electronic states of the complex. Although only the ground‐state surface was used for the mobility calculations, the ab initio determination of the ground state necessitated the inclusion of the first‐excited state owing to the presence of a crossing between the two. This crossing is also described. Mobilities calculated from the global surfaces are in good agreement with experiment. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Basis set and density functional dependence of vibrational Raman optical activity calculations

We present an extensive investigation of the dependence of the scattering intensity difference of right and left circularly polarized light observed in vibrational Raman optical activity (VROA) on the choice of basis set and exchange-correlation functional. These dependencies are investigated for five molecules for which accurate experimental data are available: (S)-methyloxirane, (R)-epichlorhydrin, (S)-glycidol, (M)-spiro[2,2]pentane-1,4-diene, and (M)-sigma-[4]-helicene. Calculations are presented using the SVWN exchange-correlation functional (LDA), the BLYP exchange-correlation functional, and the B3LYP hybrid functional, using six different basis sets: the cc-pVDZ, cc-pVTZ, aug-cc-pVDZ, aug-cc-pVTZ, Sadlej's polarized basis set, and a minimal VROA basis set recently proposed by Zuber and Hug. It is demonstrated that results from pure gradient-corrected and hybrid functionals are comparable and that the aug-cc-pVDZ and aug-cc-pVTZ basis sets yield similar results. Furthermore, the combination of the small basis set by Zuber and Hug with an accurate force field represents the best compromise between computational accuracy and computational efficiency.     

Revised self-consistent continuum solvation in electronic-structure calculations

The solvation model proposed by Fattebert and Gygi [J. Comput. Chem. 23, 662 (2002)] and Scherlis et al. [J. Chem. Phys. 124, 074103 (2006)] is reformulated, overcoming some of the numerical limitations encountered and extending its range of applicability. We first recast the problem in terms of induced polarization charges that act as a direct mapping of the self-consistent continuum dielectric; this allows to define a functional form for the dielectric that is well behaved both in the high-density region of the nuclear charges and in the low-density region where the electronic wavefunctions decay into the solvent. Second, we outline an iterative procedure to solve the Poisson equation for the quantum fragment embedded in the solvent that does not require multigrid algorithms, is trivially parallel, and can be applied to any Bravais crystallographic system. Last, we capture some of the non-electrostatic or cavitation terms via a combined use of the quantum volume and quantum surface [M. Cococcioni, F. Mauri, G. Ceder, and N. Marzari, Phys. Rev. Lett. 94, 145501 (2005)] of the solute. The resulting self-consistent continuum solvation model provides a very effective and compact fit of computational and experimental data, whereby the static dielectric constant of the solvent and one parameter allow to fit the electrostatic energy provided by the polarizable continuum model with a mean absolute error of 0.3 kcal/mol on a set of 240 neutral solutes. Two parameters allow to fit experimental solvation energies on the same set with a mean absolute error of 1.3 kcal/mol. A detailed analysis of these results, broken down along different classes of chemical compounds, shows that several classes of organic compounds display very high accuracy, with solvation energies in error of 0.3-0.4 kcal/mol, whereby larger discrepancies are mostly limited to self-dissociating species and strong hydrogen-bond-forming compounds.     

Basis set error estimation for DFT calculations of electronic g‐tensors for transition metal complexes

We present a detailed study of the basis set dependence of electronic g‐tensors for transition metal complexes calculated using Kohn–Sham density functional theory. Focus is on the use of locally dense basis set schemes where the metal is treated using either the same or a more flexible basis set than used for the ligand sphere. The performance of all basis set schemes is compared to the extrapolated complete basis set limit results. Furthermore, we test the performance of the aug‐cc‐pVTZ‐J basis set developed for calculations of NMR spin‐spin and electron paramagnetic resonance hyperfine coupling constants. Our results show that reasonable results can be obtain when using small basis sets for the ligand sphere, and very accurate results are obtained when an aug‐cc‐pVTZ basis set or similar is used for all atoms in the complex. © 2014 Wiley Periodicals, Inc.     

Non self-consistent field theory

Roothaan's SCF method [2] is reformulated so that two non-SCP methods are developed to solve the eigenequation. The results from these methods can be used as starting eigenfunctions for Roothaan's SCF method.

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Zusammenfassung Die self-consistent field Methode von Roothaan [2] wird neu formuliert: dabei werden zwei Nicht-SCF Methoden zur Lösung der Eigenwertgleichung entwickelt. Deren Resultate können als Anfangsfunktionen bei Rechnungen mit der SCF-Methode von Roothaan benutzt werden.

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Résumé La méthode SCF de Roothaan [2] est reformulée en développant deux méthodes non-SCF pour la solution de l'équation aux valeurs propres. Les résultats de ces deux méthodes peuvent être utilisées comme fonctions de départ pour la méthode SCF de Roothaan.

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The title Theoretical Chemistry has been transferred to the Division of Physical Chemistry.