Self‐Consistent Perturbation Theory. II. Extension to Open Shells
01 Dec 1968-Journal of Chemical Physics (American Institute of Physics)-Vol. 49, Iss: 11, pp 4852-4856
TL;DR: In this article, the self-consistent perturbation theory developed in earlier papers is extended to the open-shell case and density matrices for both shells are calculated iteratively until first-order selfconsistency is achieved.
Abstract: The self‐consistent perturbation theory developed in earlier papers is extended to the open‐shell case. Density matrices for both shells are calculated iteratively until first‐order self‐consistency is achieved. A numerical application indicates the importance of considering both shells separately when discussing the effects of polarization on the charge density and the spin density.
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TL;DR: A description of the ab initio quantum chemistry package GAMESS, which can be treated with wave functions ranging from the simplest closed‐shell case up to a general MCSCF case, permitting calculations at the necessary level of sophistication.
Abstract: A description of the ab initio quantum chemistry package GAMESS is presented. Chemical systems containing atoms through radon can be treated with wave functions ranging from the simplest closed-shell case up to a general MCSCF case, permitting calculations at the necessary level of sophistication. Emphasis is given to novel features of the program. The parallelization strategy used in the RHF, ROHF, UHF, and GVB sections of the program is described, and detailed speecup results are given. Parallel calculations can be run on ordinary workstations as well as dedicated parallel machines. © John Wiley & Sons, Inc.
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TL;DR: In this paper, an open-shell complete basis set (CBS) model chemistry, based on the unrestricted Hartree-Fock (UHF) zero-order wave function, is defined to include corrections for basis set truncation errors.
Abstract: The major source of error in most ab initio calculations of molecular energies is the truncation of the one‐electron basis set. An open‐shell complete basis set (CBS) model chemistry, based on the unrestricted Hartree–Fock (UHF) zero‐order wave function, is defined to include corrections for basis set truncation errors. The total correlation energy for the first‐row atoms is calculated using the unrestricted Mo/ller–Plesset perturbation theory, the quadratic configuration interaction (QCI) method, and the CBS extrapolation. The correlation energies of the atoms He, Li, Be, B, C, N, O, F, and Ne, calculated using atomic pair natural orbital (APNO) basis sets, vary from 85.1% to 95.5% of the experimental correlation energies. However, extrapolation using the asymptotic convergence of the pair natural orbital expansions retrieves from 99.3% to 100.6% of the experimental correlation energies for these atoms. The total extrapolated energies (ESCF+Ecorrelation) are then in agreement with experiment to within ±0...
2,389 citations
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TL;DR: This tutorial review provides an overview of the theoretical and experimental investigations that resulted in the recognition of anion-pi interactions, i.e., non-covalent forces between electron deficient aromatic systems and anions.
Abstract: This tutorial review provides an overview of the theoretical and experimental investigations that resulted in the recognition of anion-π interactions, i.e., non-covalent forces between electron deficient aromatic systems and anions. Several pioneering theoretical studies revealed that these interactions are energetically favorable (∼20–50 kJ mol–1). Anion-π interactions are gaining significant recognition, and their pivotal role in many key chemical and biological processes is being increasingly appreciated. The design of highly selective anion receptors and channels represent important advances in this nascent field of supramolecular chemistry.
926 citations
TL;DR: In this article, a method for calculating the EPR g-tensor based on coupled perturbed Hartree-Fock (HF) and density functional theory (DFT) is presented.
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.
517 citations
TL;DR: A biocompatible molecule that functions as an ex situ monitor and an in situ inhibitor for protein fibrillation, using insulin as a model protein to monitor amyloidosis kinetics and inhibit fibril formation is developed.
Abstract: Amyloid fibrillation of proteins is associated with a great variety of pathologic conditions. Development of new molecules that can monitor amyloidosis kinetics and inhibit fibril formation is of great diagnostic and therapeutic value. In this work, we have developed a biocompatible molecule that functions as an ex situ monitor and an in situ inhibitor for protein fibrillation, using insulin as a model protein. 1,2-Bis[4-(3-sulfonatopropoxyl)phenyl]-1,2-diphenylethene salt (BSPOTPE) is nonemissive when it is dissolved with native insulin in an incubation buffer but starts to fluoresce when it is mixed with preformed insulin fibril, enabling ex situ monitoring of amyloidogenesis kinetics and high-contrast fluorescence imaging of protein fibrils. Premixing BSPOTPE with insulin, on the other hand, inhibits the nucleation process and impedes the protofibril formation. Increasing the dose of BSPOTPE boosts its inhibitory potency. Theoretical modeling using molecular dynamics simulations and docking reveals that BSPOTPE is prone to binding to partially unfolded insulin through hydrophobic interaction of the phenyl rings of BSPOTPE with the exposed hydrophobic residues of insulin. Such binding is assumed to have stabilized the partially unfolded insulin and obstructed the formation of the critical oligomeric species in the protein fibrillogenesis process.
336 citations
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TL;DR: In this paper, it is shown that the Fock-Dirac density matrix can be computed in terms of the unperturbed Hamiltonian and density matrix, and the perturbation can be expressed as a series of series of perturbations.
Abstract: In Hartree-Fock theory and its various generalizations, it is customary to solve an eigenvalue problem involving an effective one-body Hamiltonian. The eigenvectors determine the Fock-Dirac density matrix, which also appears in the effective Hamiltonian, and solution proceeds iteratively until self-consistency is achieved.An alternative (necessary and sufficient) condition for a solution is that the density matrix ($\ensuremath{\rho}$) is idempotent and commutes with the Hamiltonian (h). The change in $\ensuremath{\rho}$, accompanying a change $\ensuremath{\Delta}$ in h, can then be expressed as a perturbation series. Formulas for the perturbation, to all orders, are obtained in terms of the unperturbed Hamiltonian and density matrix. It is also shown that the whole perturbation may be obtained directly, without separating the orders, and that the approach is related to earlier steepest-descent methods.
646 citations
TL;DR: In this article, the theory of wave functions which have the form of a single determinant, but without the restriction to doubly occupied orbitals, is developed in general terms.
Abstract: The theory of wave functions which have the form of a single determinant, but without the restriction to doubly occupied orbitals, is developed in general terms. The unrestricted molecular orbitals, the natural spin orbitals, the natural orbitals and the corresponding orbitals are defined and some of their properties deduced. The use of annihilators and projection operators to produce eigenfunctions of spin is investigated. The role of molecular symmetry and of a truncated set of basic functions in forcing a single determinant to be an eigenfunction of spin is discussed. A theorem on the diagonalization of a rectangular matrix by two unitary matrices is proved and applied to density matrices.
501 citations
TL;DR: Junkes and Salpeter as discussed by the authors presented a spectral atlas of thorium from 9400 to 2000 A. The spectral atlases produced by the Astrophysical Laboratory of the Vatican's Astronomical Observatory are today so world famous that no special general comment is necessary to present this new atlas on the spectrum of Thorium.
Abstract: Spectrum of thorium from 9400 to 2000 A. By J.Junkes and E.W. Salpeter. Specola Vaticana, Città del Vaticano 1964, 8 pp and 16 photographic charts, 24 30 cm, U.S. $10. The spectral atlases produced by the Astrophysical Laboratory of the Vatican's Astronomical Observatory are today so world famous that no special general comment is necessary to present this new atlas on the spectrum of Thorium from 9400 to 2000 Â. Few words may be perhaps spent on its usefulness. As the authors state the Th spectrum shows a well marked superiority on the currently adopted Fe spectrum as reference spectrum for wavelength measurements because the Th lines, expecially when excited at low pressure and low temperature by high frequency in a TA-halide lamp or in a hollow cathode suffer
423 citations
TL;DR: In this article, the selfconsistent perturbation theory was applied to various types of perturbations, such as one-element change of the one-electron Hamiltonian matrix (i.e., of Coulomb or resonance integral), uniform electric field, point charge near the system.
Abstract: The self‐consistent perturbation theory developed in an earlier paper is formulated more explicitly and applied to various types of perturbation: (i) one‐element change of the one‐electron Hamiltonian matrix (i.e., of Coulomb or resonance integral), (ii) uniform electric field, (iii) point charge near the system. The applications are to π‐electron systems, where the results have considerable chemical interest.
191 citations