An efficient linear scaling procedure for constructing localized orbitals of large molecules based on the one-particle density matrix

We have developed a linear-scaling algorithm for obtaining the Boys localized molecular orbitals from the one-particle density matrix. The algorithm is made up of two steps: the Cholesky decomposition of the density matrix to obtain Cholesky molecular orbitals and the subsequent Boys localization process. Linear-scaling algorithms have been proposed to achieve linear-scaling calculations of these two steps, based on the sparse matrix technique and the locality of the Cholesky molecular orbitals. The present algorithm has been applied to compute the Boys localized orbitals in a number of systems including α-helix peptides, water clusters, and protein molecules. Illustrative calculations demonstrate that the computational time of obtaining Boys localized orbitals with the present algorithm is asymptotically linear with increasing the system size.     

草酸根桥联双核铜(Ⅱ)体系的磁耦合机理

应用密度泛函理论,采用对称性破损方法分析了草酸根桥联双核铜(Ⅱ)体系的磁耦合机理。在该双核体系中,两铜(Ⅱ)原子的自旋布居大小相等,符号相反,磁中心间的作用为反铁磁耦合。草酸根桥配体向磁中心的电子转移使得铜(Ⅱ)原子的自旋显著离域,这种离域有利于反铁磁耦合,草酸根桥配体中的碳原子上出现自旋极化。当铜(Ⅱ)原子的配位环境由平面四方形向四面体或四方锥变化时,反铁磁耦合的强度减弱。体系的沿前轨道主要由铜(Ⅱ)原子d轨道和配体原子p轨道构成,这种构成利于草酸根桥配体与磁中心之间的电子转移。     

The role of orbital transformations in coupled-pair functionals

The replacement of single excitations by orbital transformations in coupled-pair functionals derived from a single double configuration interaction approach is discussed. It is demonstrated that this modification leads to considerably improved density matrices and better agreement with results from coupled cluster singles doubles calculations taken as a reference. A comparison between the variationally optimized orbitals and the Brueckner orbitals shows that these two sets of orbitals are different.     

n→π*-Übergänge in Dicarbonylverbindungen Der Einfluss der n,n- und π*, π*-Wechselwirkung

By CNDO-CI calculations we have found that dicarbonyl compounds exhibit only two n → π* transitions in the visible or near UV. region, instead of four as expected from simpler MO-models. The dominant features of the long-wavelength electronic spectra may be characterized by the relative energy of the two n and the two lowest π* orbitals. In general we distinguish between three cases:

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A theory of molecules in molecules IV. Application to the Hydrogen Bonding Interaction in NH3 · H2O

The theory of molecules in molecules introduced in previous articles is applied to study the hydrogen bonding interaction between an ammonia molecule as proton acceptor and a water molecule as proton donor. The localized orbitals which are assumed to be least affected by the formation of the hydrogen bond are transferred unaltered from calculations on the fragments NH₃ and H₂O, the remaining orbitals are recalculated. A projection operator is used to obtain orthogonality to the transferred orbitals. Additional approximations have been introduced in order to be able to save computational time. These approximations can be justified and are seen to lead to binding energies and bond lengths which are in satisfactory agreement with the SCF values. The point charge approximation for the calculation of the interaction energy between the two sets of transferred localized orbitals is, however, not applicable in this case. An energy analysis of the effect of the hydrogen bond on the localized orbitals of the two fragments is given.     

The Fock Matrix Analysis for Atomic Orbitals in Molecular Orbitals I. A New Look on the Covalent Bond in H2?

The character of the molecular orbitals can be better accounted for in terms of molecular adapted atomic orbitals and the Fock matrix expanded in these atomic orbital sets. A clean‐cut and unique criterion for the diradicals and the covalent bonds can be given for the molecular orbitals in both restricted and unrestricted Hartree‐Fock wavefunctions. Instead of the picture that overlap charge migrates into the bonding region, the new analysis displays another picture that the charge densities for the electrons with α and β spins give rise to two opposite spin density shifts. If the α one shifts from atom A toward atom B then it is vice versa for the β one. The spin density shifts proceed until the bonding molecular orbitals form.     

Momentum–space electron densities—localized orbitals in hydrocarbons,boranes, and transition metal complexes

Position and momentum space plots are presented for localized molecular orbitals in hydrocarbons, boranes, a carborane, and two octahedral transition metal complexes. The p-space representation proves to be valuable for visualizing such orbitals since it highlights the differences in their character from one molecule to another. Factors influencing the form of the orbitals in p space, including the oscillatory behavior caused by contributions to an orbital from more than one center, are examined in detail. © 1996 John Wiley & Sons, Inc.     

HeI photoelectron spectroscopic study of the electronic structure of SSF2 and FSSF compounds

HeI photoelectron (PE) spectra are re-recorded for SSF₂ and FSSF. The assignment of bands has been made with the aid of band shapes, band intensities and ab initio calculations. In the PE spectrum of SSF₂, two sharp peaks at 10.48 and 11.22 eV are considered to result from through-space interaction of lone-pair orbitals in the two S atoms and two sharp peaks at 12.50 and 12.90 eV from through-space interaction of lone-pair orbitals in the two F atoms. The larger splitting of the S atoms can be attributed to the larger 3p orbital of S. The lack of sharp peaks in the PE spectrum of FSSF shows that there is no orbital which embodies the character of a lone-pair. So the PE spectra of SSF₂ and FSSF are examples embodying through-space interaction of lone-pair orbitals.     

Core-shell photoabsorption and photoelectron spectra of gas-phase pentacene: experiment and theory

The C K-edge photoabsorption and 1s core-level photoemission of pentacene (C22H14) free molecules are experimentally measured, and calculated by self-consistent-field and static-exchange approximation ab initio methods. Six nonequivalent C atoms present in the molecule contribute to the C 1s photoemission spectrum. The complex near-edge structures of the carbon K-edge absorption spectrum present two main groups of discrete transitions between 283 and 288 eV photon energy, due to absorption to pi* virtual orbitals, and broader structures at higher energy, involving sigma* virtual orbitals. The sharp absorption structures to the pi* empty orbitals lay well below the thresholds for the C 1s ionizations, caused by strong excitonic and localization effects. We can definitely explain the C K-edge absorption spectrum as due to both final (virtual) and initial (core) orbital effects, mainly involving excitations to the two lowest-unoccupied molecular orbitals of pi* symmetry, from the six chemically shifted C 1s core orbitals.     

The HeHe Coulomb and exchange interaction energy

The Coulomb and exchange interaction energy between two helium atoms is calculated, increasing systematically the basis set, by a supermolecular method which excludes the superposition error by using non-orthogonal orbitals. At 5.6 bohr an energy limit of 9.69 K is found at the Hartree-Fock level; for correlated wavefunctions the corresponding value is 11.86 K using only s orbitals, 10.70 K including p orbitals and 10.58 K adding d orbitals.     

Multiconfiguration self-consistent field,theory of localized orbitals: Choice of localization potential

We investigate the properties of two different choices for localization potentials for the direct construction of localized fixed orbitals by multiconfiguration self-consistent field theory. The first potential yields maximally screened orbitals by solution of a complicated orbital equation which depends explicitly on the complete set of orbitals for the system, and contains both one-and two-center matrix elements. The second localization potential yields somewhat less well screened orbitals by solution of a considerably simpler orbital equation which only contains simple one-center matrix elements.     

价键结构函数与键函数 2.水分子的计算和分析

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The Exact Icosahedral Symmetry Relations for Atomic Overlaps,Molecular Orbitals and Vibrational Species of C60 Buckyballs

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The Bond Order of C2 from a Strictly N‐Representable Natural Orbital Energy Functional Perspective

The bond order of the ground electronic state of the carbon dimer has been analyzed in the light of natural orbital functional theory calculations carried out with an approximate, albeit strictly N‐representable, energy functional. Three distinct solutions have been found from the Euler equations of the minimization of the energy functional with respect to the natural orbitals and their occupation numbers, which expand upon increasing values of the internuclear coordinate. In the close vicinity of the minimum energy region, two of the solutions compete around a discontinuity point. The former, corresponding to the absolute minimum energy, features two valence natural orbitals of each of the following symmetries, σ, σ*, π and π*, and has three bonding interactions and one antibonding interaction, which is very suggestive of a bond order large than two but smaller than three. The latter, features one σ–σ* linked pair of natural orbitals and three degenerate pseudo‐bonding like orbitals, paired each with one triply degenerate pseudo‐antibonding orbital, which points to a bond order larger than three. When correlation effects, other than Hartree–Fock for example, between the paired natural orbitals are accounted for, this second solution vanishes yielding a smooth continuous dissociation curve. Comparison of the vibrational energies and electron ionization energies, calculated on this curve, with their corresponding experimental marks, lend further support to a bond order for C ₂ intermediate between acetylene and ethylene.     

The Fock Matrix Analysis for Atomic Orbitals in Molecular Orbitals II. The Electronic Structure of N2 Molecules

Weinhold's natural hybrid orbitals can be chosen as the molecular adapted atomic orbitals to build the canonical molecular orbitals of N₂ molecules. The molecular Fock matrix expanded in the natural hybrid orbitals can reveal deeper insight of the electronic structure and reaction of the N₂ molecule. For example, the magnitude of F_ab can signify the bonding character of the paired electrons as well as the diradical character of the unpaired electrons for both σ‐ and π‐types. Discarding the concept of the overlap between non‐orthogonal atomic orbitals, the different orbitals for different spins in the unrestricted Hartree‐Fock wavefunction reveal that there are three pairs of opposite spin density flows between two atoms, which proceed until the bonding molecular orbitals form.     

Minimal set of molecule-adapted atomic orbitals from maximum overlap criterion

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The bonding in the ozone molecule: From a different perspective

A new qualitative treatment of the bonding in ozone is presented. It is based upon a combination of several simple concepts: the nonparticipation of the pairs of electrons tightly held in the atomic 2s orbitals; simple overlap of the 2p orbitals to form sigma bonds; interaction of three 2p orbitals to yield bonding and nonbonding pi molecular orbitals that are populated by electron pairs; and van der Waals repulsion between the two terminal oxygen atoms forcing these atoms apart to yield the bond angle of 117° as a compromise. Both the assumptions and the resulting bonding picture are in accord with the photoelectron spectroscopic data, the results from sophisticated molecular orbital calculations, and the common physical properties of ozone.     

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The possibility to obtain unoccupied orbitals with correct energies in the new semi-empirical method HAM/3 implies new means to study frontier orbitals of chemical reactions. The transition state can often be identified as the state where the frontier orbitals are degenerate. The coplanar rectangular decomposition of cyclobutane into two ethylenes is chosen as a representative example. It is found that the activation energy is smaller than according to previous studies and thus not much different from the experimental value. It is pointed out that with a better parametrization of the HAM method it will be possible to study chemical reactions in detail and to calculate reliable activation energies.     

Orbital overlap and chemical bonding

The chemical bonds in the diatomic molecules Li(2)-F(2) and Na(2)-Cl(2) at different bond lengths have been analyzed by the energy decomposition analysis (EDA) method using DFT calculations at the BP86/TZ2P level. The interatomic interactions are discussed in terms of quasiclassical electrostatic interactions DeltaE(elstat), Pauli repulsion DeltaE(Pauli) and attractive orbital interactions DeltaE(orb). The energy terms are compared with the orbital overlaps at different interatomic distances. The quasiclassical electrostatic interactions between two electrons occupying 1s, 2s, 2p(sigma), and 2p(pi) orbitals have been calculated and the results are analyzed and discussed. It is shown that the equilibrium distances of the covalent bonds are not determined by the maximum overlap of the sigma valence orbitals, which nearly always has its largest value at clearly shorter distances than the equilibrium bond length. The crucial interaction that prevents shorter bonds is not the loss of attractive interactions, but a sharp increase in the Pauli repulsion between electrons in valence orbitals. The attractive interactions of DeltaE(orb) and the repulsive interactions of DeltaE(Pauli) are both determined by the orbital overlap. The net effect of the two terms depends on the occupation of the valence orbitals, but the onset of attractive orbital interactions occurs at longer distances than Pauli repulsion, because overlap of occupied orbitals with vacant orbitals starts earlier than overlap between occupied orbitals. The contribution of DeltaE(elstat) in most nonpolar covalent bonds is strongly attractive. This comes from the deviation of quasiclassical electron-electron repulsion and nuclear-electron attraction from Coulomb's law for point charges. The actual strength of DeltaE(elstat) depends on the size and shape of the occupied valence orbitals. The attractive electrostatic contributions in the diatomic molecules Li(2)-F(2) come from the s and p(sigma) electrons, while the p(pi) electrons do not compensate for nuclear-nuclear repulsion. It is the interplay of the three terms DeltaE(orb), DeltaE(Pauli), and DeltaE(elstat) that determines the bond energies and equilibrium distances of covalently bonded molecules. Molecules like N(2) and O(2), which are usually considered as covalently bonded, would not be bonded without the quasiclassical attraction DeltaE(elstat).