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The band structure of poly( para -phenylene-vinylene) (PPV) has been calculated. A Hartree–Fock (HF) crystal orbital calculation served as a starting point for a quasi-particle (QP) method to take the electron correlation into account. A double zeta basis set was used with polarization functions. The calculated ionization potential (using Koopmans' theorem) is somewhat larger than the experimental one and the width of the correlation corrected valence band is in quite good agreement with the value obtained from previous calculations. On the other hand, although the correlation correction decreased the fundamental gap substantially as compared with its HF value (from 7.42 to 4.89 eV), it is still twice as large as its directly measured value. The main reason for this large disagreement is that we have calculated a single chain of PPV, while the measured value refers to a layer. Looking at the crystal structure of PPV one finds that it is closely packed with the smallest interchain distance of ∼2.5 A. In such case no Madelung potential can be used to describe the rest of the crystal around the calculated chain. For this reason we plan different two-dimensional calculations to resolve the contradiction concerning the fundamental gap.

The method of separated molecular orbitals (SMO) has already proved to be useful for describing the energy partitioning at the Hartree–Fock (HF) level in several weakly interacting systems. In the present paper, the total energy decomposition into different contributions according to the interacting units is discussed at the HF level for a zeolite model system. The effect of the basis set superposition is considered by the use of SMO in a simple and straightforward manner.

The correlation-corrected band structures of quasi 1D poly(para-phenylene) (PPP) and poly(peri-naphthalene) (PPN) are presented, using the ab initio quasi-particle method based on the iterative solution of the inverse Dyson equation. A double zeta basis set is used with polarization functions for PPN and a double zeta basis is used for PPP.

The results presented in this paper for the dimer of H2O as well as for the dative complexes formed by the interaction of BH3 + H2O and AlH3 + H2O suggest that about 50% of the dispersion energy can be recovered, using a 6-31G(d) basis set, in cases when only the contributions of those localized molecular orbitals are included which are in the vicinity of the interaction region. The reduction in computing time is about an order of magnitude. The procedure applied makes it possible to avoid basis set superposition errors at the correlated level. The method presented opens the way for studying large clusters containing various atoms beyond the HF level.

Ab initio self-consistent field (SCF) calculations are performed with the standard 6-31G* basis set for all-trans conjugated oligomers C2n+2H2n+4. The canonical occupied and virtual molecular orbitals (MOs) are separately localized by unitary transformations. Due to the localization, the perturbation operator is partitioned into two-particle and into single-particle terms; the MBPT is, therefore, a double-perturbation expansion in this case. By using the localized representation of the MBPT, the correlation energy contributions can be partitioned into local and nonlocal effects. It can be shown that the local effects are very important and well transferable, which makes possible the calculation of the correlation energy of larger molecules if the localized molecular orbitals (occupied and virtual) of smaller related molecules are known. © 1994 John Wiley & Sons, Inc.

We studied the transferability of the localized orbitals (LOs) of interacting Ne atoms using several basis sets. Both at SCF and at MP2 and MP3 levels, the contributions of the LOs have been calculated and discussed for the Ne2 and Ne3 systems. It was shown that for the LOs the transferability is satisfied to a good extent and due to the transferability the interaction energy at the correlated level can be calculated by using only the LOs of the supermolecule. The basis set superposition error (BSSE) is simply extracted from the intramolecular parts of the correlation energy. The two- and three-body interaction energies have been investigated for the studied systems. © John Wiley & Sons, Inc.

The dispersion interaction energy with the molecules BH3 and NH3 was computed using a specific supermolecule method. The essence of the approach used lies in applying a localized representation in the virtual space. This method makes it sensible to investigate the above systems surrounded by several water molecules.

Supermolecular model of the intermolecular interaction energy is studied. The correlation energy components are calculated by using the many-body perturbation theory (MBPT) in the canonical representation as well as in the localized one. The components of the corrections of the different order are analyzed individually. The effects of the localization procedure and the basis set are also investigated. An H2O trimer is used to study the two- and three-body components of the interaction energy. © 1993 John Wiley & Sons, Inc.

The singlet potential energy surface of Ga 2 H 2 has been studied using the self-consistent-field (SCF), single and double excitation configuration interaction (CISD), and single and double excitation coupled cluster (CCSD) methods. Optimized geometries and harmonic vibrational frequencies were obtained for four geometrical isomers with a double-zeta plus polarization basis set (DZP). Relative energies of the above structures were also predicted using a triple-zeta plus polarization basis set augmented with a set of f functions on the gallium atoms (TZP + f). For final energetic predictions with this basis set we included the effects of triple excitations perturbatively using the CCSD(T) method. The planar dibridged structure is the global minimum — two additional low-lying minima were found, corresponding to trans-bent and vinylidene-like structures. Our analysis also predicts the existence of a remarkable low-lying monobridged minimum, which has recently been observed experimentally for Si 2 H 2 , and predicted by ab initio methods for the valence-isoelectronic Al 2 H 2 .

Anm 5-dependent integral transformation procedure from atomic orbital basis to localized molecular orbitals is described for spatially extended systems with some Abelian symmetry groups. It is shown that exploiting spatial symmetry, the number of non-redundant integrals for normal saturated hydrocarbons can be reduced by a factor of 2.5-3.5, depending on the size of the system and on the basis. Starting from a list of integrals over basis functions in canonical order, the number of multiplications of the four-index transformation is reduced by a factor of 2.8-3.5 as compared to that of Diercksen's algorithm. It is pointed out that even larger reduction can be achieved if negligible integrals over localized molecular orbitals are omitted from the transformation in advance.

We have studied the transferability of the localized molecular orbitals (LMOs) of interacting water molecules for distances around the intermolecular energy minimum. The Fock matrix elements (e) and the “effective volumes”Vieff of the LMOs have been calculated and discussed. It was shown that for the valence shell LMOs the transferability is satisfied to a large extent, the deviation is less than 5 %. Due to this transferability the dispersion interaction energy can be calculated by using only the LMOs of the supermolecule and the BSSE can be neglected.

The interaction energy between the Li+ ion and the water molecule has been studied at the ab initio SCF+MBPT(2) level in localized representation.

An ab initio self-consistent field (SCF) method with standard STO-3G and 6-31G ∗ basis sets was used to study some normal saturated hydrocarbons. The occupied and virtual canonical orbitals were localized separately by Boys' procedure and the correlation energy corrections were calculated in the localized representation of the many-body perturbation theory. Introducing the concept of “neighbourhood order” the local and non-local effects can be separated and the correlation energy corrections can be partitioned accordingly. It was found that the correlation energy corrections in these molecules are predominantly of local origin. The contributions to the pair correlation energies are transferable to a good approximation. In analysing the contributions of the localized virtual orbitals, some interesting structural features were identified.

In this paper, we present a method for the calculation of dispersion interaction energies of molecules, which is based on the localized molecular orbitals of the supermolecule. It is shown (using various basis sets) that the energy contributions of the localized molecular orbitals, for distances around the intermolecular energy minimum, are transferable to a fairly good approximation from the noninteracting monomers to the supermolecule. The correlation energy component of the interaction energy can be separated into inter‐ and intraparts. We show how the basis set superposition errors can be located and separated at the correlated level. Results are presented for several systems [(H2O)2, (NH3)2, and Ne2 ] with different basis sets from the minimal one to the split shell plus polarization functions. The method applies the well‐known Boys’ localization procedure and has the advantage that for the dispersion energy at a given geometry, the integral transformation should only be carried out once (from the ba...

The ab initio SCF method was applied to the all-trans polyacetylenes C 2 n + 2 H 2 n + 4 ( n = 0, 2, 4, 6, 8, 10), by using standard STO-3G basis set. The localized molecular orbitals obtained by Boys' procedure were studied and compared. It is shown that, in spite of the “tails”, the contributions of the localized molecular orbitais (orbital energy, charge distribution, effective volume etc.) on increasing the length of the molecule converge to definite values, depending upon the position of the corresponding localized orbital in the molecule. It is shown that the difference with respect to the transferability between the aliphatic hydrocarbons and the all-trans conjugated polyenes is only quantitative. In the latter compounds the effects of the fourth neighbours should also be included.

Diagrammatic formulation of the MBPT is applied when the occupied and the virtual canonical orbitals are separately localized by unitary transformations. In this localized representation, due to the off-diagonal Fock matrix elements, the perturbation operator contains extra terms generating the so-called localization corrections. These corrections enter the perturbation energy in third and higher orders. Their magnitude depends on the type of localization, but they represent only a small fraction of the canonical corrections. The calculation of the localization corrections, however, does not need a significant amount of extra computer time. It is shown that by introducing an “order of neighborhood” local and nonlocal effects of the electron correlation can be separated and the contribution of the nonlocal effects can be neglected to a good approximation. Ab initio calculations have been carried out for the normal saturated hydrocarbons: C2n+1H4n+4 and for the all-trans conjugated polyenes C2n+2H2n+4. As to the ratio of the local and nonlocal corrections, it is shown that there is only a quantitative difference for these two kinds of systems (strongly or weakly localizable). Neglecting nonlocal effects, considerable amount of computer time can be saved.

The application of the MBPT in the localized representation requires that both the occupied and the virtual orbitals obtained by the canonical HF equation should be localized. The localization of the occupied orbitals is straightforward in general by any localization method. It is shown that by using Boys' method the localized virtual orbitals are spatially well separated and transferable not only in minimal basis sets.

Recent experimental sind theoretical studied reporting remarkable monobridged structures for Si 2 H 2 , Al 2 H 2 , and Ga 2 H 2 have motivated us to re-investigate the singlet potential energy surface of Ge 2 H 2 using the self-consistent-field (CCP), single and double excitation configuration interaction (CISD), and single and double excitation coupled cluster (CCSD) methods in conjunction with a double-ζ plus polarization basis set (DZP). In addition to the dibridged (or butterfly) ground state and the low-lying vinylidene-like minimum reported earlier by Grev and DeLeeuw, our study predicts the existence of a monobridged isomer, which is characterized as a minimum by means of harmonic vibrational frequency analyses

The ionization potential of the closed shell H2CO, H2COH+, H2COH22+ as well as the proton affinity of H2CO and H2COH+ have been studied at a variable CO bond length in the ground singlet and some of the low lying excited triplet and ionized doublet states.

The behaviour of the localization corrections of the MBPT is investigated. It is shown that calculating the third and fourth order localization corrections we obtain sufficiently accurate results to the second order correlation energy both for cyclic polyenes and for saturated hydrocarbons. The evaluation of the localization diagrams does not require significant extra computer time. The extra computer time can be recovered if small non-local effects will be neglected.

An ab initio SCF method has been applied to normal saturated hydrocarbons C2n+1H4n+4 (n=0,1,2,3,4), by using a standard STO-3G basis set. The localized orbitals of the molecules obtained by Boys'procedure are investigated and compared. It is shown that, in spite of the “tails” the contributions of the localized orbitals (orbital energy, charge distribution, effective volume, etc.), by increasing the length of the system, converge to definite values depending only upon the position of the corresponding localized orbital in the molecule. This offres a possibility of explaining the transferability of certain molecular properties in a natural way.

The localized molecular orbitals of some related ten- and eighteen-electron systems have been studied. The transferability of the kinetic, self-interaction, Coulomb and exchange interaction energies on localized orbitals have been shown. The standard deviation of the kinetic and of the interaction energies (including exchange) are less than 2.5% except for lone pair orbitals of the oxygen atoms where the standard deviation is close to 4%.

Vertical proton affinities were calculated with closed and open shell direct SCF-MO methods for the ground, excited triplet and ionized doublet states of CH2O and CH2OH+. The computed gas phase basicity of CH2O follows the order: CH2O(1 A 1) > CH2O*(3 A 1 or 3 A 2) > CH2O+(2 B 2 or 2 B 1).

The second-order energy corrections are calculated for some normal saturated hydrocarbons by using the many body-perturbation theory (MBPT) based on localized orbitals. The correlation energies are expressed as the sum of contributions from virtual orbital pairs. We have found that these contributions are transferable and have interesting structural features: the trans-coplanar effects are relatively large. Partitioning the correlation energies according to the “order of neighbourhood” we have found that the zero order effects are the largest but the first and second neighbour contributions are also important.

Ab initio double-zeta quality molecular orbital calculations have been carried out on an extensive series of ten-electron hydrides. The Edmiston–Ruedenberg energy-localized molecular orbitals were calculated and the total molecular and localized orbital densities analyzed in terms of dipole moments, contour plots, and a simplified model for the orbital density involving analysis of the first and second moments. The simplified moment analysis model may be easily visualized in terms of threedimensional geometric objects, spheres, and ellipsoids. The model summarizes the information on the effective functional distribution inherent in the more detailed orbital contour plots in a clear and concise manner.

A relationship between e i the energy contribution of the i th localized molecular orbital, and 〈 R 3 〉 i = (〈 x ′ 2 〉〈 y ′ 2 〉〈 z ′ 2 〉) 1 2 , the “statistical effective volume” of the i th LMO, is discussed for a series of ten-electron hydrides. The equation 1/ e i = m (〈 R 3 〉 i ) 2 3 where m is a constant holds accurately for core, bond, and lone pair LMO densities.

The effects of Gaussian basis set contraction and addition of polarization functions on H2O localized orbitals have been studied at the experimental geometry. It is shown that the electric moments and moment features of localized orbitals are not influenced very much by basis set quality variations, as going from medium size to enlarged basis sets. The difference between bond pair and lone pair charge densities was found to be larger on approaching the Hartree-Fock limit. A minimal basis set, however, does not suitably characterize the localized charge distributions.

In a series of papers a new method which uses the molecular symmetry for treatment of extended molecules is investigated. In this paper it is shown that in the presence of model geometries the method — on which a new ab initio program named SYCETY is based — is effective for calculation of large, related systems.

An ab initio SCF method with a standard STO-3G basis set was used to study normal saturated hydrocarbons C 2 n +1 H 4 n +4 ( n =0,1,2,3,…). The occupied and the virtual canonical orbitals were localized separately by Boys'procedure and the second-order correlation energy was calculated in the localized representation of the MBPT. In order to separate local and non-local effects the concept of “neighbourhood order” was introduced and the correlation energies were partitioned according to this. It was shown that: (1) by taking into account only the zero-, first- and second-order “neighbourhoods”, more than 99% of the total second-order correlation energy could be recovered; (2) the contributions to the pair correlation energies were transferable to a good approximation; and (3) by increasing the system, the contributions of the most important pair correlation energies converged to definite values, depending only upon the position of the corresponding LMO in the molecule.

Closed-shell SCF calculations on the ground states and direct SCF calculations on the ionized doublet states were carried out for a series of ten-electron hydrides. The correlation of ionization potentials with the degree of protonation and the nuclear charge has been studied for hole states derived from excitation out of both the core and valence molecular orbitals. Calculated proton affinities of the ground states and hole states derived from a given symmetry orbital show a similar trend to that of the ionization potentials.

A new measure of orbital localizability is proposed. The actual improvement in classical electrostatic interpretations of electronic energy contributions on localization of CH 4 , NH 3 , H 2 O, HF and Ne LCAO wavefunctions is computed to be small. Substantial valence LMO spatial overlapping remains.

The parallel between orbital first and second electric moments and statistical first and second central moments is noted. Three measures of orbital spatial distribution in terms of their moments are proposed, and applied to the LMO's in a series of ten-electron hydrides. Consistent differences between bond and lone pair distributions are found. Using the statistical interpretation, for each LMO an “effective” solid angle around the central atom is postulated.

Assuming that truncated strongly orthogonal geminals for a system are already known, the possibility of using rij‐dependent correction functions in the geminals is discussed with an emphasis on the violation of the strong orthogonality conditions. It is shown that for given truncated geminals there always exists at least one optimally decomposed complete set of one‐electron functions, which makes it possible to pick out the configurations giving rise to strong orthogonality condition violating terms in the energy expression. The latter can be neglected, as compared with others which are of second order in the correction functions, when the system consists of spatially separated pairs in the sense that the one‐electron functions contributing appreciably to one pair do not have significant differential overlap with the starting basis functions of other pairs. In this case interorbital effects are also small. For systems consisting of weakly localizable pairs, when the strong orthogonality condition violatin...

Localized charge densities of some small molecules at their experimental and calculated equilibrium geometries have been studied using the 6-31G and 6-31G/d basis sets. Introducing polarization functions it has been found that the bond-pair charge distributions are “more”, while the lone-pair- ones are “less” localized at their theoretically determined total-energy minima than at the corresponding experimental geometries.

While single protonation is always exothermic in the gas phase multiple protonations are shown to be endothermic. The relevance of these results to acid catalysed reactions is discussed.

The ionization potential of the closed shell H2CO, H2COH+, H2COH22+ as well as the proton affinity of H2CO and H2COH+ have been studied at a variable CO bond length in the ground singlet and some of the low lying excited triplet and ionized doublet states.

Diagrammatic formulmion of the MBPT has been extended to the case when both the occupied orbita'ls and the virtual ones are separately localized, i.e., they are unitary transforms of the · canonical HF orbitals. All diagrams representing ground state correlation energy are generated through the fifth order. For cyclic polyenes C4n+z H4n+z as model systems, in PPP approximation, all perturbation energy corrections through the fourth order have been calculated for a wide range of the coupling constant: (J-1. Some fifth order energy corrections have also been evaluated and the convergence of the localization corrections has been studied. For CsHs the results of the canonical and the localized versions have been compared with those obtained by full CI. We have shown that in the localized representation the energy corrections can be partitioned into local and nonlocal contributions.