A study of molecular one-electron properties in terms of localized molecular orbital components

A number of molecular one-electron progperties have been analyzed by partitioning their electronic components over energy localized molecular orbitals (LMO ). The ammonia and ethane molecules, calculated in an Approximately double zeta qualtiy basis set, were considered. The partitioning of the electronic components of certain one-electron properteies over LMO allows a quantitative rationalization of the sensitivity of certain properties to basis set effects due to the differeing degree of difficulty of accurately determining different LMO as measures of the molecular electron density.     

An extended PCILO method

The perturbative configuration interaction using localized orbitals (the PCILO method) was extended in the way that current limitations to the two-centre bond approach were overcome. The localized molecular orbitals contain an arbitrary number of the basis set components; this follows from the a priori stated localized bonding model of a molecule. The extended PCILO method was formulated for the CNDO, INDO and NDDO Hamiltonian approximations. The configuration interaction was performed using the Rayleigh-Schrödinger many-body perturbation theory with the Møller-Plesset type of Hamiltonian partitioning, similar to that used in the so-called modified PCILO method. Applications to molecules with semi-localized and/or semi-delocalized bonds, as benzene or diborane, are presented.     

Determination of extremely localized molecular orbitals in the framework of density functional theory

Extremely localized molecular orbitals are rigorously localized on only a preselected set of atoms and do not have any tails outside the localization region. The importance of these orbitals lies in their ability to be transferred from one molecule to another one. A new algorithm to determine extremely localized molecular orbitals in the framework of the density functional theory method is presented. This could also be a valuable tool in the quantum mechanics/molecular mechanics methodology where localized molecular orbitals are used to describe covalent bonds across the frontier region. The present approach is used to build up the electron density of thymopentin, a polypeptide constituted by five residues, starting from extremely localized molecular orbitals determined on a set of model molecules. The results obtained confirm good transferability properties for these orbitals.Proceedings of the 11th International Congress of Quantum Chemistry satellite meeting in honor of Jean-Louis Rivail     

On the transferability of Fock matrix elements

The transferability of Fock matrix elements in the linear combination of atomic orbitals molecular orbital scheme is analysed using localized orbitals. It is shown that this transferability is dependent on the transferability of these localized orbitals and the neglect of long-range contributions from partially cancelling Coulomb nuclear attraction and electron repulsion terms. A theoretical basis is thus provided for the simulated ab initio molecular orbital and related methods. Various corrections previously introduced in an ad hoc manner are shown to be justified. Transferability in both the closed shell and open shell schemes is analysed.     

Fast orbital localization scheme in molecular fragments resolution

The method for localizing orbitals on a set of predefined molecular fragments is introduced. Regional localized molecular orbitals (RLMO) are obtained through block diagonalization of the one-electron density matrix and further refinement of the resulting eigenvectors. The algorithm is fast and reliable, as is illustrated by a few examples. Potential applications range from conceptual insight into a chemical bonding to reduced scaling computational techniques. RLMOs are particularly well suited for fragmentation computational methods and for exploiting the locality of electronic correlation in post-HF methods.     

Distortion of interacting atoms and ions

The distortion of atoms in HeNe and ions in LiF and NaCl is studied by use of non-orthogonal, least distorted, localized molecular orbitals in the restricted Hartree-Fock approximation. We find that the least distortion criterion is effective in producing localized orbitals. In addition we find that point-by-point the localized orbitals differ little from the Hartree-Fock orbitals of the corresponding atoms or ions, although the differences are energetically important. We infer from our calculations that the effective potential which distorts atomic orbitals into localized molecular orbitals must be quite weak.     

A modified PCILO method

The perturbative configuration interaction using strictly localized molecular orbitals, called the modified PCILO method, for which the use of the Rayleigh-Schrödinger many-body perturbation theory with the Moller-Plesset Hamiltonian partitioning is characteristic, has been proposed in this communication. On the CNDO/2 and INDO levels of Hamiltonian approximations strictly localized molecular orbitals have been constructed by solving modified Roothaan equations. From the zero and second order energy interatomic distances and harmonic force constants for some diatomic molecules have been calculated. The linear dependence of the correlation energy on the number of valence electrons in the series of the molecules CH₄, CH₃F, CH₂F₂, CHF₃ and CF₄ is perfect.     

Localized charge distributions

A localized molecular orbital has been found to extend slightly and regularly into regions away from the chemical bond which contains most of its charge cloud. This was made the basis for a method of transferring localized orbitals among similar molecules. Each localized orbital induces a set of so-called molecule invariant fragments consisting of one bond fragment and collections of geminal fragments, vicinal fragments, and third and fourth neighbor fragments. Localized orbital expansion coefficients in a hybrid basis can be calculated for these molecule invariant fragments without solving any equations or performing any laborious computations. The present work is an application to acylic hydrocarbons. The results are based on the analysis of 33 INDO-SCF molecular orbital wavefunctions in the localized representation. Computational methods for obtaining close approximations to localized orbitals are also discussed. The application of a suggested pseudo-eigenvalue localization method and its accompanying self-consistent iteration process are found to not converge.     

LocalSCF method for semiempirical quantum-chemical calculation of ultralarge biomolecules

A linear-scaling semiempirical method, LocalSCF, has been proposed for the quantum-chemical calculations of ultralarge molecular systems by treating the large-scale molecular task as a variational problem. The method resolves the self-consistent field task through the finite atomic expansion of weakly nonorthogonal localized molecular orbitals. The inverse overlap matrix arising from the nonorthogonality of the localized orbitals is approximated by preserving the first-order perturbation term and applying the second-order correction by means of a penalty function. This allows for the separation of the orbital expansion procedure from the self-consistent field optimization of linear coefficients, thereby maintaining the localized molecular orbital size unchanged during the refinement of linear coefficients. Orbital normalization is preserved analytically by the variation of virtual degrees of freedom, which are orthogonal to the initial orbitals. Optimization of linear coefficients of localized orbitals is performed by a gradient procedure. The computer program running on a commodity personal computer was applied to the GroEL-GroES chaperonin complex containing 119,273 atoms.     

Semiempirical quantum-chemical calculations on the conformations of methyl formate and methyl thiolformate

The cis, trans, and gauche conformations of the methyl esters of formic and thiolformic acids have been investigated by different semiempirical methods. Total geometry optimization (CNDO/2, MINDO/3) and bond angle optimization (PCILO, NDDO) have been performed for the O-alkyl ester. The S-alkyl ester has been studied by the MINDO/3 method at the total geometry optimization level and by CNDO/2 and PCILO methods at the bond angle optimization level. The influence of sulphur d orbitals on the optimized molecular geometry as well as on the magnitude and direction of the dipole moment vector has been investigated in the CNDO/2 framework. The total energy differences of the conformers are compared to the experimental and ab initio results. CNDO/2 and NDDO energy partitioning have been performed to obtain information on the origin of the cis—trans energy difference and of the rotation barrier. The extent of the lone-pair delocalization has been studied in the different conformations using localized molecular orbitals. Calculations have been performed on the staggered and eclipsed positions of the methyl group in the planar conformations of both esters.     

A simple extension of the external magnasco-perico localization procedure to the virtual MO-Space

The external localization procedure of Magnasco and Perico is extended to the unoccupied molecular orbitals of the Fock-operator. The formal correspondence between bonding orbitals and localized antibonding MOs is demonstrated. Localized occupied and virtual one-electron functions are calculated within a semiempirical INDO-Hamiltonian and are analyzed; the externally localized occupied MOs are compared with energy localized orbitals computed by the Edmiston and Ruedenberg procedure. Various applications of the fully localized (occupied and virtual) MO set are discussed.     

Are atoms sic to molecular electronic wavefunctions? II. Analysis of fors orbitals

Electronic wavefunctions that describe molecules in the full optimized reaction space (FORS) are multiconfigurational wavefunctions which are invariant under non-singular linear transformations of the occupied molecular orbitals. They offer therefore a considerably wider scope for orbital interpretations than the single-configuration Hartree-Fock approximation. For example they can be analyzed in terms of natural MOs and in terms of localized MOs. The latter turn out to be remarkably atomic in character and a new localization procedure can be formulated which yields atom-adapted molecular orbitals. These have the character of minimal-basis-set AOs that are optimally adapted to the molecular environment and furnish an unambigious atomic population analysis. On the other hand, chemically adapted molecular orbitals can be defined by an appropriate compromise between natural orbitals and localized orbitals. The freedom to use, as configuration-generating molecular orbitals, atom-adapted FORS MOs as well as chemically adapted FORS MOs makes FORS wavefunctions particularly suitable for chemical interpretations. The ensuing analysis establishes the minimal basis set (in molecule-adapted form) as a theoretically sound concept for the understanding of accurate molecular wavefunctions. An illustrative example is discussed.     

Optimal virtual orbitals to relax wave functions built up with transferred extremely localized molecular orbitals

Extremely localized molecular orbitals (ELMOs), namely orbitals strictly localized on molecular fragments, are easily transferable from one molecule to another one. Hence, they provide a natural way to set up the electronic structure of large molecules using a data base of orbitals obtained from model molecules. However, this procedure obviously increases the energy with respect to a traditional MO calculation. To gain accuracy, it is important to introduce a partial electron delocalization. This can be carried out by defining proper optimal virtual orbitals that supply an efficient set for nonorthogonal configurations to be employed in VB-like expansions.     

Topological localized molecular orbitals

Intrinsic and external π-orbital localization procedures which rely only on molecular topology are proposed and discussed. Localized molecular orbitals obtained by application of these procedures are referred to as ‘topological localized molecular orbitals”.     

Quadratically convergent calculation of localized molecular orbitals

Two iterative procedures for the transformation of canonical self-consistent field molecular orbitals to intrinsic localized molecular orbitals are proposed. A first-order method based on a series of (n × n) unitary transformations may be applied to orbitals which are far from convergence. The second method, based on Newton's method, yields quadratic convergence. Numerical results based on Boys' criterion are presented for water, carbon monoxide, boron fluoride, nitric oxide, and methylacetylene. A composite method may be used to obtain rapid convergence for large molecules for which it is not practical to calculate the entire hessian matrix. The performance of the composite method is demonstrated by application to the dinitrogen tetroxide molecule. Highly converged localized molecular orbitals may be obtained for most molecules with five to eight first-order iterations followed by three or four iterations based on either the second-order or composite method.     

A comparison of the IGLO and LORG methods for the calculations of nuclear magnetic shieldings

The individual gauge for localized orbitals (IGLO) and localized orbital/local origin (LORG) methods for the calculation of chemical shieldings are compared from their theoretical and computational viewpoints. A detailed analysis of the fluorine α-substituent effect in a series of fluoromethanes is given in terms of the IGLO and LORG bond contributions. The performance of both methods is discussed for molecular systems of fairly different sizes.     

A quantitative analysis of the through-space and the through-bond interactions between lone-pairs in azines: pyridazine,pyrimidine and pyrazine

The INDO calculations were performed on the three azines: pyridazine, pyrimidine, and pyrazine. The cannonical molecular orbitais obtained by these calculations were then transformed into the localized molecular orbitals. With the use of the localized molecular orbitals, the variation in the lone-pair orbital energies of these molecules were pursued in the light of the through-space and/or the through-bond interactions between the specified localized molecular orbitals in a molecule selectively. The interactions were expressed by the summation of several terms: through-space, through-bond, through-virtuals and coupling terms.     

Localized orbitals in hydrogen bonded systems

The localized molecular orbitals for a variety of hydrogen bonded systems are obtained from their INDO and CNDO/2 wavefunctions. The bonding of these systems is qualitatively discussed in light of the localized orbitals.     

Direct determination of localized SCF orbitals

The determination of SCF molecular orbitals by a perturbation method proposed by Lefebvre and Moser is used for the direct determination of localized SCF orbitals. Comparisons are made with the canonical SCF procedure. Advantages of the present method for conformational studies and for the determination of “local SCF orbitals” are also examined.