Bond orbital approach for optical rotatory strength calculations

Directly determined localized approximate molecular Orbitals are used in excitation energy and optical rotatory strength calculations within the CNDO/2 scheme. Using strictly localized bond orbitals one obtains qualitatively good excitation energies, but quantitative agreement can be found only by considering delocalization effects, which have been proved to be crucial in determining the optical rotatory strength. The delocalization interactions are classified as through space and through bond ones and even the latter is found to have significant contributions. The chiroptical properties of the lowest lying transitions in the twisted glyoxal molecule are analysed in terms of localized molecular orbital contributions.     

Aromaticity: an ab initio evaluation of the properly cyclic delocalization energy and the pi-delocalization energy distortivity of benzene

A complete active space self-consistent field (CASSCF) calculation of the pi system of a conjugated molecule enables one to define optimal valence pi and pi* molecular orbitals (MOs). One may define from them a set of atom-centered orthogonal pi orbitals, one per carbon atom, and the resulting upper multiplet is used to define the pi-electron delocalization energy. This quantity is confirmed to be slightly distortive, i.e., to prefer bond-alternated geometries. One may also define strongly localized bond MOs corresponding to a Kekule structure and then perturb the associated strongly localized single determinant under the effect of the delocalization between the bonds and of the electronic correlation. The third order of perturbation introduces the contribution of the cyclic circulation of the electrons around the benzene ring, i.e. the aromatic energy contribution. Its value is about 1.5 eV. It is antidistortive, but remains important under bond alternation. The cyclic correlation effects are of minor importance.     

Ab-Initio MRD-CI calculations for breaking a chemical bond in a molecule in a crystal or other solid environment. II.H3C—NO2 decomposition of nitromethane in a nitromethane crystal with voids

Recently we extended our strategy for MRD-CI (multireference double excitation-configuration interaction) calculations based on localized/local orbitals and an “effective” CI Hamiltonian for molecular decompositions of large molecules to breaking a chemical bond in a molecule in a crystal or other solid environment. Our technique involves solving a quantum chemical ab-initio SCF explicitly for a system of a reference molecule surrounded by a number of other molecules in the multipole environment of more distant neighbors. The resulting canonical molecular orbitals are then localized and the localized occupied and virtual orbitals in the region of interest are included explicitly in the MRD-CI with the remainder of the occupied localized orbitals being folded into an “effective” CI Hamiltonian. The MRD-CI calculations are carried out for breaking a bond in the reference molecule. This method is completely general. The space treated explicitly quantum chemically and the surrounding space can have voids, defects, deformations, dislocations, impurities, dopants, edges and surfaces, boundaries, etc. We previously applied this procedure successfully to the H₃C? NO₂ bond dissociation of nitromethane in a nitromethane crystal with extensive testing of the number of molecules that have to be included explicitly in the SCF and how many molecules have to be represented by more distant multipoles. The results indicated that it took more energy to dissociate the H₃C? NO₂ bond when the nitromethane molecule was in the crystal than it did to dissociate that bond in the free nitromethane molecule. In this present study we have investigated the effect of voids (both in the nitromethane molecules treated explicitly in the SCF and those in the environment represented by multipoles) on the calculated H₃C? NO₂ bond dissociation energies.     

Transient bonds and chemical reactivity of molecules

Electron delocalization between the reagent and reactant molecules is the principal driving force of chemical reactions. It brings about the formation of new bonds and the cleavage of old bonds. By taking the aromatic substitution reaction as an example, we have shown the orbitals participating in electron delocalization. The interacting orbitals obtained are localized around the reaction sites, showing the chemical bonds that should be generated and broken transiently along the reaction path. By projecting a reference orbital function that has been chosen to specify the bond being formed on to the MOs of the reactant molecules, the reactive orbitals that are very similar to the interacting orbital have been obtained. The local potential of the reaction site for electron donation estimated for substituted benzene molecules by using these projected orbitals shows a fair correlation with the experimental scale of the electron-donating and -withdrawing strength of substituent groups. The reactivity is shown to be governed by local electronegativity and local chemical hardness and also by the localizability of interaction on the reaction site. © 1996 John Wiley & Sons, Inc.     

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.     

块定域波函数方法及其应用

提出了块定域波函数方法以定量分析分子内的电子定域现象或分子间的电荷传递效应。对于一个假想的严格定域的分子,我们通过将全部的电子和基轨道配分成几个子空间来构造其相应的波函数。其中每一个分子轨道只对某一个子空间展开,各子空间内的分子轨道相互正交,但不同子空间内的分子轨道间是非正交的。Hartree-Fock波函数和块定域波函数之间的能量之差即为分子内的电子定域能或分子间的电荷传递能。我们应用块定域波函数方法讨论了丁二烯分子中的旋转势垒。     

Ab initio MRD-CI calculations for breaking a chemical bond in a molecule in a crystal or other solid environment. III. Me2N?NO2 decomposition of dimethylnitramine in a large crystalline environment

Recently we extended our strategy for MRD-CI (multireference double excitation-configuration interaction) calculations, based on localized/local orbitals and an “effective” CI Hamiltonian, for molecular decompositions of large molecules to breaking a chemical bond in a molecule in a crystalline or other solid environment. Our technique begins with an explicit quantum chemical SCF calculation for a reference molecule surrounded by a number of other molecules in the multipole environment of more distant neighbors. The resulting canonical molecular orbitals are then localized, and the localized occupied and virtual orbitals in the region of interest are included explicitly in the MRD-CI with the remainder of the occupied localized orbitals being folded into an “effective” CI Hamiltonian. The MRD-CI calculations are then carried out for breaking a bond in the reference molecule. This method is completely general in that the space treated explicitly, as well as the surrounding space, may contain voids, defects, deformations, dislocations, impurities, dopants, edges and surfaces, boundaries, etc. Dimethylnitramine is the smallest prototype of the energetic R₂N—NO₂ nitramines, such as the 6-member ring RDX or the 8-member ring HMX. Decomposition of energetic compounds is initiated in the solid by a breaking of the target bond. Thus, it is crucial to know the difference in energy between breaking a bond in an isolated energetic molecule versus in the molecule in a solid. In the present study, we have carried out MRD-CI calculations for the Me₂N—NO₂ dissociation of dimethylnitramine in a dimethylnitramine crystal. The cases we investigated were one dimethylnitramine molecule (surrounded by 53 and 685 neighboring dimethylnitramine molecules represented by multipoles), three dimethylnitramine molecules, and three dimethylnitramine molecules (surrounded by 683 neighbors). All multipoles were cumulative atomic multipoles up through quadrupoles. The MRD-CI calculations on dimethylnitramine required large numbers of reference configurations from which were allowed all single and double excitations.     

Delocalization corrections to the strictly localized molecular orbitals: A linearized SCF approximation

An explicit formula is derived for calculating the delocalization corrections (tails) to be added to the strictly localized bond orbitals. It was obtained by solving analytically the SCF problem for the interbond interactions in a linearized approximation. The model calculations at the CNDO/2 level show that this simple approach is sufficient to account for the molecular conformations.     

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.     

Nature of bonding in the sulfuryl group

The SO sulfuryl bond in a number of representative sulfoxides and sulfones has been studied at the B3LYP/6-311+G(d,p) level in the atoms-in-molecules (AIM) approach involving the AIM delocalization index and the Cioslowski-Mixon localized orbitals and associated covalent bond order. The sulfur-oxygen covalent bond is strongly polarized toward oxygen and the oxygen lone pairs provide significant backbonding to create short and strong SO bonds, similar in nature to those found in the analogous phosphoryl (PO) bond. Although the sulfoxides in general have larger delocalization indices than the sulfones, there is no correlation between these quantities and the bond dissociation energies.     

Natural bond orbital analysis in the ONETEP code: Applications to large protein systems

First principles electronic structure calculations are typically performed in terms of molecular orbitals (or bands), providing a straightforward theoretical avenue for approximations of increasing sophistication, but do not usually provide any qualitative chemical information about the system. We can derive such information via post‐processing using natural bond orbital (NBO) analysis, which produces a chemical picture of bonding in terms of localized Lewis‐type bond and lone pair orbitals that we can use to understand molecular structure and interactions. We present NBO analysis of large‐scale calculations with the ONETEP linear‐scaling density functional theory package, which we have interfaced with the NBO 5 analysis program. In ONETEP calculations involving thousands of atoms, one is typically interested in particular regions of a nanosystem whilst accounting for long‐range electronic effects from the entire system. We show that by transforming the Non‐orthogonal Generalized Wannier Functions of ONETEP to natural atomic orbitals, NBO analysis can be performed within a localized region in such a way that ensures the results are identical to an analysis on the full system. We demonstrate the capabilities of this approach by performing illustrative studies of large proteins—namely, investigating changes in charge transfer between the heme group of myoglobin and its ligands with increasing system size and between a protein and its explicit solvent, estimating the contribution of electronic delocalization to the stabilization of hydrogen bonds in the binding pocket of a drug‐receptor complex, and observing, in situ, the n → π* hyperconjugative interactions between carbonyl groups that stabilize protein backbones. © 2012 Wiley Periodicals, Inc.     

Extremely localized molecular orbitals (ELMO): a non-orthogonal Hartree-Fock method

A new optimization method for extremely localized molecular orbitals (ELMO) is derived in a non-orthogonal formalism. The method is based on a quasi Newton-Raphson algorithm in which an approximate diagonal-blocked Hessian matrix is calculated through the Fock matrix. The Hessian matrix inverse is updated at each iteration by a variable metric updating procedure to account for the intrinsically small coupling between the orbitals. The updated orbitals are obtained with approximately n ² operations. No n ³ processes such as matrix diagonalization, matrix multiplication or orbital orthogonalization are employed. The use of localized orbitals allows for the creation of high-quality initial “guess” orbitals from optimized molecular orbitals of small systems and thus reduces the number of iterations to converge. The delocalization effects are included by a Jacobi correction (JC) which allows the accurate calculation of the total energy with a limited number of operations. This extension, referred to as ELMO(JC), is a variational method that reproduces the Hartree-Fock (HF) energy with an error of less than 2 kcal/mol for a reduced total cost compared to standard HF methods. The small number of variables, even for a very large system, and the limited number of operations potentially makes ELMO a method of choice to study large systems. Received: 30 December 1996 / Accepted: 5 June 1997     

Analyzing molecular properties calculated with two-component relativistic methods using spin-free natural bond orbitals: NMR spin-spin coupling constants

An analysis method for static linear response properties employing two-component (spin-orbit) relativistic density functional theory along with scalar relativistic "natural localized molecular orbitals" (NLMOs) and "natural bond orbitals" (NBOs) has been developed. The spin-orbit NLMO/NBO analysis has been applied to study the indirect spin-spin coupling (J-coupling) constants in Tl-I, PbH(4), and a dinuclear Pt-Tl bonded complex with a very large Pt-Tl coupling constant (expt.: 146.8 kHz). For Tl-I it is shown that the analysis scheme based on scalar relativistic NLMOs is applicable even if spin-orbit coupling is responsible for most of the coupling's magnitude. For PbH(4) it is shown that electron delocalization plays a much larger role for the Pb-H coupling than it is the case for the C-H coupling in methane. For the Pt-Tl complex the analysis clearly demonstrates the strong influence of the ligands on the Pt-Tl coupling constant and quantifies the effect of the delocalization of the Pt-Tl bond on the Pt-Tl coupling constant.     

Symmetry breaking in benzene and larger aromatic molecules within generalized valence bond coupled cluster methods

The origin of symmetry breaking (SB) in benzene in generalized valence bond methods is investigated within a coupled cluster formalism that correlates all valence electrons. Retention of a limited number of pair correlation amplitudes (as in the perfect- and imperfect-pairing models) that incompletely describes interpair correlations leads to symmetry breaking as the orbitals and amplitudes are optimized. Local correlation models that are exact for one, two, and three interacting pairs at the doubles excitation level are compared against the exact pair correlation treatment, which correlates four interacting pairs at once in the connected double substitution operator. For simplicity, this comparison is performed with a second-order model of electron correlation, which is reasonably faithful to the infinite-order result. The significant SB known for the one-pair model (perfect pairing) is not eliminated at the two-pair level, but is virtually eliminated at the three-pair level. Therefore, a tractable hybrid model is proposed, which combines three-pair correlations at the second-order level and infinite-order treatment for the strong imperfect-pairing correlations involving one and two-pair correlations. This model greatly reduces SB in benzene and larger delocalized pi systems such as naphthalene and the phenalenyl cation and anion. The resulting optimized orbitals are localized in the sigma space but exhibit significant delocalization in the pi space. This means that correlation effects associated with different resonance structures are treated in a more balanced way than if the pi orbitals localize, leading to reduced SB.     

Basis set dependence of localized orbitals

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.     

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.     

Localization measure and maximum delocalization in molecular systems

A mathematically well-defined measure of localization is presented based on Mulliken's orbital populations. It is shown that this quantity equals 1 for core- and lone-pair orbitals, 2 for two-atomic bonds, 6 for benzene rings, etc., and it is applicable for delocalized canonical HF orbitals as well. The definition of this quantity is general in the sense that ab initio MOS with overlapping AO expansion, and semiempirical wave functions using the ZDO approximation as well, can be treated. The localization quantity is essentially “intrinsic,” i.e., no subdivision of the molecule is required. For N-electron wave functions, mean delocalization can be defined. This measure is not invariant to unitary transformations of the one-electron orbitals, characterizing in this way the localized or extended representation of the N-electron wave function. It can be proven, however, that for unitary transformed wave functions a maximum delocalization exists which depends only on the physical (N-electron) properties of the molecule. It is shown that inhomogeneous charge distribution can cause strong electron localization in molecular systems. The delocalization of the canonical Hartree–Fock orbitals, the Parr–Chen circulant orbitals, and the optimum delocalized orbitals is studied by numerical calculations in extended systems.     

Coherent superposition of resonance wave function in terms of weighted orthogonalized natural localized configurations

In this research, the projection technique has been applied in order to decompose the electronic wave function into its weighted orthogonalized resonance components. These components have been constructed by determinants whose orbitals are selected among natural bond orbitals. However, the procedure is general and any other localized orbitals can be used as well. Both σ and π delocalize systems have been considered in order to check the reliability of the calculated resonance weights. For π‐systems, the presented procedure could predict significant decrease of weight of certain resonance structures when the molecular planarity was destroyed. Water cyclic clusters were also tested and the results confirmed the existence of strong σ‐delocalization in the clusters. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008