A simple computational scheme for obtaining localized bonding schemes and their weights from a CASSCF wave function

We devise and apply a simple computational scheme for obtaining localized bonding schemes and their weights from a CASSCF wave function. These bonding schemes are close to resonance structures drawn by chemists. Firstly, a CASSCF wave function is computed. Secondly, the CASSCF computation is repeated but now the delocalized complete active space MOs are substituted by Weinhold's localized natural atomic orbitals. In this way the original CASSCF wave function is represented by a sequence of Slater determinants composed of localized natural atomic orbitals. Thus, a standard CASSCF wave function can be reinterpreted in terms of a local picture. To test the method we obtain localized bonding schemes and their weights for the ground and the pi-pi* excited state of ethylene. Moreover, bonding schemes and their weights are derived for the ground, the 1(1)B(u), and the 2(1)Ag pi-pi* excited states of trans-butadiene. The large weight bonding schemes are shown to be a qualitative indicator for the known photochemistry of butadiene. The remarkable stability of the Arduengo carbene is discussed by obtaining bonding schemes that indicate a stabilizing delocalization of the pi electrons. We illustrate that the large weight bonding schemes are in line with the observed reactivity of the Arduengo carbene.     

Orthogonal natural atomic orbitals form an appropriate one-electron basis for expanding CASSCF wave functions into localized bonding schemes and their weights

Localized bonding schemes and their weights have been obtained for the pi-electron system of nitrone by expanding complete active space self-consistent field wave functions into a set of Slater determinants composed of orthogonal natural atomic orbitals (NAOs) of Weinhold and Landis (Valency and Bonding: A Natural Bond Orbital Donor-Acceptor Perspective, 2005). Thus, the derived bonding schemes are close to orthogonal valence bond structures. The calculated sequence of bonding scheme weights accords with the sequence of genuine resonance structure weights derived previously by Ohanessian and Hiberty (Chem Phys Lett 1987, 137, 437), who employed nonorthogonal atomic orbitals. This accord supports the notion that NAOs form an appropriate orthogonal one-electron basis for expanding complete active space self-consistent field wave functions into meaningful bonding schemes and their weights.     

The behavior of transition metal nitrido bonds towards protonation rationalized by means of localized bonding schemes and their weights

A new computational scheme is applied to rationalize the different protonation behaviors of the nitrido complexes [L'Mn(V)(N)(acac)](+), [LCr(V)(N)(acac)](+), and [LV(V)(N)(acac)](+). L and L' represent the macrocycles 1,4,7-triazacyclononane and its N-methylated derivative, respectively, and acac is the bidentate monoanion pentane-2,4-dionate. The bonds of the complexes are partitioned into bonds to be investigated and bonds of lesser interest. The investigated bonds are the transition metal nitrido bonds M(V)[triple chemical bond]N| (M = Mn, Cr, and V) and the bonds of lesser interest are located in the ligands. The ligand bonds are described by means of the strongly occupied natural bond orbitals. The electrons in the M(V)[triple chemical bond]N| nitrido bonds, however, are treated more accurately. A full configuration interaction procedure is applied in the space spanned by the strongly occupied natural bond orbitals and their corresponding antibonding orbitals. Localized bonding schemes and their weights are obtained for the d(pi)-p(pi) bonds of interest. This is achieved by representing the two-center natural bond orbitals for a d(pi)-p(pi) bond by the one-center natural hybrid orbitals localized at the bond atoms. The obtained bonding schemes are close to orthogonal valence bond structures. Their weights indicate that the nitrido nitrogen in [LV(V)(N)(acac)](+) is more easily protonated than the nitrido nitrogens in [L'Mn(V)(N)(acac)](+) and [LCr(V)(N)(acac)](+). This result is in good accord with experiment.     

On the transition from localized to delocalized electronic states in divalent-metal clusters

The transition from van der Waals to covalent bonding, which is expected to occur in divalent-metal clusters with increasing cluster size, is discussed. We propose a model which takes into account, within the same electronic theory, the three main competing contributions, namely the kinetic energy of the electrons, the Coulomb interactions between electrons, and thes ?p intraatomic transitions responsible for van der Waals like bonding. The model is solved by taking into account electron correlations using a generalized Gutzwiller approximation (slave boson method). The occurrence of electron localization is studied as a function of the interaction parameters and cluster size.     

Extracting covalent and ionic structures from usual delocalized wave functions: the electron-expansion methodology

We present easily programmable expansions, allowing the calculation of the weights of local covalent and ionic structures of a chemical bond from usual delocalized wave functions; they are obtained in the framework of the electron-expansion methodology, in which the hole conditions (involved by definition in a covalent or ionic structure) are expanded in terms involving only electrons. From the derived relations, true for both HF and correlated levels, one can also express the covalency/ionicity and the localization of a usual two-electron two-center (2e/2c) bond in terms of electronic populations. The three-electron populations are crucial for bond localization. On the contrary, in 2e/2c bonding, and particularly in Charge-Shift bonds (which show enhanced covalent-ionic interactions) although the three-electron populations can be non-negligible, they are not important for the covalency/ionicity of these bonds. Numerical applications and discussion are given for correlated MO wave functions of butadiene, hexatriene, and pyrrole molecules on the basis of both natural atomic orbitals (NAOs) (orthogonal orbitals) and pre-NAOs (nonorthogonal orbitals).     

On the bonding in doubly charged diatomics

Summary The potential energy of interacting atomic ions A⁺+B⁺ often shows a shallow local minimum separated by a broad potential barrier from the dissociation products at much lower energy. Early interpretations of dication potential shapes were based on the similarity of the electronic structure between isoelectronic neutral and ionic species and led to a picture of a chemical bond superimposed on a repulsive Coulomb potential. More recently, barriers in dication potentials have commonly been interpreted as avoided curve crossings involving covalent and ionic structures. In this paper, we demonstrate that the former model is the appropriate one except in cases with very small asymptotic ionic/covalent energy splittings. By deriving dication wavefunctions from their neutral isoelectronic counterparts, we obtain upper bound dication potential curves which show all the characteristic features. By further modeling induction effects, we arrive at an almost quantitative fit of accurateab initio dication potentials. The chemical bond plus electrostatic repulsion interpretation of dication interactions also explains why the accurate calculation of potential curves appears to be much more demanding for dications than for isoelectronic neutrals.Dedicated in the honor of Prof. Klaus Ruedenberg     

On the molecular electrostatic potentials obtained from CNDO wave functions

The various approximations proposed for computing molecular potentials with CNDO wave functions are tested on the case of guanine and shown to be unable to reproduce correctly the essential fine features of theab initio potential.     

Use of single determinant wave functions constructed from localized orbitals in the mapping analysis of concerted reactions

Wave functions expressed as a single determinant of completely localized orbitals make possible considerable simplification in the mapping analysis of concerted reactions. The formal basis for and several examples of such simplification are presented.Work supported by Petroleum Research Grant PRF-1830-G2.     

Aluminum‐poor hexacarbalane structures: The transition from localized organoaluminum structures to delocalized polyhedra

The series of hexacarbalanes C₆Al_n–6Me_n (n = 7–11) represent a progression from localized organoaluminum structures to delocalized polyhedral structures en route to experimentally known 13‐ and 14‐vertex hexacarbalanes such as (AlMe)₈(CCH₂Ph)₅(µ₄ H), (AlMe)₈(CCH₂Ph)₅(CCPh), [R₄N⁺]₂[(AlH)₈(CR)₆], and (AlNMe₃)₂(AlR)₆(CR)₆. In this connection, the lowest energy seven‐vertex C₆AlMe₇ structure has a tetrahapto benzene ring with the four Al C(cage) bonding interactions required to give the aluminum the favored octet configuration. Related eight‐vertex C₆Al₂Me₈ structures are found with a benzene ring bound to an Al₂ unit with a short AlAl distance of ∼2.55 Å suggesting a formal double bond. However, the lowest energy C₆Al₂Me₈ structure has a dialuminacyclobutene unit fused to a tricyclohexane unit through an Al₂ edge. Other relatively low‐energy C₆AlMe₇ and C₆Al₂Me₈ structures consist of a six‐carbon hexatriene chain either forming a seven‐membered C₆Al ring in the seven‐vertex structure or acting as a “flyover” between an Al₂ unit. The lowest energy nine‐vertex hexacarbalane C₆Al₃Me₉ has two separate C₃ units bridged by both an Al₂ pair and a single aluminum atom. Higher energy C₆Al₃Me₉ hexacarbalanes contain a pentadienyl chain and an isolated carbon atom with an imbedded bonded Al₃ triangle. The low‐energy 10‐vertex C₆Al₄Me₁₀ structures have a central Al₄ butterfly with nonbonding distances between the wingtips ranging from 3.35 to 3.91 Å. The lowest energy 11‐vertex C₆Al₅Me₁₁ structure has a central Al₄ quadrilateral with a diagonal bridged by the fifth aluminum atom. Higher energy C₆Al₅Me₁₁ structures have an edge rather than a diagonal of the central Al₄ quadrilateral bridged by the fifth aluminum atom.     

Changes in electronic,magnetic and bonding properties from Zr2FeH5 to Zr3FeH7 addressed from ab initio

Potential hydrogen storage ternaries Zr₃FeH₇ and Zr₂FeH₅, are studied from ab initio with the purpose of identifying changes in electronic structures and bonding properties. Cohesive energy trends: E_coh. (ZrH₂) > E_coh. (Zr₂FeH₅) > E_coh. (Zr₃FeH₇) > E_coh. (hypothetic-FeH) indicate a progressive destabilization of the binary hydride ZrH₂ through adjoined Fe so that Zr₃FeH₇ is found less cohesive than Zr₂FeH₅. From the energy volume equations of states EOS the volume increase upon hydriding the intermetallics leads to higher bulk moduli B₀ explained by the Zr/Fe–H bonding. Fe–H bond in Zr₂FeH₅ leads to annihilate magnetic polarization on Fe whereas Fe magnetic moment develops in Zr₃FeH₇ identified as ferromagnetic in the ground state. These differences in magnetic behaviors are due to the weakly ferromagnetic Fe largely affected by lattice environment, as opposed to strongly ferromagnetic Co. Hydrogenation of the binary intermetallics weakens the inter-metal bonding and favors the metal–hydrogen bonds leading to more cohesive hydrides as with respect to the pristine binaries. Charge analyses point to covalent like Fe versus ionic Zr and hydrogen charges ranging from covalent H^−0.27 to more ionic H^−0.5.     

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.     

On calculations of correlated wave functions with heavy configurational mixing

We discuss aspects of the theory and computation of wave functions and energies of discrete states of polyelectronic atoms that are represented in zero order by configurations with holes in subshells below the valence subshell. Both in zero order and in the remaining correlation components, such wave functions have particularities stemming from the state‐specific self‐consistent field and the heavy configurational mixing associated with near‐degeneracies and hole‐filling correlations. By referring to a variety of examples from small‐ and large‐scale calculations, it is noted that appropriate penetration into the many‐body problem can provide, in an economic and physically transparent way, reliable interpretations and semi‐ and fully quantitative understanding of issues related to states with inner holes and to cases of near‐degeneracies that result in strongly correlated wave functions. Whenever hole‐filling correlations are allowed, multiple correlations (i.e., beyond single‐ and double‐orbital substitutions in the single reference configuration) acquire increased importance relative to that in ordinary electronic structures. This is demonstrated via large‐scale multiconfigurational Hartree–Fock (MCHF) plus configuration interaction (CI) calculations on the Cl KL3s3p^{6 2}S discrete state, which is the lowest of its symmetry. The calculations incorporated correlations up to selected sextuple orbital excitations from the M shell. MCHF plus CI calculations at the level of quadruple orbital substitutions were also carried out for the Cl KL3s²3p^{5 2}P^o ground state and the excitation energy at this level of calculation was found to be 85,364 cm^?1, in excellent agreement with the experimental value of the fine‐structure‐weighted average, 85,385 cm^?1 (10.59 eV). Within the approximations of the calculation, the hole‐filling triple and quadruple orbital correlations, which, of course, are absent from the ²P^o state, contribute about 1 eV, which is significant. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Long-range molecular interaction coefficients computed from frost-model wave functions

The average long-range interaction energy between two molecules can be written as an inverse asymptotic series in the intermolecular separation distanceR. Using Frost-model wave functions, the dispersion coefficients of the first three (R ^–6,R ^–8,R ^–10 terms in the series are obtained. Coefficients of three- and four-body non-additive interaction energies are also calculated and the form of the dispersion interaction when retardation effects are included is examined.     

Møller–Plesset correlation energies in a localized orbital basis using a Laplace transform technique

Summary.  In electronic structure calculations requiring the handling of large amounts of integrals, storage requirements can often be reduced through the use of localized orbitals which gives rise to sparse integral arrays. However, conventional M?ller–Plesset perturbation theory is constrained to canonical orbitals due to the explicit use of orbital energies in the energy expressions, and it is therefore not straightforward to reduce the storage requirements through such orbital localization. This work shows how the constraint of canonical orbitals can be lifted using a Laplace transform technique, and investigates the reduction in storage requirement that can result from the localization of orbitals made possible by such an approach. Received July 31, 1995/Final version received September 11, 1996/Accepted September 11, 1996     

On the molecular electrostatic potentials obtained with CNDO and INDO wave functions

Molecular electrostatic potentials computed with CNDO/2 and INDO wave functions are shown to present systematic differences with respect to ab initio potentials in the case of out-of-plane potentials and in-plane vicinal hetero atoms in planar hetero molecules.     

Analytical Hartree–Fock wave functions for the atoms Cs to Lr

 Analytical approximations to Hartree–Fock wave functions are constructed using Slater-type functions for the ground states of all 49 neutral atoms from Cs (Z=55) to Lr (Z=103). The current compilation is more extensive and more accurate than previous ones. The wave functions are available upon request from the authors or from the Web page http://www.unb.ca/chem/ajit/download.htm on the Internet. Received: 6 December 1999 / Accepted: 29 February 2000 / Published online: 12 May 2000     

On expectation value calculations of one-electron properties using the coupled cluster wave functions

The ability of various approximate coupled cluster (CC) methods to provide accurate first-order one-electron properties calculated as expectation values is theoretically analysed and computationally examined for BH and CO. For actual calculations the infinite number of terms of the expectation value expansion (O=¦exp (T ⁺)O exp (T)¦_c) was truncated so that T ₁ T ₂, T ₃, and (1/2) T ₂T₂ clusters were retained on both sides of O. The role of individual clusters is carefully discussed. Inclusion of T ₁, is unavoidable, but if triples are essential in the energy evaluation, they may play an even more important role in the property expansion, as shown in the case of CO. It is shown that the CC wave function, which is exact to second order, effectively satisfies the Hellmann-Feynman theorem.