Valence Virtual Orbitals: An Unambiguous ab Initio Quantification of the LUMO Concept

A unique approach to address avoided crossings in the charge stabilization curve for LUMO identification

In quantum chemistry, Lowest Unoccupied Molecular Orbital (LUMO) is important for studying various chemical processes, including photochemical reactions, electron attached states, and electron excites states. Recently, an effective method has been introduced that involves the use of the Parametric Equation of Motion (PEM) in conjunction with the nuclear charge stabilization method for precise identification of true LUMO. However, the inclusion of extra diffuse functions in the basis set, which is necessary for describing electron-attached and electron-excited states, can cause issues due to the presence of the same symmetry states, leading to avoided crossing. Identifying the true LUMO among these avoided crossings is challenging due to the mixing of states and the exchange of their orbital character. This article introduces a modification of the PEM to identify the true LUMO by preventing the stabilization of specific states involved in avoided crossings. The present method is highly effective and requires minimal computational cost.

Analysis of bonding motifs in unusual molecules I: planar hexacoordinated carbon atoms

The bonding structures of CO3Li3+ and CS3Li3+ are studied by means of oriented quasi-atomic orbitals (QUAOs) to assess the possibility of these molecules being planar hexacoordinated carbon (phC) systems. CH3Li and CO32- are employed as reference molecules. It is found that the introduction of Li+ ions into the molecular environment of carbonate has a greater effect on the orbital structure of the O atoms than it does on the C atom. Partial charges computed from QUAO populations imply repulsion between the positively charged C and Li atoms in CO3Li3+. Upon the transition from CO3Li3+ to CS3Li3+, the analysis reveals that the substitution of O atoms by S atoms inverts the polarity of the carbon-chalcogen σ bond. This is linked to the difference in s- and p-fractions of the QUAOs of C and S, as element electronegativities do not explain the observed polarity of the CSσ bond. Partial charges indicate that the larger electron population on the C atom in CS3Li3+ makes C-Li attraction possible. Upon comparison with the C-Li bond in methyllithium, it is found that the C-Li covalent interactions in CO3Li3+ and CS3Li3+ have about 14% and 6% of the strength of the C-Li covalent interaction in CH3Li, respectively. Consequently, it is concluded that only CS3Li3+ may be considered to be a phC system.

An Innovative Approach for Precise Identification of the Lowest Unoccupied Molecular Orbital Using the Parametric Equation of Motion

The lowest unoccupied molecular orbital (LUMO) plays a crucial role in quantum chemistry, but current quantum chemistry calculations fail to provide useful virtual orbitals, making it challenging to explore various processes such as photochemical reactions, electron attachment, reduction, or excitation processes. The LUMO obtained from the self-consistent field (SCF) solution can not be relied upon and needs to be identified as they are often present among the continuum states having almost similar energies. The nuclear charge stabilization method has been proven useful in identifying LUMO. Herein, we have proposed the application of parametric equations of motion (PEM) in conjunction with nuclear charge stabilization method to identify the LUMO obtained from the SCF solution exhibiting stability with different basis sets including diffuse functions.

Quasi-atomic orbital analysis of halogen bonding interactions

A quasi-atomic orbital analysis of the halogen bonded NH3⋯XF complexes (X = F, Cl, Br, and I) is performed to gain insight into the electronic properties associated with these σ-hole interactions. It is shown that significant sharing of electrons between the nitrogen lone pair of the ammonia molecule and the XF molecule occurs, resulting in a weakening of the X-F bond. In addition, the N-X bond shows increasing covalent character as the size of the halogen atom X increases. While the Mulliken outer complex NH3⋯XF appears to be overall the main species, the strength of the covalent interaction of the N-X bond becomes increasingly similar to that of the N-X bond in the [NH3X]+ cation as the size of X increases.

The General Atomic and Molecular Electronic Structure System (GAMESS): Novel Methods on Novel Architectures

The primary focus of GAMESS over the last 5 years has been the development of new high-performance codes that are able to take effective and efficient advantage of the most advanced computer architectures, both CPU and accelerators. These efforts include employing density fitting and fragmentation methods to reduce the high scaling of well-correlated (e.g., coupled-cluster) methods as well as developing novel codes that can take optimal advantage of graphical processing units and other modern accelerators. Because accurate wave functions can be very complex, an important new functionality in GAMESS is the quasi-atomic orbital analysis, an unbiased approach to the understanding of covalent bonds embedded in the wave function. Best practices for the maintenance and distribution of GAMESS are also discussed.

Analysis of the bonding in tetrahedrane and phosphorus-substituted tetrahedranes

The bonding structures of tetrahedrane, phosphatetrahedrane, diphosphatetrahedrane and triphosphatetrahedrane are studied by employing an intrinsic quasi-atomic orbital analysis. Ethane, cyclopropane and tetrahedral P4 are employed as reference systems. The orbital analysis is paired with the computation of strain energies via isodesmic reactions. The results show that the increase in geometric strain upon transition from ethane to cyclopropane to tetrahedrane weakens the CC bonds, despite leading to shorter C-C interatomic distances. With the increase in strain, the orbitals centered on C and involved in the bonding of the cage structure are observed to have elevated p-character, and the orbital structure of C deviates from sp3 hybridization. The systematic substitution of CH groups by P atoms in the cage structure of tetrahedrane leads to stronger CC bonds, larger angles in the cage structures of the resulting phosphatetrahedranes, lower p-character in the orbitals involved in the bonding of the cages, and lower strain energies. It is found that P is more amenable to strained molecular arrangements than is C, and that the propensity of a given atom to hybridize s and p functions, or the lack thereof, has implications in the stability of molecules with strained geometries. The combination of the calculations presented here with the existing literature provides insight into the apparent propensity of tetrahedrane and P4 to 'break' their tetrahedral structures. Trends in the bonding interactions, such as bond strengths, s- and p-orbital characters and charge transfer are identified and related to the strain energy observed in each of the analyzed systems.

A Theoretical Investigation of Novel Sila- and Germa-Spirocyclic Imines and Their Relevance for Electron-Transporting Materials and Drug Discovery

A new class of spirocyclic imines (SCIs) has been theoretically investigated by applying a variety of quantum chemical methods and basis sets. The uniqueness of these compounds is depicted by various peculiarities, e.g., the incidence of planar six-membered rings each with two imine groups (two π bonds) and the incorporation of the isosteres carbon, silicon, or germanium spiro centers. Additional peculiarities of these novel SCIs are mirrored by their three-dimensionality, the simultaneous occurrence of nucleophilic and electrophilic centers, and the cross-hyperconjugative (spiro-conjugation) interactions, which provoke charge mobility along the spirocyclic scaffold. Substitution of SCIs with strong electron-withdrawing substituents, like the cyano group or fluorine, enhances their docking capability and impacts their reactivity and charge mobility. To gain thorough knowledge about the molecular properties of these SCIs, their structures have been optimized and various quantum chemical concepts and models were applied, e.g., full NBO analysis and the frontier molecular orbitals (FMOs) theory (HOMO-LUMO energy gap) and the chemical reactivity descriptors derived from them. For the assessment of the charge density distribution along the SCI framework, additional complementary quantum chemical methods were used, e.g., molecular electrostatic potential (MESP) and Bader's QTAIM. Additionally, using the aromaticity index NICS (nuclear independent chemical shift) and other criteria, it could be shown that the investigated cross-hyperconjugated sila and germa SCIs are spiro-aromatics of the Heilbronner Craig-type Möbius aromaticity.

Effect of Substituents on Molecular Reactivity during Lignin Oxidation by Chlorine Dioxide: A Density Functional Theory Study

Lignin is a polymer with a complex structure. It is widely present in lignocellulosic biomass, and it has a variety of functional group substituents and linkage forms. Especially during the oxidation reaction, the positioning effect of the different substituents of the benzene ring leads to differences in lignin reactivity. The position of the benzene ring branched chain with respect to methoxy is important. The study of the effect of benzene substituents on the oxidation reaction's activity is still an unfinished task. In this study, density functional theory (DFT) and the m062x/6-311+g (d) basis set were used. Differences in the processes of phenolic oxygen intermediates formed by phenolic lignin structures (with different substituents) with chlorine dioxide during the chlorine dioxide reaction were investigated. Six phenolic lignin model species with different structures were selected. Bond energies, electrostatic potentials, atomic charges, Fukui functions and double descriptors of lignin model substances and reaction energy barriers are compared. The effects of benzene ring branched chains and methoxy on the mechanism of chlorine dioxide oxidation of lignin were revealed systematically. The results showed that the substituents with shorter branched chains and strong electron-absorbing ability were more stable. Lignin is not easily susceptible to the effects of chlorine dioxide. The substituents with longer branched chains have a significant effect on the flow of electron clouds. The results demonstrate that chlorine dioxide can affect the electron arrangement around the molecule, which directly affects the electrophilic activity of the molecule. The electron-absorbing effect of methoxy leads to a low dissociation energy of the phenolic hydroxyl group. Electrophilic reagents are more likely to attack this reaction site. In addition, the stabilizing effect of methoxy on the molecular structure of lignin was also found.

Optimal Mode Combination in the Multiconfiguration Time-Dependent Hartree Method through Multivariate Statistics: Factor Analysis and Hierarchical Clustering

The multiconfiguration time-dependent Hartree (MCTDH) method and its multilayer extension (ML-MCTDH) are powerful algorithms for the efficient computation of nuclear quantum dynamics in high-dimensional systems. By providing time-dependent variational orbitals and an optimal choice of layered effective degrees of freedom, one is able to reduce the computational cost to an amenable number of configurations. However, choices related to selecting properly the mode grouping and tensor tree are strongly system dependent and, thus far, subjectively based on intuition and/or experience. Therefore, herein we detail a new protocol based on multivariate statistics─more specifically, factor analysis and hierarchical clustering─for a reliable and convenient guiding in the optimal design of such complex "system-of-systems" tensor-network decompositions. The advantages of employing the new algorithm and its applicability are tested on water and two floppy protonated water clusters with large amplitude motions.

Ambient-light-induced intermolecular Coulombic decay in unbound pyridine monomers

Intermolecular Coulombic decay (ICD) is a process whereby photoexcited molecules relax by ionizing their neighbouring molecules. ICD is efficient when intermolecular interactions are active and consequently it is observed only in weakly bound systems, such as clusters and hydrogen-bonded systems. Here we report an efficient ICD between unbound molecules excited at ambient-light intensities. On the photoexcitation of gas-phase pyridine monomers, well below the ionization threshold and at low laser intensities, we detected the parent and heavier-than-parent cations. The isotropic emission of slow electrons revealed ICD as the underlying process. π-π* excitation in unbounded pyridine monomers triggered an associative interaction between them, which leads to an efficient three-centre ICD. The cation resulting from the molecular association of the three pyridine centres relaxed through fragmentation. This below-threshold ionization under ambient light has implications for the understanding of radiation damage and astrochemistry.

Non-iterative Method for Constructing Valence Antibonding Molecular Orbitals and a Molecule-adapted Minimum Basis

While bonding molecular orbitals exhibit constructive interference relative to atomic orbitals, antibonding orbitals show destructive interference. When full localization of occupied orbitals into bonds is possible, bonding and antibonding orbitals exist in 1:1 correspondence with each other. Antibonding orbitals play an important role in chemistry because they are frontier orbitals that determine orbital interactions, as well as much of the response of the bonding orbital to perturbations. In this work, we present an efficient method to construct antibonding orbitals by finding the orbital that yields the maximum opposite spin pair correlation amplitude in second order perturbation theory (AB2) and compare it with other techniques with increasing the size of the basis set. We conclude the AB2 antibonding orbitals are a more robust alternative to the Sano orbitals as initial guesses for valence bond calculations, due to having a useful basis set limit. The AB2 orbitals are also useful for efficiently constructing an active space, and work as good initial guesses for valence excited states. In addition, when combined with the localized occupied orbitals, and relocalized, the result is a set of molecule-adapted minimal basis functions that is built without any reference to atomic orbitals of the free atom. As examples, they are applied to population analysis of halogenated methane derivatives, H-Be-Cl, and \ce{SF6} where they show some advantages relative to good alternative methods.

Finding Valence Antibonding Levels while Avoiding Rydberg, Pseudo-continuum, and Dipole-Bound Orbitals

Electronic structure methods are now widely used to assist in the interpretation of many varieties of experimental data. The energies and physical characteristics (e.g., sizes, shapes, and spatial localization) of valence antibonding π* and σ* orbitals play key roles in a variety of chemical processes including photochemical reactions and electron attachment reductions and are used in Woodward-Hoffmann-type analyses to probe reaction energy barriers and energy surface intersections leading to internal conversion or intersystem crossings. One's ability to properly populate such valence antibonding orbitals within electronic structure calculations is often hindered by the presence of other molecular orbitals having similar energies. These intruding orbitals can be of Rydberg, pseudo-continuum, or dipole-bound characteristic. This article shows how, within the most widely available electronic structure codes, one can avoid the pitfalls presented by these intruding orbitals to properly populate a valence π* or σ* orbital and how to subsequently use that orbital in a calculation that includes electron correlation effects and thereby offers the possibility of chemically useful precision. Special emphasis is given to cases in which the electronic state is metastable.

DFT Study for Adsorbing of Bromine Monochloride onto BNNT (5,5), BNNT (7,0), BC2NNT (5,5), and BC2NNT (7,0)

The study of intermolecular interactions is of great importance. This study attempted to quantitatively examine the interactions between bromine monochloride (BrCl) with pristine boron nitride nanotube (BNNT) armchair (5,5) and zigzag (7,0) as well as armchair (5,5) BC2NNT and zigzag (7,0) BC2NNT in vacuum. Quantum mechanical studies of such systems are possible in the density functional theory (DFT) framework. For this purpose, various functionals, such as B3LYP-D3, [Formula: see text]B97XD, and M062X, have been used. One of the most suitable basis functionals for the systems studied in this research is 6-311G (d), which has been used in both optimization calculations and calculations related to wave function analyses. The main part of this work is the study of various analyses that reveal the nature of the intermolecular interactions between the two components introduced above. The results of conceptual DFT, natural bond orbital, non-covalent interactions, and quantum theory of atoms in molecules (QTAIM) were consistent and in favor of physical adsorption in all systems. Gallium had more adsorption energy than other dopants. The HOMO–LUMO energy gaps were as follows: BNNT (5,5): 10.296, BNNT (7,0): 9.015, BC2NNT (5,5): 7.022, and BC2NNT (7,0): 5.979[Formula: see text]eV at B3LYP-D3/6-311G (d) model chemistry. The strongest interaction is related to the BC2NNT (7,0)/BrCl cluster: [Formula: see text][Formula: see text]eV. The results of QTAIM and NCI analysis identified the intermolecular interactions of the type of strong van der Waals interaction for these nanotubes. The sensitivity of the adsorption increased when a gas molecule interacted with carbon-doped BNNT, and the change in the frontier orbital gap could be used to design nanosensors to detect BrCl gas.

Non-covalent interactions of cysteine onto C60, C59Si, and C59Ge: a DFT study

The study of intermolecular interactions is of great importance. This study attempted to quantitatively examine the interactions between cysteine (C₃H₇NO₂S) and fullerene nanocages, C₆₀, in vacuum. As the frequent introduction of elements as impurities into the structure of nanomaterials can increase the intensity of intermolecular interactions, nanocages doped with silicon and germanium have also been studied as adsorbents, C₅₉Si and C₅₉Ge. Quantum mechanical studies of such systems are possible in the density functional theory (DFT) framework. For this purpose, various functionals, such as B3LYP-D3, ωB97XD, and M062X, have been used. One of the most suitable basis functionals for the systems studied in this research is 6-311G (d), which has been used in both optimization calculations and calculations related to wave function analyses. The main part of this work is the study of various analyses that reveal the nature of the intermolecular interactions between the two components introduced above. The results of conceptual DFT, natural bond orbital, non-covalent interactions, and quantum theory of atoms in molecules were consistent and in favor of physical adsorption in all systems. Germanium had more adsorption energy than other dopants. The HOMO-LUMO energy gaps were as follows: C₆₀: 5.996, C₅₉Si: 5.309, and C59Ge: 5.188 eV at B3LYP-D3/6-311 G (d) model chemistry. The sensitivity of the adsorption increased when an amino acid molecule interacted with doped C₆₀, and this capability could be used to design nanocarrier to carry cysteine amino acid.

Hybrid Atomic Orbital Basis from First Principles: Bottom-Up Mapping of Self-Energy Correction to Large Covalent Systems

Construction of hybrid atomic orbitals is proposed as the approximate common eigenstates of finite first moment matrices. Their hybridization and orientation can be a priori tuned as per their anticipated neighborhood. Their Wannier function counterparts constructed from the Kohn-Sham (KS) single particle states constitute an orthonormal multiorbital tight binding (TB) basis resembling hybrid atomic orbitals locked to their immediate atomic neighborhood, while spanning the subspace of KS states. The proposed basis thus renders predominantly single TB parameters from first principles for each nearest neighbor bond involving no more than two orbitals irrespective of their orientation and also facilitates an easy route for the transfer of such TB parameters across isostructural systems exclusively through mapping of neighborhoods and projection of orbital charge centers. With hybridized 2s, 2p and 3s, 3p valence electrons, the spatial extent of the self-energy correction (SEC) to TB parameters in the proposed basis is found to be localized mostly within the third nearest neighborhood, thus allowing effective transfer of self-energy-corrected TB parameters from smaller reference systems to much larger target systems, with nominal additional computational cost beyond that required for explicit computation of SEC in the reference systems. The proposed approach promises inexpensive estimation of the quasi-particle structures of large covalent systems with workable accuracy.

Multiple Bonding in Rhodium Monoboride. Quasi-atomic Analyses of the Ground and Low-Lying Excited States

The bonding structures of the ground state and the lowest five excited states of rhodium monoboride are identified by determining the quasi-atomic orbitals in full valence space MCSCF wave functions and the interactions between these orbitals. A quadruple bond, namely two π-bonds and two σ-bonds, is identified and characterized for the X¹Σ⁺ ground state, in agreement with a previous report (Cheung J. Phys. Chem. Lett. 2020, 11, 659-663). However, in all excited states, the bonding is predicted to be weaker because, in these states, one of the σ-bonding interactions has a small magnitude. In the a³Δ and A¹Δ states, the bond order is between a triple and quadruple bond. In the b³Σ⁺ state, the Rh-B linkage is a triple bond. In the c³Π and B¹Π states, the atoms are linked by a double bond due to an additional weakening of the two π-bonds. The decreases in the predicted bond strengths are reflected in the decreases of the predicted binding energies and in the increases of the predicted bond lengths from the X¹Σ⁺ ground state to the c³Π and the B¹Π excited states. Notably, the 5pσ orbital of rhodium, which is vacant in the ground state of the atom, plays a significant role in the molecule.

Ultrafast Transfer and Transient Entrapment of Photoexcited Mg Electron in Mg@C_{60}

Electron relaxation is studied in endofullerene Mg@C_{60} after an initial localized photoexcitation in Mg by nonadiabatic molecular dynamics simulations. Two approaches to the electronic structure of the excited electronic states are used: (i) an independent particle approximation based on a density-functional theory description of molecular orbitals and (ii) a configuration-interaction description of the many-body effects. Both methods exhibit similar relaxation times, leading to an ultrafast decay and charge transfer from Mg to C_{60} within tens of femtoseconds. Method (i) further elicits a transient trap of the transferred electron that can delay the electron-hole recombination. Results shall motivate experiments to probe these ultrafast processes by two-photon transient absorption or photoelectron spectroscopy in gas phase, in solution, or as thin films.

Generalization of Block-Localized Wave Function for Constrained Optimization of Excited Determinants

The block-localized wave function method is useful to provide insights on chemical bonding and intermolecular interactions through energy decomposition analysis. The method relies on block localization of molecular orbitals (MOs) by constraining the orbitals to basis functions within given blocks. Here, a generalized block-localized orbital (GBLO) method is described to allow both physically localized and delocalized MOs to be constrained in orbital-block definitions. Consequently, GBLO optimization can be conveniently tailored by imposing specific constraints. The GBLO method is illustrated by three examples: (1) constrained polarization response orbitals through dipole and quadrupole perturbation in a water dimer complex, (2) the ground and first excited-state potential energy curves of ethene about its C-C bond rotation, and (3) excitation energies of double electron excited states. Multistate density functional theory is used to determine the energies of the adiabatic ground and excited states using a minimal active space (MAS) comprising specifically charge-constrained and excited determinant configurations that are variationally optimized by the GBLO method. We find that the GBLO expansion that includes delocalized MOs in configurational blocks significantly reduces computational errors in comparison with physical block localization, and the computed ground- and excited-state energies are in good accordance with experiments and results obtained from multireference configuration interaction calculations.

Why is Si2H2 Not Linear? An Intrinsic Quasi-Atomic Bonding Analysis

The molecular energy of Si₂H₂ geometric structures increases in the order dibridged < trans-bent < linear, in contrast to acetylene, C₂H₂, for which the linear structure is the global minimum. In this study, the intra-atomic (antibonding) and bonding contributions to the total molecular energy of these valence isoelectronic molecules are computed by expressing the density matrices of the full valence space multiconfiguration self-consistent field wave function in terms of quasi-atomic orbitals. The analysis shows that the intra-atomic contributions to the molecular energy become less favorable in the order dibridged → trans-bent → linear for both C₂H₂ and Si₂H₂. By contrast, the inter-atomic bonding contributions become energetically more favorable in that order for both C₂H₂ and Si₂H₂. The two systems differ as follows. For Si₂H₂, the antibonding intra-atomic energy changes that occur when the dibridged molecule reconstructs into the trans-bent and linear structures prevail over the interatomic interactions that induce bond formation. In contrast, for C₂H₂, the interatomic interactions that create bonds prevail over the intra-atomic energy changes that occur when the dibridged molecule reconstructs into the trans-bent and linear structures. The intra-atomic energy changes that occur in these systems are related to the hybridization of the heavy atoms in an analogous manner to the hybridization of C in CH₄ from (2s)²(2p)² to sp³ hybrid orbitals.

Recent developments in the general atomic and molecular electronic structure system

A discussion of many of the recently implemented features of GAMESS (General Atomic and Molecular Electronic Structure System) and LibCChem (the C++ CPU/GPU library associated with GAMESS) is presented. These features include fragmentation methods such as the fragment molecular orbital, effective fragment potential and effective fragment molecular orbital methods, hybrid MPI/OpenMP approaches to Hartree-Fock, and resolution of the identity second order perturbation theory. Many new coupled cluster theory methods have been implemented in GAMESS, as have multiple levels of density functional/tight binding theory. The role of accelerators, especially graphical processing units, is discussed in the context of the new features of LibCChem, as it is the associated problem of power consumption as the power of computers increases dramatically. The process by which a complex program suite such as GAMESS is maintained and developed is considered. Future developments are briefly summarized.

Active space approaches combining coupled-cluster and perturbation theory for ground states and excited states

We evaluate the performance of approaches that combine coupled-cluster and perturbation theory based on a predefined active space of orbitals. Coupled-cluster theory is used to treat excitations that are internal to the active space and perturbation theory is used for all other excitations, which are at least partially external to the active space. We consider a variety of schemes that differ in how the internal and external excitations are coupled. Such approaches are presented for ground states and excited states within the equation-of-motion formalism. Results are given for the ionization potentials and electron affinities of a test set of small molecules and for the correlation energy and band gap of a few periodic solids.

Ionic liquids from a fragmented perspective

The efficacy of using fragmentation methods, such as the effective fragment potential, the fragment molecular orbital and the effective fragment molecular orbital methods is discussed. The advantages and current limitations of these methods are considered, potential improvements are suggested, and a prognosis for the future is provided.

Quasi-Atomic Bond Analyses in the Sixth Period: II. Bond Analyses of Cerium Oxides

The role of the 4f orbitals in bonding is examined for the molecules cerium monoxide and cerium dioxide that have cerium formally in the +2 and +4 oxidation states, respectively. It is shown that the 4f orbitals are used primarily for polarization of the 5d orbitals when cerium is in the lower oxidation state, while the 4f orbitals play a significant role in chemical bonding via 5d/4f hybridization when cerium is in the +4 oxidation state.

Constructing Molecular π-Orbital Active Spaces for Multireference Calculations of Conjugated Systems

Molecules with conjugated π systems often feature strong electron correlation and therefore require multireference methods for a reliable computational description. A key prerequisite for the successful application of such methods is the choice of a suitable active space. Herein the automated π-orbital space (PiOS) method for selecting active spaces for multireference calculations of conjugated π systems is presented. This approach allows the construction of small but effective active spaces based on Hückel theory. To demonstrate its performance, π → π* excitations for benzene, octatetraene, and free-base porphine are computed. In addition, this technique can be combined with the automated atomic valence active space method to compute excitations in complex systems with multiple conjugated fragments. This combined approach was used to generate two-dimensional potential energy surfaces for multiple electronic states associated with photoinduced electron-coupled double proton transfer in the blue-light-using flavin photoreceptor protein. These types of methods for the automated selection of active space orbitals are important for ensuring consistency and reproducibility of multireference approaches for a wide range of chemical and biological systems.

A Quasi-Atomic Analysis of Three-Center Two-Electron Zr-H-Si Interactions

A comprehensive analysis of the bonding structure of the disilyl zirconocene amide cation {Cp₂Zr[N(SiHMe₂)₂]}⁺ is conducted by application of an intrinsic orbital localization method that yields quasi-atomic orbitals (QUAOs). An emphasis is placed on describing a previously characterized three-center two-electron interaction between zirconium, hydrogen, and silicon that presents structural and spectroscopic features similar to that of agostic bonds. Expressions of the first-order density matrix in terms of the QUAOs yields bond orders (BOs), kinetic bond orders (KBOs), and the extent of transfer of charge that are useful to determine the electronic nature of the Zr-H-Si bond. The interactions between the QUAOs demonstrate the importance of vicinal interactions in the stabilization of the molecule. In addition, the evolution of the QUAOs during reactions with Lewis bases reveals the role of the Zr-H-Si interaction in facilitating the reaction.

Identification and Characterization of Molecular Bonding Structures by ab initio Quasi-Atomic Orbital Analyses

The quasi-atomic analysis of ab initio electronic wave functions in full valence spaces, which was developed in preceding papers, yields oriented quasi-atomic orbitals in terms of which the ab initio molecular wave function and energy can be expressed. These oriented quasi-atomic orbitals are the rigorous ab initio counterparts to the conceptual bond forming atomic hybrid orbitals of qualitative chemical reasoning. In the present work, the quasi-atomic orbitals are identified as bonding orbitals, lone pair orbitals, radical orbitals, vacant orbitals and orbitals with intermediate character. A program determines the bonding characteristics of all quasi-atomic orbitals in a molecule on the basis of their occupations, bond orders, kinetic bond orders, hybridizations and local symmetries. These data are collected in a record and provide the information for a comprehensive understanding of the synergism that generates the bonding structure that holds the molecule together. Applications to a series of molecules exhibit the complete bonding structures that are embedded in their ab initio wave functions. For the strong bonds in a molecule, the quasi-atomic orbitals provide quantitative ab initio amplifications of the Lewis dot symbols. Beyond characterizing strong bonds, the quasi-atomic analysis also yields an understanding of the weak interactions, such as vicinal, hyperconjugative and radical stabilizations, which can make substantial contributions to the molecular bonding structure.