A Comprehensive Analysis in Terms of Molecule-Intrinsic, Quasi-Atomic Orbitals. II. Strongly Correlated MCSCF Wave Functions

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.

Chemical Bonding and the Role of Node-Induced Electron Confinement

The chemical bond is the cornerstone of chemistry, providing a conceptual framework to understand and predict the behavior of molecules in complex systems. However, the fundamental origin of chemical bonding remains controversial and has been responsible for fierce debate over the past century. Here, we present a unified theory of bonding, using a separation of electron delocalization effects from orbital relaxation to identify three mechanisms [node-induced confinement (typically associated with Pauli repulsion, though more general), orbital contraction, and polarization] that each modulate kinetic energy during bond formation. Through analysis of a series of archetypal bonds, we show that an exquisite balance of energy-lowering delocalizing and localizing effects are dictated simply by atomic electron configurations, nodal structure, and electronegativities. The utility of this unified bonding theory is demonstrated by its application to explain observed trends in bond strengths throughout the periodic table, including main group and transition metal elements.

Intermolecular interactions in clusters of ethylammonium nitrate and 1-amino-1,2,3-triazole

The intermolecular interaction energies, including hydrogen bonds (H-bonds), of clusters of the ionic liquid ethylammonium nitrate (EAN) and 1-amino-1,2,3-triazole (1-AT) based deep eutectic propellants (DeEP) are examined. 1-AT is introduced as a neutral hydrogen bond donor (HBD) to EAN in order to form a eutectic mixture. The effective fragment potential (EFP) is used to examine the bonding interactions in the DeEP clusters. The resolution of the Identity (RI) approximated second order Møller-Plesset perturbation theory (RI-MP2) and coupled cluster theory (RI-CCSD(T)) are used to validate the EFP results. The EFP method predicts that there are significant polarization and charge transfer effects in the EAN:1-AT complexes, along with Coulombic, dispersion and exchange repulsion interactions. The EFP interaction energies are in good agreement with the RI-MP2 and RI-CCSD(T) results. The quasi-atomic orbital (QUAO) bonding and kinetic bond order (KBO) analyses are additionally used to develop a conceptual and semi-quantitative understanding of the H-bonding interactions as a function of the size of the system. The QUAO and KBO analyses suggest that the H-bonds in the examined clusters follow the characteristic hydrogen bonding three-center four electron interactions. The strongest H-bonding interactions between the (EAN)1:(1-AT)n and (EAN)2:(1-AT)n (n = 1-5) complexes are observed internally within EAN; that is, between the ethylammonium cation [EA]+ and the nitrate anion ([NO3]-). The weakest H-bonding interactions occur between [NO3]- and 1-AT. Consequently, the average strengths of the H-bonds within a given (EAN)x:(1-AT)n complex decrease as more 1-AT molecules are introduced into the EAN monomer and EAN dimer. The QUAO bonding analysis suggests that 1-AT in (EAN)x:(1-AT)n can act as both a HBD and a hydrogen bond acceptor simultaneously. It is observed that two 1-AT molecules can form H-bonds to each other. Although the KBOs that correspond to H-bonding interactions in [EA]+:1-AT, [NO3]-:1-AT and between two 1-AT molecules are weaker than the H-bonds in EAN, those weak H-bond networks with 1-AT could be important to form a stable DeEP.

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.

Carbon-[n]Triangulenes and Sila-[n]Triangulenes: Which Are Planar?

Using our recently suggested concept of a quasi-molecule ("tile") and, in the case of the planarity here at stake, its generalization to larger than tetratomics, we explain why carbon [n]triangulenes tend to be planar, while hybrids, where just a few or even all a- or b-type carbon atoms are silicon-substituted (sila-[n]triangulenes), tend to be planar/nonplanar when compared with the unsubstituted carbon-[n]triangulenes. Because other spin states of the parent carbon- and sila-[n]triangulenes tend to correlate with the same tiles, it is conjectured that no structural changes are expected to depend on their spin state. Other polycyclic and sila-compounds are also discussed.

Energy natural orbital characterization of nonadiabatic electron wavepackets in the densely quasi-degenerate electronic state manifold

Dynamics and energetic structure of largely fluctuating nonadiabatic electron wavepackets are studied in terms of Energy Natural Orbitals (ENOs) [K. Takatsuka and Y. Arasaki, J. Chem. Phys. 154, 094103 (2021)]. Such huge fluctuating states are sampled from the highly excited states of clusters of 12 boron atoms (B₁₂), which have densely quasi-degenerate electronic excited-state manifold, each adiabatic state of which gets promptly mixed with other states through the frequent and enduring nonadiabatic interactions within the manifold. Yet, the wavepacket states are expected to be of very long lifetimes. This excited-state electronic wavepacket dynamics is extremely interesting but very hard to analyze since they are usually represented in large time-dependent configuration interaction wavefunctions and/or in some other complicated forms. We have found that ENO gives an invariant energy orbital picture to characterize not only the static highly correlated electronic wavefunctions but also those time-dependent electronic wavefunctions. Hence, we first demonstrate how the ENO representation works for some general cases, choosing proton transfer in water dimer and electron-deficient multicenter chemical bonding in diborane in the ground state. We then penetrate with ENO deep into the analysis of the essential nature of nonadiabatic electron wavepacket dynamics in the excited states and show the mechanism of the coexistence of huge electronic fluctuation and rather strong chemical bonds under very random electron flows within the molecule. To quantify the intra-molecular energy flow associated with the huge electronic-state fluctuation, we define and numerically demonstrate what we call the electronic energy flux.

Quantum Chemical Modeling of Propellant Degradation

An ab initio quantum chemical approach for the modeling of propellant degradation is presented. Using state-of-the-art bonding analysis techniques and composite methods, a series of potential degradation reactions are devised for a sample hydroxyl-terminated-polybutadiene (HTPB) type solid fuel. By applying thermochemical procedures and isodesmic reactions, accurate thermochemical quantities are obtained using a modified G3 composite method based on the resolution of the identity. The calculated heats of formation for the different structures produced presents an ∼2 kcal/mol average error when compared against experimental values.

Nature of chemical bond and potential barrier in an invariant energy-orbital picture

Physical nature of the chemical bond and potential barrier is studied in terms of energy natural orbitals (ENOs), which are extracted from highly correlated electronic wavefunctions. ENO provides an objective one-electron picture about energy distribution in a molecule, just as the natural orbitals (NOs) represent one electron view about electronic charge distribution. ENO is invariant in the same sense as NO is, that is, ENOs converge to the exact ones as a series of approximate wavefunctions approach the exact one, no matter how the methods of approximation are adopted. Energy distribution analysis based on ENO can give novel insights about the nature of chemical bonding and formation of potential barriers, besides information based on the charge distribution alone. With ENOs extracted from full configuration interaction wavefunctions in a finite yet large enough basis set, we analyze the nature of chemical bonding of three low-lying electronic states of a hydrogen molecule, all being in different classes of the so-called covalent bond. The mechanism of energy lowering in bond formation, which gives a binding energy, is important, yet not the only concern for this small molecule. Another key notion in chemical bonding is whether a potential basin is well generated stiff enough to support a vibrational state(s) on it. Based on the virial theorem in the adiabatic approximation and in terms of the energy and force analyses with ENOs, we study the roles of the electronic kinetic energy and its nuclear derivative(s) on how they determine the curvature (or the force constant) of the potential basins. The same idea is applied to the potential barrier and, thereby, the transition states. The rate constant within the transition-state theory is formally shown to be described in terms of the electronic kinetic energy and the nuclear derivatives only. Thus, the chemical bonding and rate process are interconnected behind the scenes. Besides this aspect, we pay attention to (1) the effects of electron correlation that manifests itself not only in the orbital energy but also in the population of ENOs and (2) the role of nonadiabaticity (diabatic state mixing), resulting in double basins and a barrier on a single potential curve in bond formation. These factors differentiate a covalent bond into subclasses.

Orbital contraction and covalent bonding

According to Ruedenberg's classic treatise on the theory of chemical bonding [K. Ruedenberg, Rev. Mod. Phys. 34, 326-376 (1962)], orbital contraction is an integral consequence of covalent bonding. While the concept is clear, its quantification by quantum chemical calculations is not straightforward, except for the simplest of molecules, such as H₂ ⁺ and H₂. This paper proposes a new, yet simple, approach to the problem, utilizing the modified atomic orbital (MAO) method of Ehrhardt and Ahlrichs [Theor. Chim. Acta 68, 231 (1985)]. Through the use of MAOs, which are an atom-centered minimal basis formed from the molecular and atomic density operators, the wave functions of the species of interest are re-expanded, allowing the computation of the kinetic energy (and any other expectation value) of free and bonded fragments. Thus, it is possible to quantify the intra- and interfragment changes in kinetic energy, i.e., the effects of contraction. Computations are reported for a number of diatomic molecules H₂, Li₂, B₂, C₂, N₂, O₂, F₂, CO, P₂, and Cl₂ and the polyatomics CH₃-CH₃, CH₃-SiH₃, CH₃-OH, and C₂H₅-C₂H₅ (where the single bonds between the heavy atoms are studied) as well as dimers of He, Ne, Ar, and the archetypal ionic molecule NaCl. In all cases, it is found that the formation of a covalent bond is accompanied by an increase in the intra-fragment kinetic energy, an indication of orbital contraction and/or deformation.

Metavalent bonding in chalcogenides: DFT-chemical pressure approach

Understanding the chemical bond nature has attracted considerable attention as it is crucial to analyze and comprehend the different physical and chemical properties of materials. This work is considered a complementary part of our previous work in studying the nature of different types of bonding interactions in a wide variety of molecules and materials using the DFT Chemical Pressure (CP) approach. Recently, a new type of chemical bond, the metavalent bond (MVB), has been defined. We show how the CP formalism can be used to analyze and study the establishment of MVB in two chalcogenides, GeSe and PbSe, in a similar fashion as the electron localization function (ELF) profiles. This is accomplished by analyzing the CP maps of these two chalcogenides at different pressures (up to 40 GPa for GeSe and 10 GPa for PbSe). The CP maps show distinctive features related to the MVB, providing insights into the existence of such chemical interaction in the crystal structure of the two compounds. Similar to ELF profiles, CP maps can visualize and track the strength of the MVB in GeSe and PbSe under pressure.

From six to eight Π-electron bare rings of group-XIV elements and beyond: can planarity be deciphered from the "quasi-molecules" they embed?

Ab initio molecular orbital theory is used to study the structures of six and eight π-electron bare rings of group-XIV elements, and even larger [n]annulenes up to C₁₈H₁₈, including some of their mono-, di-, tri-, and tetra-anions. While some of the above rings are planar, others are nonplanar. A much spotlighted case is cyclo-octatetraene (C₈H₈), which is predicted to be nonplanar together with its heavier group-XIV analogues Si₈H₈ and Ge₈H₈, with the solely planar members of its family having the stoichiometric formulas C₄Si₄H₈ and C₄Ge₄H₈. A similar situation arises with the six π-electron bare rings, where benzene and substituted ones up to C₃Si₃H₆ or so are planar, while others are not. However, the explanations encountered in the literature find support in ab initio calculations for such species, often rationalized from distinct calculated features. Using second-order Møller-Plesset perturbation theory and, when affordable (particularly tetratomics, which may allow even higher levels), the coupled-cluster method including single, double, and perturbative triple excitations, a common rationale is suggested based on a novel concept of quasi-molecules or the (3+4)-atom partition scheme. Any criticism of tautology is therefore avoided. The same analysis has also been successfully applied to even larger [n]annulenes, to their mixed family members involving silicon and germanium atoms, and to the C₁₈ carbon ring. Furthermore, it has been extended to annulene anions to check the criteria of the popular Hückel rule for planarity and aromaticity. Exploratory work on cycloarenes is also reported. Besides a partial study of the involved potential energy surfaces, equilibrium geometries and harmonic vibrational frequencies have been calculated anew, for both the parent and the actual prototypes of the quasi-molecules.

A Comparison of Partial Atomic Charges for Electronically Excited States

Partial atomic charges are a useful and intuitive concept for understanding molecular properties and chemical reaction mechanisms, showing how changes in molecular geometry can affect the flow of electronic charge within a molecule. However, the use of partial atomic charges remains relatively uncommon in the characterization of excited-state electronic structure. Here, we show how well-established partial atomic charge methods perform for interatomic, intermolecular, and interbond electron transfer in electronically excited states. Our results demonstrate the utility of real-space partial atomic charges for interpreting the electronic structures that arise in excited-state processes. Furthermore, we show how this analysis can be used to demonstrate that analogous electronic structures arise near photochemically relevant conical intersection regions for several conjugated polyenes. On the basis of our analysis, we find that charges computed using the iterative Hirshfeld approach provide results which are consistent with chemical intuition and are transferable between homologous molecular systems.

Bonding analysis of water clusters using quasi-atomic orbitals

The quasi-atomic orbital (QUAO) bonding analysis introduced by Ruedenberg and co-workers is used to develop an understanding of the hydrogen bonds in small water clusters, from the dimer through the hexamer (bag, boat, book, cyclic, prism and cage conformers). Using kinetic bond orders as a metric, it is demonstrated that as the number of waters in simple cyclic clusters increases, the hydrogen bonds strengthen, from the dimer through the cyclic hexamer. However, for the more complex hexamer isomers, the strength of the hydrogen bonds varies, depending on whether the cluster contains double acceptors and/or double donors. The QUAO analysis also reveals the three-center bonding nature of hydrogen bonds in water clusters.

Highs and Lows of Bond Lengths: Is There Any Limit?

Two distinct points on the potential energy curve (PEC) of a pairwise interaction, the zero‐energy crossing point and the point where the stretching force constant vanishes, allow us to anticipate the range of possible distances between two atoms in diatomic, molecular moieties and crystalline systems. We show that these bond‐stability boundaries are unambiguously defined and correlate with topological descriptors of electron‐density‐based scalar fields, and can be calculated using generic PECs. Chemical databases and quantum‐mechanical calculations are used to analyze a full set of diatomic bonds of atoms from the s‐p main block. Emphasis is placed on the effect of substituents in C−C covalent bonds, concluding that distances shorter than 1.14 Å or longer than 2.0 Å are unlikely to be achieved, in agreement with ultra‐high‐pressure data and transition‐state distances, respectively. Presumed exceptions are used to place our model in the correct framework and to formulate a conjecture for chained interactions, which offers an explanation for the multimodal histogram of O−H distances reported for hundreds of chemical systems.

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.

Substituent Effects on the Quantum Interference of Two-Center One-Electron Bonds: [B2X6]- (X = H, F, Cl, CN, OH, CH3, and OCH3)

The interference energy analysis (IEA) provided by the generalized product function energy partitioning (GPF-EP) method was applied to investigate the influence of the neighboring atoms on the nature of the two-center one-electron (2c1e) bonds in the anion dimers of BX₃ species (X = H, F, Cl, CN, OH, CH₃, and OCH₃). The species were studied at the GVB-PP(6/12).SC(1,2)/6-31**G++ level of calculation. The IEA has revealed that there is a balance between two main factors determining the chemical stability of the species. Quantum interference acts as the sole stabilizing effect in the formation of the chemical bonds, particularly as the result of the drop in kinetic energy, and the electronegativity of the substituent has a direct influence on the magnitude of this effect. The quasi-classical energy is responsible for the destabilizing factors, mainly the group bulkiness, and the "electron-withdrawing" effect in the case of the cyano group.

Spin-Coupled Generalized Valence Bond Theory: New Perspectves on the Electronic Structure of Molecules and Chemical Bonds

Spin-Coupled Generalized Valence Bond (SCGVB) theory provides the foundation for a comprehensive theory of the electronic structure of molecules. SCGVB theory offers a compelling orbital description of the electronic structure of molecules as well as an efficient and effective zero-order wave function for calculations striving for quantitative predictions of molecular structures, energetics, and other properties. The orbitals in the SCGVB wave function are usually semilocalized, and for most molecules, they can be interpreted using concepts familiar to all chemists (hybrid orbitals, localized bond pairs, lone pairs, etc.). SCGVB theory also provides new perspectives on the nature of the bonds in molecules such as C₂, Be₂ and SF₄/SF₆. SCGVB theory contributes unparalleled insights into the underlying cause of the first-row anomaly in inorganic chemistry as well as the electronic structure of organic molecules and the electronic mechanisms of organic reactions. The SCGVB wave function accounts for nondynamical correlation effects and, thus, corrects the most serious deficiency in molecular orbital (RHF) wave functions. Dynamical correlation effects, which are critical for quantitative predictions, can be taken into account using the SCGVB wave function as the zero-order wave function for multireference configuration interaction or coupled cluster calculations.

Stability and Dissociation of Ethylenedione (OCCO)

This work examines the electronic structure and apparent instability of ethylenedione (OCCO), including an analysis of the singlet and triplet potential energy surfaces along the bending vibrations. While the singlet state is inherently unstable due to the Renner-Teller effect, theory predicts the triplet state to have a stable minimum on the potential energy surface. The stability of the triplet state is examined in detail, taking into account spin-orbit interactions. Using multireference quantum chemical methods, the lifetime of the triplet state is estimated to be in the picosecond range, significantly lower than previously computed. A quasi-atomic molecular orbital (QUAO) analysis is also used to elucidate the nature of bonding along the potential energy surface in both the singlet and triplet states. These calculations confirm the transient nature of the OCCO molecule, although they do not fully explain the lack of experimental detection via spectroscopy, which is known have the capability to probe even shorter lifetimes.

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.

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.

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.

Proton Transfer in 1,2,4-Triazolium Dinitramide: Effect of Aqueous Microsolvation

The gas phase proton transfer process in 1,2,4-triazolium dinitramide (TD) was studied using second-order perturbation theory to determine how the presence of one and two water molecules modifies the potential energy surface that connects the ion pair to the neutral pair. The presence of one water molecule can introduce small proton transfer energy barriers that separate the ion pair from the lower-energy neutral pair. These energy barriers are easily surmounted. Reaction paths were determined for single proton transfers and double proton transfers via one water molecule. In the presence of two water molecules, the global minimum is an ion pair, as are most of the lower-energy local minima. Energy barriers for single, double, and triple proton transfers were also found for TD in the presence of two water molecules. One TD ion pair structure with two water molecules has no corresponding neutral pair energy minimum. A quasi-atomic orbital analysis is used to understand the nature of the bonding in the various species studied in this work.

Chemical Pressure Maps of Molecules and Materials: Merging the Visual and Physical in Bonding Analysis

The characterization of bonding interactions in molecules and materials is one of the major applications of quantum mechanical calculations. Numerous schemes have been devised to identify and visualize chemical bonds, including the electron localization function, quantum theory of atoms in molecules, and natural bond orbital analysis, whereas the energetics of bond formation are generally analyzed in qualitative terms through various forms of energy partitioning schemes. In this Article, we illustrate how the chemical pressure (CP) approach recently developed for analyzing atomic size effects in solid state compounds provides a basis for merging these two approaches, in which bonds are revealed through the forces of attraction and repulsion acting between the atoms. Using a series of model systems that include simple molecules (H₂, CO₂, and S₈), extended structures (graphene and diamond), and systems exhibiting intermolecular interactions (ice and graphite), as well as simple representatives of metallic and ionic bonding (Na and NaH, respectively), we show how CP maps can differentiate a range of bonding phenomena. The approach also allows for the partitioning of the potential and kinetic contributions to the interatomic interactions, yielding schemes that capture the physical model for the chemical bond offered by Ruedenberg and co-workers.

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.

Accurately extracting the signature of intermolecular interactions present in the NCI plot of the reduced density gradient versus electron density

An electron density (ED)-based methodology is developed for the automatic identification of intermolecular interactions using pro-molecular density. The expression of the ED gradient in terms of atomic components furnishes the basis for the Independent Gradient Model (IGM). This model leads to a density reference for non interacting atoms/fragments where the atomic densities are added whilst their interaction turns off. Founded on this ED reference function that features an exponential decay also in interference regions, IGM model provides a way to identify and quantify the net ED gradient attenuation due to interactions. Using an intra/inter uncoupling scheme, a descriptor (δg^inter) is then derived that uniquely defines intermolecular interaction regions. An attractive feature of the IGM methodology is to provide a workflow that automatically generates data composed solely of intermolecular interactions for drawing the corresponding 3D isosurface representations.

Intrinsic Resolution of Molecular Electronic Wave Functions and Energies in Terms of Quasi-atoms and Their Interactions

A general intrinsic energy resolution has been formulated for strongly correlated wave functions in the full molecular valence space and its subspaces. The information regarding the quasi-atomic organization of the molecular electronic structure is extracted from the molecular wave function without introducing any additional postulated model state wave functions. To this end, the molecular wave function is expressed in terms of quasi-atomic molecular orbitals, which maximize the overlap between subspaces of the molecular orbital space and the free-atom orbital spaces. As a result, the molecular wave function becomes the superposition of a wave function representing the juxtaposed nonbonded quasi-atoms and a wave function describing the interatomic electron migrations that create bonds through electron sharing. The juxtaposed nonbonded quasi-atoms are shown to consist of entangled quasi-atomic states from different atoms. The binding energy is resolved as a sum of contributions that are due to quasi-atom formation, quasiclassical electrostatic interactions, and interatomic interferences caused by electron sharing. The contributions are further resolved according to orbital interactions. The various transformations that generate the analysis are determined by criteria that are independent of the working orbital basis used for calculating the molecular wave function. The theoretical formulation of the resolution is quantitatively validated by an application to the C₂ molecule.

A Comprehensive Analysis in Terms of Molecule-Intrinsic, Quasi-Atomic Orbitals. III. The Covalent Bonding Structure of Urea

The analysis of molecular electron density matrices in terms of quasi-atomic orbitals, which was developed in previous investigations, is quantitatively exemplified by a detailed application to the urea molecule. The analysis is found to identify strong and weak covalent bonding interactions as well as intramolecular charge transfers. It yields a qualitative as well as quantitative ab initio description of the bonding structure of this molecule, which raises questions regarding some traditional rationalizations.