Natural resonance-theoretic conceptions of extreme electronic delocalization in soft materials.

In the broad context of Dalton's atomic hypothesis and subsequent classical vs. quantum understanding of macroscopic materials, we show how Pauling's resonance-type conceptions, as quantified in natural resonance theory (NRT) analysis of modern wavefunctions, can be modified to unify description of interatomic interactions from the Lewis-like limit of localized e-pair covalency in molecules to the extreme delocalized limit of supramolecular "soft matter" aggregation. Such "NRT-centric" integration of NRT bond orders for hard- and soft-matter interactions is illustrated with application to a long-predicted and recently synthesized organometallic sandwich-type complex ("diberyllocene") that exhibits bond orders ranging from the soft limit (bBeC ≈ 0.01) to the typical values (bCC ≈ 1.35) of molecular resonance-covalency in the organic domain, with intermediate value (bBeBe ≈ 0.86) for intermetallic Be⋯Be interaction.

Comment on "Superposition of Waves or Densities: Which Is the Nature of Chemical Resonance?" [J. Comput. Chem. 2021, 42, 412-417].

We reply to specific criticisms and misrepresentations of natural resonance theory (NRT) in a recent article [Y. Wang, J. Comput. Chem. 2021, 42, 412-417] and argue that it presents a false dichotomy with respect to theoretical efforts to comprehend the nature of resonance-type phenomena.

Coupled Cluster Studies of Platinum-Actinide Interactions. Thermochemistry of PtAnOn+ (n = 0-2 and An = U, Np, Pu).

Accurate Pt-An bond dissociation enthalpies (BDEs) for PtAnOn+ (An = U, Np, Pu and n = 0-2) and the corresponding enthalpies for the Pt + OAnOn+ substitution reactions have been studied for the first time using an accurate composite coupled cluster approach. Analogous O-AnOn+ bond dissociation enthalpies are also presented. To make the study possible, new correlation consistent basis sets optimized using the all-electron third-order Douglas-Kroll-Hess (DKH3) scalar relativistic Hamiltonian are developed and reported for Pt and Au, with accompanying benchmark calculations of their atomic ionization potentials to demonstrate the effectiveness of the new basis sets. For the charged PtAnOn+ species (n = 1, 2), a low-spin state (LSS) for which the Pt-An σ bond is doubly occupied is studied together with a high-spin state (HSS) obtained by unpairing the σ bond orbital and placing one electron into the An 5f shell. The relative energies of the two spin states have been compared and qualitatively assessed via natural population and natural bond analyses. The enthalpies for the Pt substitution reactions, i.e., Pt + OAnOn+ → PtAnOn+ + O, are calculated to range from about 14-62 kcal/mol, and the Pt-AnOn+ bond dissociation enthalpies range from about 78-149 kcal/mol for the ground electronic states. For the PtAnO+ species, the LSSs were all predicted to be the ground state, whereas the PtAnO2+ molecules all favored the HSSs. The prediction for PtUO2+ is consistent with previous theoretical findings. The natural bond orbital analyses indicate a triple bond between An and O, with a double to quadruple bond between the An and Pt.

Pauling's Conceptions of Hybridization and Resonance in Modern Quantum Chemistry.

We employ the tools of natural bond orbital (NBO) and natural resonance theory (NRT) analysis to demonstrate the robustness, consistency, and accuracy with which Linus Pauling's qualitative conceptions of directional hybridization and resonance delocalization are manifested in all known variants of modern computational quantum chemistry methodology.

Coupled Cluster Study of the Interactions of AnO2, AnO2+, and AnO22+ (An = U, Np) with N2 and CO.

Thermochemical and spectroscopic properties for actinyl complexes involving UO22+/1+/0 and NpO22+/1+/0 with N2 and CO, together with the UO2-O2, UO2+-O2, and UO2+-NO complexes, have been studied for the first time using an accurate composite coupled cluster approach. Two general bonding motifs were investigated, end-on (η1) and side-on (η2) relative to the metal center of the actinyls. For end-on CO complexes, both C-coordinated (An-C) and O-coordinated (An-O) structures were examined, with the former always being lower in energy. All of the η1 complexes were calculated to be stable, with dissociation energies ranging from 2 to 36 kcal/mol, except for that of UO2+-O2 (the η1 orientation for UO2+-NO was not amenable to single reference coupled cluster). In agreement with a previous study, the η2 structure for UO2+-O2 was calculated to be relatively strongly bound, by 22.3 kcal/mol in this work. The closely related NO complex, however, had a calculated dissociation energy of just 4.0 kcal/mol. The binding energy of O2 to neutral UO2 in a η2 orientation was calculated to be very strong, 75.4 kcal/mol, and strongly resembled a UO2+(O2-) complex at equilibrium. The N-N and C-O bonds were found to be somewhat activated for all the side-on (η2) neutral An(IV) complexes, with stretching frequencies of N2 or CO being red-shifted by as much as 480 cm-1 with a 0.06 Šbond length elongation. Dissociation energies for the η1 complexes are strongly correlated with the extent of electron transfer from ligand to actinyl. The nature of bonding in the actinyl complexes is examined using natural resonance theory (NRT). The correlation between bonding motif and small molecule activation is in agreement with experiments in condensed phases.

Resonance Theory Reboot.

What is now called "resonance theory" has a long and conflicted history. We first sketch the early roots of resonance theory, its heritage of diverse physics and chemistry conceptions, and its subsequent rise to reigning chemical bonding paradigm of the mid-20th century. We then outline the alternative "natural" pathway to localized Lewis- and resonance-structural conceptions that was initiated in the 1950s, given semi-empirical formulation in the 1970s, recast in ab initio form in the 1980s, and successfully generalized to multi-structural "natural resonance theory" (NRT) form in the 1990s. Although earlier numerical applications were often frustrated by the ineptness of then-available numerical solvers, the NRT variational problem was recently shown to be amenable to highly efficient convex programming methods that yield provably optimal resonance weightings at a small fraction of previous computational costs. Such convexity-based algorithms now allow a full "reboot" of NRT methodology for tackling a broad range of chemical applications, including the many familiar resonance phenomena of organic and biochemistry as well as the still broader range of resonance attraction effects in the inorganic domain. We illustrate these advances for prototype chemical applications, including (i) stable near-equilibrium species, where resonance mixing typically provides only small corrections to a dominant Lewis-structural picture, (ii) reactive transition-state species, where strong resonance mixing of reactant and product bonding patterns is inherent, (iii) coordinative and related supramolecular interactions of the inorganic domain, where sub-integer resonance bond orders are the essential origin of intermolecular attraction, and (iv) exotic long-bonding and metallic delocalization phenomena, where no single "parent" Lewis-structural pattern gains pre-eminent weighting in the overall resonance hybrid.

To Be or Not to Be: Demystifying the 2nd-Quantized Picture of Complex Electronic Configuration Patterns in Chemistry with Natural Poly-Electron Population Analysis.

We provide a didactic introduction to 2nd-quantized representation of complex electron-hole (e/h) excitation patterns in general configuration interaction wave functions built from orthonormal local orbitals of natural atomic orbital or natural bond orbital (NBO) type. Such local excitation patterns of chemically oriented basis functions can be related to the resonance concepts of valence bond theory, and quantitative evaluation of the associated excitation probabilities then provides an alternative assessment of resonance "weighting" that may be compared with those of NBO-based natural resonance theory. We illustrate the usefulness of anticommutation relations in deriving Pauli-compliant expressions for allowed excitation patterns, showing how the exciton-like promotions φλ → φν (creating an e/h excitation with h in φλ and e in φν ) impose strict constraints on associated e/h-probabilities (requiring, e.g., that the e-probability for an electron "to be" or "not to be" in φν must be rigorously linked to the complementary h-probabilities in φλ ). Specific examples are presented of the quantum Boolean logic for four or six local spin-orbitals, with emphasis on Natural Poly-Electron Population Analysis (NPEPA) evaluation of VB-type covalent and ionic contributions in conventional 2-center bonding, resonance weightings in 3-center hydrogen bonding, and general characteristics of higher-order m-center bonding motifs for m > 3. Numerical results are presented for methylamine, acrolein, and water dimer to illustrate current NPEPA implementation in the NBO program. © 2019 Wiley Periodicals, Inc.

NBO 7.0: New vistas in localized and delocalized chemical bonding theory.

We briefly outline some leading features of the newest version, NBO 7.0, of the natural bond orbital (NBO) wavefunction analysis program. Major extensions include: (1) a new NPEPA module implementing Karafiloglou's "polyelectron population analysis" in the NBO framework; (2) new RDM2 program infrastructure for describing electron correlation effects based on full evaluation of the second-order reduced density matrix; (3) improved convex-solver implementation of natural resonance theory (NRT), allowing a greatly expanded range of applications and associated "resonance NBO" (RNBO) visualization of chemical reactivity; (4) a variety of other improvements in well-established NBO algorithms. We also provide brief introduction to the new NBOPro@Jmol utility program, a plugin to the Jmol chemical structure viewer that serves as a convenient tool to provide on-demand NBO descriptors or orbital visualizations for a broad variety of chemical inquiries in research or classroom applications. © 2019 Wiley Periodicals, Inc.

Efficient optimization of natural resonance theory weightings and bond orders by gram-based convex programming.

We describe the formal algorithm and numerical applications of a novel convex quadratic programming (QP) strategy for performing the variational minimization that underlies natural resonance theory (NRT). The QP algorithm vastly improves the numerical efficiency, thoroughness, and accuracy of variational NRT description, which now allows uniform treatment of all reference structures at the high level of detail previously reserved only for leading "reference" structures, with little or no user guidance. We illustrate overall QPNRT search strategy, program I/O, and numerical results for a specific application to adenine, and we summarize more extended results for a data set of 338 species from throughout the organic, bioorganic, and inorganic domain. The improved QP-based implementation of NRT is a principal feature of the newly released NBO 7.0 program version. © 2019 Wiley Periodicals, Inc.

Actinyl cation-cation interactions in the gas phase: an accurate thermochemical study.

Gas phase actinyl cation-cation interactions (CCIs) were studied by an accurate composite coupled cluster thermochemical approach for the first time. A number of CCI dimers were constructed from the monomers UO22+, UO2+, NpO22+, NpO2+, PuO2+, and AmO2+. All CCI dimers studied were calculated to be thermodynamically unstable, with dissociation energies ranging from -60 to -90 kcal mol-1, but in many cases kinetic stability was indicated by calculated local minima with well depths as large as ∼15 kcal mol-1. Most of the dimers studied involved a T-shaped geometry, although one side-on dimer, (UO2+)2, was included since it was amenable to coupled cluster methods. In the T-shaped isomers the most stable dimers were calculated to arise when the oxo-group of an An(v) actinyl cation was oriented towards the metal center of an An(vi) actinyl cation. For both mixed-valent An(vi)/An(v) and mono-valent An(v) dimers, the stability as estimated from the depth of the calculated local minimum decreased in the donor series U(v) > Np(v) > Pu(v) > Am(v). These trends correlate well with experimental trends in condensed phase CCIs. A rationale for the bonding in CCIs was investigated by carrying out charge transfer analyses using the natural bond orbital (NBO) method. Augmenting the usual Lewis acid-base explanation, CCIs are the direct result of a competition between charge transfer stabilization, which can be as much as 0.11e or 30.7 kcal mol-1 at equilibrium, and Coulombic repulsive destabilization.

NBO 6.0: natural bond orbital analysis program.

We describe principal features of the newly released version, NBO 6.0, of the natural bond orbital analysis program, that provides novel "link-free" interactivity with host electronic structure systems, improved search algorithms and labeling conventions for a broader range of chemical species, and new analysis options that significantly extend the range of chemical applications. We sketch the motivation and implementation of program changes and describe newer analysis options with illustrative applications.

Ab initio calculations of nitrogen oxide reactions: formation of N2O2, N2O3, N2O4, N2O5, and N4O2 from NO, NO2, NO3, and N2O.

Ab initio computational methods were used to obtain Delta(r)H(o), Delta(r)G(o), and Delta(r)S(o) for the reactions 2 NO <=> N(2)O(2) (I), NO+NO(2) <=> N(2)O(3) (II), 2 NO(2) <=> N(2)O(4) (III), NO(2)+NO(3) <=> N(2)O(5) (IV), and 2 N(2)O <=> N(4)O(2) (V) at 298.15 K. Optimized geometries and frequencies were obtained at the CCSD(T) level for all molecules except for NO, NO(2), and NO(3), for which UCCSD(T) was used. In all cases the aug-cc-pVDZ (avdz) basis set was employed. The electronic energies of all species were obtained from complete basis set extrapolations (to aug-cc-pV5Z) using five different extrapolation methods. The [U]CCSD(T)/avdz geometries and frequencies of the N(x)O(y) compounds are compared with literature values, and problems associated with the values and assignments of low-frequency modes are discussed. The standard entropies are compared with values cited in the NIST/JANAF tables [NIST-JANAF Thermochemical Tables, J. Phys. Chem. Ref. Data Monograph No. 9, 4th ed. edited by M. W. Chase, Jr. (American Chemical Society and American Institute of Physics, Woodbury, NY, 1988)]. With the exception of I, in which the dimer is weakly bound, and V, for which thermodynamic data appears to be lacking, the calculated standard thermodynamic functions of reaction are in good agreement with literature values obtained both from statistical mechanical and various equilibrium methods. A multireference-configuration interaction calculation (MRCI+Q) for I provides a D(e) value that is consistent with previous calculations. The combined uncertainties of the NIST/JANAF values for Delta(r)H(o), Delta(r)G(o), and Delta(r)S(o) of II, III, and IV are discussed. The potential surface for the dissociation of N(2)O(4) was explored using multireference methods. No evidence of a barrier to dissociation was found.

Ab initio study of the torsional potential energy surfaces of N2O3 and N2O4: origin of the torsional barriers.

Intrinsic reaction coordinate (IRC) torsional potentials were calculated for N(2)O(4) and N(2)O(3) based on optimized B3LYP/aug-cc-pVDZ geometries of the respective 90 degrees -twisted saddle points. These potentials were refined by obtaining CCSD(T)aug-cc-pVXZ energies [in the complete basis set (CBS) limit] of points along the IRC. A comparison is made between these ab initio potentials and an analytical form based on a two-term cosine expansion in terms of the N-N dihedral angle. The shapes of these two potential curves are in close agreement. The torsional barriers in N(2)O(4) and N(2)O(3) obtained from the CCSD(T)/CBS//B3LYP/aug-cc-pVDZ calculations are 2333 and 1704 cm(-1), respectively. For N(2)O(4) the torsion fundamental frequency from the IRC potential is 87.06 cm(-1), which is in good agreement with the experimentally reported value of 81.73 cm(-1). However, in the case of N(2)O(3) the torsional frequency found from the IRC potential, 144 cm(-1), is considerably larger than the reported experimental values 63-76 cm(-1). Consistent with this discrepancy, the torsional barrier obtained from several different calculations, 1417-1718 cm(-1), is higher than the value of 350 cm(-1) deduced from experimental studies. It is suggested that the assignment of the torsional mode in N(2)O(3) should be reexamined. N(2)O(4) and N(2)O(3) exhibit strong hyperconjugative interactions of in-plane O lone pairs with the central N-N sigma* antibond. Hyperconjugative stabilization is somewhat stronger at the planar geometries because 1,4 interactions of lone pairs on cis O atoms promote delocalization of electrons into the N-N antibond. Calculations therefore suggest that the torsional barriers in these molecules arise principally from a combination of 1,4 interactions and hyperconjugation.

High-resolution infrared spectroscopy in the 1,200-1,300 cm(-1) region and accurate theoretical estimates for the structure and ring-puckering barrier of perfluorocyclobutane.

We present experimental infrared spectra and theoretical electronic structure results for the geometry, anharmonic vibrational frequencies, and accurate estimates of the magnitude and the origin of the ring-puckering barrier in C4F8. High-resolution (0.0015 cm-1) spectra of the nu12 and nu13 parallel bands of perfluorocyclobutane (c-C4F8) were recorded for the first time by expanding a 10% c-C4F8 in helium mixture in a supersonic jet. Both bands are observed to be rotationally resolved in a jet with a rotational temperature of 15 K. The nu12 mode has b2 symmetry under D2d that correlates to a2u symmetry under D4h and consequently has +/- <-- +/- ring-puckering selection rules. A rigid rotor fit of the nu12 band yields the origin at 1292.56031(2) cm-1 with B' = 0.0354137(3) cm-1 and B' ' = 0.0354363(3) cm-1. The nu13 mode is of b2 symmetry under D2d that correlates to b2g under D4h, and in this case, the ring-puckering selection rules are +/- <-- -/+ . Rotational transitions from the ground and first excited torsional states will be separated by the torsional splitting in the ground and excited vibrational states, and indeed, we observe a splitting of each transition into strong and weak intensity components with a separation of approximately 0.0018 cm-1. The strong and weak sets of transitions were fit separately again using a rigid rotor model to give nu13(strong) = 1240.34858(4) cm-1, B' = 0.0354192(7) cm-1, and B' ' = 0.0354355(7) cm-1 and nu13(weak) = 1240.34674(5) cm-1, B' = 0.0354188(9) cm-1, and B' ' = 0.0354360(7) cm-1. High-level electronic structure calculations at the MP2 and CCSD(T) levels of theory with the family of correlation consistent basis sets of quadruple-zeta quality, developed by Dunning and co-workers, yield best estimates for the vibrationally averaged structural parameters r(C-C) = 1.568 A, r(C-F)alpha = 1.340 A, r(C-F)beta = 1.329 A, alpha(F-C-F) = 110.3 degrees , thetaz(C-C-C) = 89.1 degrees , and delta(C-C-C-C) = 14.6 degrees and rotational constants of A = B = 0.03543 cm-1 and C = 0.02898 cm-1, the latter within 0.00002 cm-1 from the experimentally determined values. Anharmonic vibrational frequencies computed using higher energy derivatives at the MP2 level of theory are all within <27 cm-1 (in most cases <5 cm-1) from the experimentally measured fundamentals. Our best estimate for the ring-puckering barrier at the CCSD(T)/CBS (complete basis set) limit is 132 cm-1. Analysis of the C4F8 electron density suggests that the puckering barrier arises principally from the sigmaCC-->sigmaCF hyperconjugative interactions that are more strongly stabilizing in the puckered than in the planar form. These interactions are, however, somewhat weaker in C4F8 than in C4H8, a fact that is consistent with the smaller barrier in the former (132 cm-1) with respect to the latter (498 cm-1).

Natural energy decomposition analysis: extension to density functional methods and analysis of cooperative effects in water clusters.

Natural energy decomposition analysis (NEDA) is a method for partitioning molecular interaction energies into physically meaningful components, including electrical interaction, charge transfer, and core repulsions. The method is a numerically stable procedure that was originally developed for analyzing Hartree-Fock (HF) wave functions based on the localized orbital description of natural bond orbital analysis. In this work, we extend NEDA to treat charge densities from density functional theory (DFT) calculations, replacing the intermolecular exchange (EX) component of the HF analysis with an exchange-correlation (XC) component. DFT/NEDA is applied to hydrogen bonding interactions and cooperative effects in water clusters. Electrical interactions and charge transfer contribute importantly to hydrogen bonding. Comparison of HF and DFT results reveals that the exchange and correlation effects of DFT slightly enhance the extent of charge transfer and core repulsions in the water clusters. Cooperative stabilization of the cyclic water trimer and tetramer is considered by performing a many-body expansion of the interaction energy. Natural energy decomposition analysis of this expansion suggests that charge transfer is the leading source of cooperative stabilization. Polarization effects have only marginal influence on cooperativity.

Ab initio study of cyclobutane: molecular structure, ring-puckering potential, and origin of the inversion barrier.

The structure and ring-puckering properties of cyclobutane and its perdeuterated isotopomer are studied using high-level ab initio methods and complete basis set extrapolations. Calculations reveal significant coupling between the ring-puckering (theta) and CH(2)-rocking (alpha) motions, with equilibrium angles (theta(eq) = 29.59 degrees and alpha(eq) = 5.67 degrees) that are within the range of experimentally determined values. Our best estimate of the inversion barrier is 482 cm(-1), in excellent agreement with recent experimental determinations. Ring-inversion transition frequencies are evaluated from the eigenstates of the intrinsic reaction coordinate potentials for cyclobutane and cyclobutane-d(8). Natural bond orbital analysis shows that sigma(CC) --> sigma(CH)* and sigma(CH) --> sigma(CH)* hyperconjugative interactions are strengthened as cyclobutane puckers, thereby suggesting that inversion barriers in four-membered ring systems are a consequence of electronic delocalization rather than torsional strain.

Influence of resonance on the acidity of sulfides, sulfoxides, sulfones, and their group 16 congeners.

The influence of resonance on the acidities of dimethyl sulfide (DMS), dimethyl sulfoxide (DMSO), and dimethyl sulfone (DMSO2) and their group 16 congeners (DMXO(n) for X = Se, Te, Po and n = 0-2) is examined using ab initio methods and the natural bond orbital (NBO) and natural resonance theory (NRT) analyses. Gas-phase acidities are evaluated using B3LYP-optimized geometries with coupled cluster energies and complete basis set extrapolation. The acidity of the DMSO(n) molecules increases with increasing coordination of the central S atom. Acidity also tends to increase when the central atom is substituted by a heavier group 16 atom. NRT analysis reveals significant resonance delocalization in the DMXO(n) molecules and their anions. On deprotonation, the DMXO(n) molecules undergo structural changes that are consistent with changes in the resonance character of the calculated charge densities. However, resonance cannot account for the trends in the deprotonation energies. Whereas the DMX- anions are more strongly resonance stabilized than their parent molecules DMX, the DMXO2(-) anions and DMXO2 molecules are nearly equally resonance stabilized. Thus, there appears to be no extra stabilization of DMXO2(-) compared to that of DMX- that would account for the enhanced acidity of DMXO2 relative to DMX.

An intrinsic reaction coordinate calculation of the torsion-internal rotation potential of hydrogen peroxide and its isotopomers.

Intrinsic reaction coordinate (IRC) calculations of the internal rotation (torsional) potentials for H(2)O(2) and its isotopomers HDO(2) and D(2)O(2) were carried out at the CCSD(T)/CBS//aug-cc-pVDZ level. Two extrapolation methods were used to obtain energies in the complete basis set (CBS) limit. The full IRC potential was constructed from scans from the C(2v) (cis) and C(2h) (trans) transition states to the equilibrium C(2) (gauche) structure. The IRC potential for H(2)O(2) was fit to a five-term Fourier function; coefficients were compared with values obtained from spectroscopic data. The twofold IRC torsional potentials were used to obtain torsional eigenvalues, which yielded values of the transitions between various ntau states. These results compare favorably with Raman and near-infrared data. Our calculations provide values of the cis and trans barriers of 2495 and 364 cm(-1), respectively, which are in good agreement with both previously calculated and experimentally derived values. It appears that coupling between torsional motion and other degrees of freedom is not significant in these molecules.