Eric D. Glendening

Natural bond orbital methods

Natural bond orbital (NBO) methods encompass a suite of algorithms that enable fundamental bonding concepts to be extracted from Hartree‐Fock (HF), Density Functional Theory (DFT), and post‐HF computations. NBO terminology and general mathematical formulations for atoms and polyatomic species are presented. NBO analyses of selected molecules that span the periodic table illustrate the deciphering of the molecular wavefunction in terms commonly understood by chemists: Lewis structures, charge, bond order, bond type, hybridization, resonance, donor–acceptor interactions, etc. Upcoming features in the NBO program address ongoing advances in ab initio computing technology and burgeoning demands of its user community by introducing major new methods, keywords, and electronic structure system/NBO communication enhancements.

NATURAL RESONANCE THEORY : I. GENERAL FORMALISM

We present a new quantum‐mechanical resonance theory based on the first‐order reduced density matrix and its representation in terms of natural bond orbitals (NBOs). This “natural” resonance theory (NRT) departs in important respects from the classical Pauling‐Wheland formulation, yet it leads to quantitative resonance weights that are in qualitative accord with conventional resonance theory and chemical intuition. The NRT variational functional leads to an optimal resonance‐weighted approximation to the full density matrix, combining the “single reference” limit of weak delocalization (incorporating diagonal population changes only) with the full “multireference” limit of strong delocalization (incorporating off‐diagonal couplings between resonance structures. The NRT variational functional yields an error measure that serves as an intrinsic criterion of accuracy of the resonance‐theoretic description. The NRT program structure, algorithms, and numerical characteristics are described in supplementary material, and detailed chemical applications are presented in two companion papers. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 593–609, 1998

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.

Natural Resonance Theory: III. Chemical Applications

We describe quantitative numerical applications of the natural resonance theory (NRT) to a variety of chemical bonding types, in order to demonstrate the generality and practicality of the method for a wide range of chemical systems. Illustrative applications are presented for (1) benzene and polycyclic aromatics; (2) CO2, formate, and related acyclic species; (3) ionic and polar compounds; (4) coordinate covalent compounds and complexes; (5) hypervalent and electron‐deficient species; (6) noncovalent H‐bonded complex; and (7) a model Diels‐Alder chemical reaction surface. The examples exhibit the general harmony of NRT weightings with qualitative resonance‐theoretic concepts and illustrate how these concepts can be extended to many new types of chemical phenomena at a quanitative ab initio level. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 628–646, 1998

Natural resonance theory: II. Natural bond order and valency

Resonance weights derived from the Natural Resonance Theory (NRT), introduced in the preceding paper are used to calculate “natural bond order,” “natural atomic valency,” and other atomic and bond indices reflecting the resonance composition of the wave function. These indices are found to give significantly better agreement with observed properties (empirical valency, bond lengths) than do corresponding MO‐based indices. A characteristic feature of the NRT treatment is the description of bond polarity by a “bond ionicity” index (resonance‐averaged NBO polarization ratio), which replaces the “covalent‐ionic resonance” of Pauling‐Wheland theory and explicity exhibits the complementary relationship of covalency and electrovalency that underlies empirical assignments of atomic valency. We present ab initio NRT applications to prototype saturated and unsaturated molecules methylamine, butadiene), polar compounds (fluoromethanes), and open‐shell species: (hydroxymethyl radical) to demonstrate the numerical stability, convergence, and chemical reasonableness of the NRT bond indices in comparison to other measures of valency and bond order in current usage. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 610–627, 1998

Natural energy decomposition analysis: An energy partitioning procedure for molecular interactions with application to weak hydrogen bonding, strong ionic, and moderate donor–acceptor interactions

We present a procedure for partitioning the Hartree–Fock self‐consistent‐field (SCF) interaction energy into electrostatic, charge transfer, and deformation components. The natural bond orbital (NBO) approach of Weinhold and co‐workers is employed to construct intermediate supermolecule and fragment wave functions that satisfy the Pauli exclusion principle, thereby avoiding the principal deficiency of the popular Kitaura–Morokuma energy decomposition scheme. The function counterpoise method of Boys and Bernardi enters the procedure naturally, providing an estimate of basis set superposition error (BSSE). We find that the energy components exhibit little basis set dependence when BSSE is small. Applications are presented for several representative molecular and ion complexes: the weak hydrogen bond of the water dimer, the strong ionic interaction of the alkali metal hydrides, and the moderate donor–acceptor interactions of BH3NH3 and BH3CO. Electrostatic interaction dominates the long‐range region of the p...

Structures and binding enthalpies of M+(H2O)n clusters, M=Cu, Ag, Au

Structures and incremental binding enthalpies were determined for the M+(H2O)n ionic clusters, M=Cu, Ag, Au; n=1–4 (5 for Cu) using correlated ab initio electronic structure methods. The effects of basis set expansion and high-level correlation recovery were found to be significant, in contrast to alkali and alkaline earth cation/water complexes, where correlation of the d electrons is unimportant. The use of a systematic sequence of one-particle basis sets permitted binding enthalpies in the complete basis set limit to be estimated. Overall, the best theoretical binding enthalpies compared favorably with the available experimental data for copper and silver. No experimental data is available for gold/water clusters. The largest deviation was noted for Ag+(H2O)2, where theory predicts an incremental binding enthalpy of 28 kcal/mol and experiment measures ∼25 kcal/mol. However, the uncertainty associated with one of the two experimental values is quite large (±3 kcal/mol) and almost encompasses the theoret...

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.

Estimating molecular collision diameters using computational methods

Abstract The collision diameters of a series of 34 atoms and both nonpolar and polar molecules were obtained from ab initio calculations. Molecular volumes, VM, were determined from a Monte Carlo integration of the electron density distribution of the optimized HF/6-31G∗ structures. The isotropic collision diameter, dvol, defined as ( 6V M π ) 1 3 was compared in all cases with the respective Lennard-Jones potential minima positions, σm. An excellent linear correlation between dvol and σm for the 34 species was found, with slope and intercept of 1.025 and −0.07 A, respectively. It is thus suggested that dvol may be used directly as an estimate of the isotropic collision diameter of a species. dvol values for several atoms and radicals, as well as for the electronically excited states of NH3 and acetone, are included. The results show that dvol values for the Rydberg excited states are larger than those of the respective ground states.

Erratum: NBO 6.0: Natural bond orbital analysis program

where DAB, DBA are conjugate off-diagonal blocks of the NAO density matrix between atoms A, B. [The (nAnB) 1/2 “normalization factor” in the original form of Eq. (3b) leads to inconsistencies between all-electron and ECP basis sets, as well as other anomalies.] The NBO 6.0 program output has subsequently been changed to include the full table of sNCU(A,B) values for all atom pairs, in addition to that shown in I/O-3. Current distributions of the NBO 6.0 program and documentation <nbo6.chem.wisc.edu> reflect these changes, which leave the numerical values and discussion of Li9 clusters unaffected.