Frank Weinhold

Natural population analysis

A method of ‘‘natural population analysis’’ has been developed to calculate atomic charges and orbital populations of molecular wave functions in general atomic orbital basis sets. The natural analysis is an alternative to conventional Mulliken population analysis, and seems to exhibit improved numerical stability and to better describe the electron distribution in compounds of high ionic character, such as those containing metal atoms. We calculated ab initio SCF‐MO wave functions for compounds of type CH3X and LiX (X=F, OH, NH2, CH3, BH2, BeH, Li, H) in a variety of basis sets to illustrate the generality of the method, and to compare the natural populations with results of Mulliken analysis, density integration, and empirical measures of ionic character. Natural populations are found to give a satisfactory description of these molecules, providing a unified treatment of covalent and extreme ionic limits at modest computational cost.

Natural bond orbital analysis of near‐Hartree–Fock water dimer

We have carried out a natural bond orbital analysis of hydrogen bonding in the water dimer for the near‐Hartree–Fock wave function of Popkie, Kistenmacher, and Clementi, extending previous studies based on smaller basis sets and less realistic geometry. We find that interactions which may properly be described as ‘‘charge transfer’’ (particularly the n‐σ*OH interaction along the H‐bond axis) play a critical role in the formation of the hydrogen bond, and without these interactions the water dimer would be 3–5 kcal/mol repulsive at the observed equilibrium distance. We discuss this result in relationship to Klemperer’s general picture of the bonding in van der Waals molecules, and to previous theoretical analyses of hydrogen bonding by the method of Kitaura and Morokuma.

Natural localized molecular orbitals

The method of natural localized molecular orbitals (NLMOs) is presented as a novel and efficient technique for obtaining LMOs for SCF and CI wave functions. It is an extension of the previously developed natural atomic orbital (NAO) and natural bond orbital (NBO) methods, and uses only the information contained in the one‐particle density matrix. Results are presented for methane and cytosine to indicate that NLMOs closely resemble LMOs obtained by the Boys and Edmiston–Ruedenberg methods, with the exception that the NLMO procedure automatically preserves the MO σ–π separation in planar molecules. The computation time is modest, generally only a small fraction of the SCF computation time. In addition, the derivation of NLMOs from NBOs gives direct insight into the nature of the LMO ‘‘delocalization tails,’’ thus enhancing the role of LMOs as a bridge between chemical intuition and molecular wave functions.

Analysis of the geometry of the hydroxymethyl radical by the “different hybrids for different spins” natural bond orbital procedure

Abstract We have carried out ab initio UHF/6-31G* calculations on the hydroxymethyl radical, CH 2 OH, and have found the equilibrium structure to be nearly planar with barriers to internal rotation occurring at staggered and eclipsed geometries, in good agreement with experiment. The electronic structure of the radical was analyzed via the “different hybrids for different spins” natural bond orbital (DHDS NBO) procedure, which finds separate Lewis structures for each of the spin systems. The α spin Lewis structure resembles that of the anion; the β spin Lewis structure resembles the corresponding cation. This simple picture, in conjunction with Bents rule, allows one to understand the principal electronic factors which dictate the structure of the radical CH 2 group and its torsional and inversion potentials. Charge transfer between oxygen non-bonding orbitals and the empty radical orbital in the β spin system is the dominant interaction determining the torsional potential. Smaller hyperconjugative interactions in the α spin system resemble interactions in closed-shell molecules and directly oppose the effect of radical hyperconjugation, thus illustrating the central idea that open-shell potential energy features result from competition between the two different spin systems.

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 bond orbital analysis of molecular interactions: Theoretical studies of binary complexes of HF, H2O, NH3, N2, O2, F2, CO, and CO2 with HF, H2O, and NH3

The binary complexes of HF, H2O, NH3, N2, O2, F2, CO, and CO2 with HF, H2O, and NH3 have been studied by ab initio molecular orbital theory and natural bond orbital (NBO) analysis. Most of the complexes involving N2, O2, F2, CO, and CO2 are found to have both hydrogen‐bonded and non‐hydrogen‐bonded structures. The NBO analysis provides a consistent picture of the bonding in this entire family of complexes in terms of charge transfer (CT) interactions, showing the close correlation of these interactions with the van der Waals penetration distance and dissociation energy of the complex. Contrary to previous studies based on the Kitaura–Morokuma analysis, we find a clear theoretical distinction between H‐bonded and non‐H‐bonded complexes based on the strength of CT interactions. Charge transfer is generally stronger in H‐bonded than in non‐H‐bonded complexes. It plays an intermediate role in non‐H‐bonded CO2 complexes which have been studied experimentally. However, the internal rotation barrier (1 kcal mol−...

NATURAL BOND ORBITALS AND EXTENSIONS OF LOCALIZED BONDING CONCEPTS

We provide a brief overview of “natural” localized bonding concepts, as implemented in the current natural bond orbital program (NBO 5.0), and describe recent extensions of these concepts to transition metal bonding. [Chem. Educ. Res. Pract. Eur.: 2001, 2, 91-104]

Metric geometry of equilibrium thermodynamics

It is shown that the principal empirical laws of equilibrium thermodynamics can be brought into correspondence with the mathematical axioms of an abstract metric space. This formal correspondence permits one to associate with the thermodynamic formalism a geometrical aspect, with intrinsic metric structure, which is distinct from that arising from graphical representations of equilibrium surfaces in phase space.