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.

Natural localized molecular orbitals

Two sets of orbitals are derived, directly connected to the Nalewajski-Mrozek valence and bond-multiplicity indices: Localized Orbitals from the Bond-Multiplicity Operator (LOBO) and the Natural Orbitals for Chemical Valence (NOCV). LOBO are defined as the eigenvectors of the bond-multiplicity operator. The expectation value of this operator is the corresponding bond index. Thus, the approach presented here allows for a discussion of localized orbitals and bond multiplicity within one common framework of chemical valence theory. Another set of orbitals discussed in the present work, NOCV, are defined as eigenvectors of the overall chemical valence operator. This set of orbitals can be especially useful for a description of bonding in transition metal complexes, as it allows for separation of the deformation density contributions originating from the ligand --> metal donation and metal --> ligand back-donation.

Bond orbitals from chemical valence theory

(1957). The Thomas-Fermi approximation in quantum mechanics. Advances in Physics: Vol. 6, No. 21, pp. 1-101.

The Thomas-Fermi approximation in quantum mechanics

This paper uses the theory of atoms in molecules to investigate the origin of molecular dipole moments. The dipole moment is given by a sum over the net charge and first moment of every atom in a molecule. The first term leads to a charge transfer contribution μc, the second to an atomic polarization contribution μa. It is shown that both terms are, in general, of equal importance in determining both the static molecular dipole moment and the moment induced by a nuclear displacement. Models which imploy only point charges and corresponding bond moments which follow rigidly the nuclear framework, i.e., models which approximate μc and ignore μa, are shown to lead to results that are incompatible with the changes that are found to occur in a molecular charge distribution during a nuclear vibration. The dipole moment is shown to be another group property that is transferable between molecules in the normal hydrocarbons, This property, along with the net charge, the energy, the correlation energy (expressed as...

Properties of atoms in molecules: Dipole moments and transferability of properties

We report the global analysis of methane (12CH4) lines from high resolution rovibrational spectra including accurate line positions and intensities in the region 0–4800 cm−1. This covers four polyads: The Ground State Monad (rotational levels), the Dyad (940–1850 cm−1, 2 vibrational levels, 2 sublevels), the Pentad (2150–3350 cm−1, 5 vibrational levels, 9 sublevels) and the Octad (3550–4800 cm−1, 8 vibrational levels, 24 sublevels) and some of the associated hot bands (Pentad–Dyad and Octad–Dyad). New Fourier transform infrared (FTIR) spectra of the Pentad and Octad regions have been recorded with a very high resolution (better than 0.001 cm−1 instrumental bandwidth, unapodized) at 78 K using the Bruker IFS 125 HR Zurich prototype (ZP2001) spectrometer in combination with a long optical path collisional cooling system [S. Albert, S. Bauerecker, M. Quack, A. Steinlin, Mol. Phys. 105 (2007) 541]. Existing spectra previously recorded with the FTIR spectrometer at the National Solar Observatory on Kitt Peak in Arizona were remeasured selectively to provide new intensities and positions of weaker lines above 4400 cm−1. These were combined with previously reported absorption data from FTIR and laser absorption, as well as high-resolution stimulated Raman and microwave spectra. The effective hamiltonian was expanded up to order 6 for the Ground State, order 6 for the Dyad, order 5 for the Pentad and order 5 for the Octad. A total of 16,738 line positions were used in the least squares adjustment characterized by the following global root mean square deviations dRMS for line positions: 1.3 × 10−4 cm−1 for the Dyad, 6.0 × 10−4 cm−1 for the Pentad, and 3.5 × 10−3 cm−1 for the Octad. Absolute intensities were also analyzed for all the cold bands and some of the hot bands in the region under consideration and we obtained dRMS = 9.6% including 3262 experimental line intensities for the Octad. This analysis represents a large improvement over the previous one [J.-C. Hilico, O. Robert, M. Loete, S. Toumi, A.S. Pine, L.R. Brown, J. Mol. Spectrosc. 208 (2001) 1] with dRMS = 0.041 cm−1 for positions and 15.6% for intensities in the Octad for a smaller data set. The new results are discussed as benchmarks in relation to accurate potential energy hypersurfaces and for atmospheric and planetary spectra.

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C. A. Coulson

Papers

The dipole moment of the C—H bond