CNDO Wave Functions Research Articles

Core model calculation of the electric field gradient: Projection operator formalism with application to NH3

AbstractA core model approach to the calculation of deuteron quadrupole coupling constants is investigated using NH3 as an example. First the deuteron quadrupole coupling constant is calculated from a CNDO wave function. This result is subsequently improved by recomputing the N—D bond orbital by means of a variational calculation using the CNDO function to construct a core potential for the bond Hamiltonian. In order to simplify integrations a single‐center basis is chosen to represent the variational wave function. A projection operator formalism is used as a computational scheme to maintain orthogonality of the bond orbital to core orbitals. Excellent agreement with experiment is obtained. The procedure is applicable to more complicated molecules.

Calculation of molecular geometries and force constants from CNDO wavefunctions by the force method

The semi-empirical quantum chemical calculation of molecular geometries and force constants by the usual energy hypersurface method rapidly becomes impractical as the size of the molecule increases. Here we show that the application of the force method to semi-empirical wavefunctions makes an economic and simple calculation of molecular geometries and force constants possible. Problems which are virtually insoluble by the classical method, such as full geometry optimization in large molecules, can be solved this way. The calculation of forces as exact negative derivatives of the total SCF energy is given for CNDO wavefunctions. Two geometry optimization schemes are discussed ; it is concluded that a steepest descent method is the most practical in semi-empirical calculations. As an example the fully optimized equilibrium geometry of pyrrole has been determined. Except for the CH and NH bond lengths, the calculated geometry agrees almost perfectly with the experimental one. The calculation of force constants from the forces is discussed. The force constants of CH4 and H2O have been determined, including the interaction ones. The signs and magnitudes of the stretch-bend interaction constants agree with experiment.

On the Bond Order between Atoms in Approximate SCF-MO Theory

The bond order between two atoms is discussed within the framework of all-valence-electron SCF-MO theories based on the Zero-Differential Overlap Approximation, and a definition of the bond order is proposed which is analogous to the procedure used to extract charge distributions from approximate SCF-MO calculations. Bond orders are calculated for a variety of small molecules and relationships similar to those found in π-electron theory between bond lengths and bond orders are observed. CNDO wave functions are used in this work, although the definition may also be used for calculations based on the INDO and NDDO approximations.

The intensities of low-energy electronic absorption transitions of some carbonyls and thiocarbonyls

The intensities of low-energy electronic transitions for some carbonyls and thiocarbonyls have been calculated from CNDO wavefunctions. Quite good agreement with experimental results has been obtained, where the latter are available. A satisfactory approximation for calculating intensities employs only one-center integrals. From the calculated trends in oscillator strengths, the absorption of thiophosgene at 4.46 eV can be identified as the π→π* 1A 1←X̃ 1A 1 system. Another, very weak, system of thiophosgene at ≈ 3.9 eV is tentatively assigned to an n→π* 1A 1 ← X̃ 1 A 1 transition, with the n orbital localized on the chlorine atoms.

Calculation of molecular quadrupole moments and a demonstration of the importance of overlap densities in the theory of polyatomic molecules

AbstractA computational method for calculating quadrupole moments from molecular wave functions in a Slater orbital basis set is described. Using both IEHT and CNDO wave functions quadrupole moments for a series of polyatomic molecules are calculated. They are compared with experimental results and the IEHT wave functions are found to give agreement with experiment while CNDO wave functions do not. The importance of bicentric densities (overlap densities) in the calculation of multipole moments is shown. This is followed by a discussion of the usefulness of these wave functions for a quantitative characterization of the electronic structure of large molecules.

Complementary DNA base interactions: application of recently refined electrostatic interaction theory.

AbstractElectrostatic interactions between the DNA bases in the Watson‐Crick hydrogen bonding configuration are examined in both the molecular and the atomic multipole representation using three different methods of calculation: (a) CNDO wave functions and definitions of moments, (b) IEHT wave functions and division of two‐center densities and (c) IHET wave functions with equally divided overlap densities. It is shown that the inclusion in the interaction series of terms at least as high as the quadrupole‐quadrupole is required to quantitatively characterize the interactions. Convergence is more rapid with the atomic multipole representation and is unaffected by the type of assignment of formal charges. A quantitative approach to the problem of the role of electrostatic interactions in hydrogen bonding in DNA is thus provided, with obvious impact on the investigation of molecular recognition processes.

Calculation of diamagnetic susceptibilities and shielding in polyatomic molecules, with analysis of wavefunctions and the importance of multicenter integrals in the theory

The diamagnetic susceptibility tensor and shielding constants are calculated for different nuclei in a representative set of molecules by use of the Van Vleck and Ramsey equations, respectively. Both IEHT wavefunctions, representing the complete electronic density, and CNDO wavefunctions with systematic neglect of two-center densities were employed. Integrals over atomic densities were calculated in exact form and by integration of the Taylor expansion of the operator over respective densities. The relative importance of the various integrals in the theory as well as the convergence of the expansion are examined. The inclusion of two-center overlap densities is found to be essential. The IEHT wavefunctions are shown to give very good agreement with experimental values of the diamagnetic susceptibility tensors. The truncation of the Taylor expansion for the integrals is shown to be of sufficient accuracy when terms up to dipole are included.

Molecular electrostatic potentials: Comparison of ab initio and CNDO results

The possibilities of utilization of CNDO wave functions for computing molecular electrostatic potentials are studied by comparison with ab initio results for H2O and H2CO.

Magnetic Circular Dichroism of the α Bands of Some Polycyclic Aromatic Hydrocarbons

The magnetic circular dichroism (MCD) of six polycyclic aromatic hydrocarbons (naphthalene, anthracene, phenanthrene, 1,2-benzanthracene, picene, and 1,2–3, 4-dibenzanthracene) has been measured in the α (1Lb) absorption region. A band in the MCD spectrum of anthracene which does not correspond to any reported absorption band has been assigned to the hitherto unobserved α band. The sign and magnitude of the MCD's observed are in good agreement with those calculated using CNDO wave-functions.