INDO Approximation Research Articles

Solvation of the nitrobenzene radical anion

An electrostatic solvation model within the INDO approximation, representing the interaction with the solvent by means of an effective solvent field, is applied to the nitrobenzene radical anion. The available solvent sensitivity data for the 1H, 13C, 14N and 17O hyperfine coupling constants are satisfactorily reproduced. The results are consistent with the assumption of a planar structure of the radical, in contrast with the results of a recent theoretical study.

Molecular orbital calculations of electric field gradients at halogen nuclei in solid chlorine and bromine

Using the MO LCAO method in CNDO and INDO approximations, calculations of the electronic structure of polyatomic clusters in solid Cl 2 and Br 2 have been performed. The energies of the molecular orbitals of the clusters are compared with the available experimental data and theoretical results. The effect of d-orbitals on intermolecular bonding is examined in the case of solid chlorine, and the parameters of the electric field gradient tensor at halogen nuclei are evaluated in both cases of solid chlorine and bromine. The calculated quadrupole coupling constants are in satisfactory agreement with the observed values, but the electric field gradient asymmetry parameter is found to be very small in every case, in contradiction of the experimental results. Finally, the possible reasons for such a discrepancy are discussed.

An INDO-LMO and 13C NMR spectroscopic study of the C-H bonds in tetracyclo[3.2.0.0 2,7.0 4,6]heptane (quadricyclane) and tricyclo[3.1.0.0 2,4]hexane

Using an INDO approximation to Von Niessen's charge density localization method, the percent s character of the C atom hybrid orbitals engaged in C-H bonds is computed for a series of open-chain and cyclic saturated and unsaturated hydrocarbons. A semi-empirical linear relationship is found between these quantities and the experimental nuclear spin-spin coupling constants J CH (standard deviation 4·98 Hz). The experimental values of J CH were measured for quadricyclane ( 1) and tricyclo[3.1.0.0 2,4]hexane ( 2) and were shown to be in fair agreement with the theoretical predictions. An analogous relationship is also established between the percent s character of the involved C atom hybrid orbital and the C-H bond distance, the standard deviation being 0·0040Å. This relation is used in order to predict the different C-H bond lengths in the vibrational ground state of 1 and 2, for which equal CH distances were assumed in the analysis of electron diffraction experiments. The results indicate that molecular geometries can be refined with the use of semi-empirical correlations of the above mentioned type.

Theoretical study of the 4-pyridylmethyl and the 2- and 5-pyrimidyl-methyl cations and radicals

Geometry optimized SCF–MO calculations in the INDO approximation have been performed on the 4-pyridyl-methyl (1), 2-pyrimidylmethyl (3), and 5-pyrimidylmethyl (5) radicals and their corresponding cations (2), (4), and (6). The spin distribution in (1), (3), and (5) and the charge distribution in (2), (4), and (6) provide evidence that mesomeric effects in these systems are similar to those in the benzyl radical and cation. The optimized geometries all have a quinonoid distortion which is more pronounced in the cation. The π-bond orders and the ring–CH2·(or ring-CH2+) rotational barriers were obtained. The results are discussed in terms of resonance hybrid structures. The ionization potentials of the radicals were obtained and found to be in the order (3) > (1) > (5). The calculated ionization potential of (1) was 8.71 V in good agreement with the experimental value of 8.40 V obtained by electron impact measurements.

Electron Spin Resonance Study of Radicals Derived from Picolines

AbstractESR spectra of the three isomeric 1‐hydropicolinyl radicals (methyl‐substituted 1‐hydropyridinyl radicals) have been measured in solution at room temperature. The radicals have been generated by in situ photoreduction of the picolines in isopropyl alcohol solution containing acetone. Most of the coupling constants could be assigned experimentally. Calculations of π spin density using the Hückel, McLachlan, and INDO approximations have been performed for the 1‐hydropicolinyls and also for 1‐hydropyridinyl. Two of the ring proton coupling constants of both 1‐hydro‐2‐methylpyridinyl and 1‐hydro‐3‐methylpyridinyl and the signs of all the proton coupling constants have been assigned on the basis of calculated McLachlan spin densities. The Q parameters of the McConnell‐type relations have been deduced from the measured coupling constants of the 1‐hydropicolinyls and of 1‐hydropyridinyl by use of the condition for conservation of spin density. The values obtained are Q = −27.7 ± 1.1 G, Q = −14.5 ± 2.6 G, and QH = 26.2 ± 1.1 G. It could be shown that only the signs of the spin density calculated by the McLachlan procedure resulted in consistent values of Q. The Karplus‐Fraenkel relation for the nitrogen coupling constant has been confirmed. The values of the Q parameters have been deduced from measured coupling constants and experimental spin densities. Values of QN = 9.6 ± 2.5 G and Q = 8.5 ± 2.9 G have been found. Comparison of the Q parameters with values previously determined for related radicals indicates that there are differences between the groups of 1‐hydropyridinyl and N,N′‐dihydrodiazine radicals.

Approximate charge density localization of molecular orbitals

A NDO approximate procedure based on the indirect intrinsic ab initio localization method of von Niessen is developed. It is shown that only when the NDO approximations are introduced at the two electron level, expressions are obtained which are the charge density counterpart of those found in the approximate energy localization methods. The results of these two methods are quite similar both in the CNDO and INDO approximations. The indeterminacies observed in the CNDO localization for unsaturated systems and for molecules with two or three lone pairs on the same atom, are removed by localizing up to an INDO level. The approximate charge density localization is however computationally much easier than the approximate energy localization method and should be more appropriate in LMO studies of large organic molecules.

INDO- and CNDO-Approximated Molecular Orbital Calculations on the Spin-Spin Coupling Constants in Some 2-Substituted Oxetanes

Spin-spin coupling constants between the methine proton in the oxetane ring and the phenyl protons and carbon nuclei have been calculated in different conformations in the INDO approximation for 2-phenyloxetane and 2-(4-fluorophenyl) oxetane, and in the CNDO approximation for 2-(2- chlorophenyl) oxetane and 2-(3-chlorophenyl) oxetane. In each case the finite perturbation method has been used. In the case of 2-(2-chlorophenyl) oxetane a fairly high energy barrier for the rotation around the C-C bond between the rings is obtained, while in the other three cases the barrier is much lower. The calculations predict an equilibrium conformation in which the oxygen atom lies almost in the plane of the aromatic ring. The calculated dipole moments of 2-(2-chlorophenyl) oxetane and 2-(3-chlorophenyl) oxetane vary significantly with conformation.

The structure of phosphino and phosphoranyl radicals

Equilibrium geometries and isotropic nuclear hyperfine coupling constants have been calculated for the radicals PX 2 and PX 4 (X = H, F, Cl) using the INDO approximations; PH 2 and PF 2 have also been investigated by ab initio methods.

Covalent bonding of Mn2+ ions in octahedral and tetrahedral coordination

This paper is divided into four parts: The first part (Sec. I) contains a brief review of different assumptions made by several authors for the numerical values of the free Mn2+ ion parameters. It is shown that if only the Racah parameters B and C are taken into account, then the Orgel-Griffith choice B=960 cm−1, C=3325 cm−1 seems to be the best one. Tanabe and Sugano's figures lead to errors as high as 3800 cm−1. Adding only the Racah-Trees correction α does not seriously improve the fitting of levels 4G, 4D, and 4F because a singular set of equations is then obtained. An exact experimental agreement can be obtained for all quartet levels by simultaneously using the Racah-Trees correction α and the seniority correction β. The best fit values of the adjustable parameters relevant to the Mn2+ ion are given; it is found that α and β do not differ very much from Shadni's values. Section II deals with the well-known use of the two normalization parameters Nt, Ne for describing covalent bonding. A routine method is developed for performing these calculations by using the three traces of the 4E, 4T1, and 4T2 matrices (if experimentally available). The interest of using these traces, rather than the energies of individual levels, lies in the fact that the energy sum of 4E(4G) and 4E(4D) levels deviates only slightly from a linear function of the Koide and Pryce covalency parameter, while the energy sum of 4T1 and 4T2 levels does not depend on any assumption upon Dq. This method is extensively applied in Sec. IV. In Sec. III is an attempt to obtain condensed analytical expressions by means of Lohr's INDO approximation for covalent bonding. These expressions allow some discussion about the validity of the method described above: It is shown that the use of the conventional Dq formalism can still be justified (with a suitable modified value of Dq) when only the metal-ligand interaction is taken into account, but it is no longer correct if the ligand-ligand terms are introduced in the calculation. In Sec. IV, we have used the ``method of traces'' described in Sec. II for deriving tables of covalency and normalization parameters for several manganese-containing crystals: MnF2, MnCl2, MnBr2, NaCl:Mn, ⋯ . We found that the accuracy of the experimental results presently available is in some cases very poor and new measurements by means of more modern techniques are needed. Specifically, an error as high as 6000 cm−1 has been found on the 4T1(4P) level in Pappalardo's classical paper on MnCl2. Nevertheless, the Dq values we obtain are in the right order Dq(MNBr2)<Dq(MnCl2)<Dq(MnF2), while the reverse order was presented in the pioneer paper by Stout. In addition, other materials of interest for luminescence studies are discussed. In ZnF2:Mn, covalency parameters are about the same as in MnF2, but Dq is stronger in zinc fluoride. In ZnS:Mn, it is shown that the first excited level above those issuing from 4G is 4T2(4D) and not 4T1(4P), except for unreasonably low values of Dq. Finally, we turned to Zn2SiO4:Mn and we have used recent data by Palumbo and Brown on the excitation spectra for computing the ligand field parameters.

On the structure of the radical SF5

Abstract Unrestricted SCF MO calculations in the INDO approximation lead to a satisfactory explanation for the absence of a detectable hyperfine interaction between the unpaired electron and the unique. 19 F nucleus of the radical SF 5 . They thus support the re-assignment of an EPR spectrum that was first attributed to the radical cation SF 4 + to SF 5 .

A theoretical study of nuclear spin coupling constants and hyperfine coupling constants of se‐heterocyclics

AbstractMO calculations based on the finite perturbation theory in the INDO approximation have been carried out on selenophene, eighteen of its monosubstituted derivatives and benzo (b)selenophene. The calculated nuclear spin coupling constants satisfactorily reproduce signs, magnitudes, internal orders and some trends of the experimental values. Comparison of different ZDO calculations provides information on the relative importance of σ and π pathways for the various coupling constants in selenophene and benzo(b)selenophene. Unrestricted Hartree‐Fock calculations at the INDO level have been performed on the radical anions of dibenzoselenophene and 2,1,3‐benzoselenadiazole, the phenoselenazine radical cation, the phenoselenazine neutral radical and the phenoselenazine nitroxide. The isotropic hyperfine coupling constants have been found to be generally in satisfactory agreement with experiment.

An Investigation of σ and π Contributions to Long-range 1H–1H Coupling Constants in Planar Aromatic Derivatives Using CNDO and INDO Molecular Orbital Calculations

Molecular orbital calculations of coupling constants based on finite perturbation theory in the CNDO/2 and INDO approximations have been carried out for styrene, benzaldehyde, and naphthalene. INDO calculations have also been carried out in which one-center exchange integrals involved in σ–π interaction are omitted (INDO(σ) calculations). Both CNDO and INDO(σ) constants give reasonable estimates of σ contributions to long-range 1H–1H couplings, with the former giving better results when strongly stereospecific σ contributions are present. INDO calculations also give reasonable, but generally overestimated, π contributions to these couplings.

Proton and fluorine-19 NMR spectra of aromatic carbonyl fluorides. CNDO/2 and INDO calculations

1H and 19F NMR parameters of substituted phenylcarbonyl fluorides and carbonyl fluorides of 5-membered heteroaromatic rings are determined. The coupling constants of these and related compounds are calculated in the CNDO/2 and INDO approximations. The correlations obtained are discussed in terms of model geometries.

Generalized open shell SCF theory

AbstractA generalized form of the coupling operator technique in SCF theory has been developed. In the formalism presented here, the monoconfigurational problem may be treated as a particular case of the multiconfigurational framework. The matrix form of the operators has been analyzed; in the LCAO context a structure has been found which is very adequate for computational purposes.Some examples are also presented which show the usefulness of the theory, emphasising the CNDO and INDO approximations. Within the application of the method to ab initio calculations, some He and second row atoms states have been studied. The He first excited singlet is also studied, the result of the analysis of such a problem being that the nonorthogonality between the singlet functions of the fundamental and of the first excited states play a primordial role in the efficiency of the method.In no case have the calculation problems, appearing in the application of the theory, been of a more difficult nature than those normally found in the application of the formalism for closed shells.

Solvation of nitroaromatic radical anions : a molecular orbital investigation of hydrogen bonding models

SCF calculations employing the INDO approximation have been applied to a study of the interaction of water and the nitrobenzene radical anion in order to examine possible mechanisms by which electron spin resonance hyperfine coupling constants are altered when the solvent medium containing the radicals is changed from aprotic to hydroxylic. Calculations have been carried out for hydrogen-bonded radical-water complexes of nine different geometries. None of these calculations agree adequately with the available experimental data. Much better agreement with experiment is obtained if the hydrogen-bond formation is accompanied by a distortion of the nitro group toward a pyramidal conformation. The calculations indicate that this pyramidal distortion, rather than a rotation of the nitro group with respect to the aromatic plane, accompanies hydrogen-bond formation and suggests an experimental method of testing the prediction.

The conformational dependence of vicinal15N-C-C-H coupling constants in peptides

The conformational dependence of vicinal 15N-C-C-H coupling in N-methylacetamide as a model compound for coupling in the peptide backbone is investigated by means of the self-consistent perturbation formulation for coupling constants in the INDO approximation of self-consistent-field molecular orbital theory. Because the calculated coupling constants cover a range of at least 7 Hz, they should be useful in determining the ψ angles in peptides. The prediction of opposite signs for gauche and trans coupling indicates the need for sign determination. Non-negligible coupling constants of positive sign for the gauche arrangements are undoubtedly due to a substituent effect involving the lone pair electrons on the nitrogen and the π-electrons of the carbonyl group. Calculated results are compared with the available experimental data.

Computational study of vertical ionization potentials using the ΔINDO + FOCI method

The computational procedure devised by Segal has been employed to estimate ionization potentials by energy differences. In order to obtain similar accuracy with both open- and closed-shell species, a first-order configuration interaction (FOCI) calculation is performed after the SCF procedure for the open-shell system. In this work, the SCF scheme is based on the INDO approximation. In general, these ΔINDO + FOCI computations provide adequate interpretations of photo-electron spectra. For closed-shell parent molecules, comparison of the ionization potentials calculated by Koopmans' Theorem and those by the ΔSCF + FOCI method leads to an estimate of the electronic reorganization taking place on ionization. The results of the present calculations indicate that electronic rcargauization is insufficient to affect the ordering of the first few cationic states predicted by Koopmans' Theorem. The major exception to this occurs for the molecules H2CO and F2CO.

Ground and excited state dipole moments and energies for n-? transitions in carbonyl compounds: INDO configuration interaction calculations

Energies for n-π* transitions and the dipole moments of the ground and excited states were calculated for twelve molecules containing ·CHO and ·CFO groups. The INDO approximations with singly excited configuration interaction were used. Agreement with experiment is good for the ground state dipole moments and satisfactory for the transition energies with the original parameters. Different parameters are needed to reproduce the observed excited state dipole moments for HCHO and FCHO. A discussion is given in terms of a basis of configuration functions for which the excited state dipole moment matrix is diagonal.

An MO theoretical treatment for the solvated electron in polar solvents using simplified models

The solvated electrons in polar solvents such as H 2O, NH 3, HF, MeOH and EtOH are treated using the dimer model and the monomer model. For the dimer model. The unrestricted Hartree-Fock method with the INDO approximation is applied and the calculation of the monomer model is performed by the INDO and ab initio UHF methods; in either case, the additional atomic orbitals for the excess electron are used. It is found conclusively that the properties of the solvated electron in H 2O, NH 3 and HF can be interpreted successfully even when the dimer model is used. Particularly with regad to the inner proton spin density, the result is scarcely affected by the choice of the model or the method of calculation. Concerning the properties of MeOH and EtOH, several reasonable results can also be obtained by using the dimer model.

An Investigation into σ and π Contributions to Long Range 1H–1H Coupling Constants in Conjugated Dienes and Diynes Using CNDO and INDO Molecular Orbital Calculations

Molecular orbital calculations based on finite perturbation theory in the CNDO/2 and INDO approximations are carried out for fourteen conjugated dienes and diynes for which experimental results are available. There is generally very good agreement between experimental and calculated (INDO) coupling constants. Comparison of results of CNDO/2 and INDO calculations elucidates the relative importance of σ and π pathways for the various long-range coupling constants.