Walsh Diagrams Research Articles

Ab initio Cl studies on ground and excited states of thioborine, HBS

Using double-ζ basis sets with polarization and diffuse functions, configuration interaction calculations were performed on linear and nonlinear HBS. For linear HBS, the ground state and 15 low-lying singlet and triplet Σ +, Σ −, Π, and Δ states were studied. Vertical and adiabatic excitation energies as well as R e and ω e values are predicted. States due to π → π ∗ excitations have T e values from 4 to 5 eV, R e(BS) values from 1.765 to 1.846 Å, R e(HB) values from 1.165 to 1.192 Å, ω e(BS) values from 811.7 to 881.5 cm −1, and ω e(HB) values from 2436.6 to 2524.4 cm −1. Excited states deduced from σ → π ∗ , π → 4 s, π → 4 pπ are found to have T e values between 7.24 and 8.77 eV, and smaller R e(BS) and larger ω e(BS) values than the π → π ∗ group of excited states. It was found that four states of nonlinear HBS, 1 3 A′, 1 3 A″, 1 1 A″, and 2 1 A′, are more stable than their linear counterparts. All are due to excitations to the 10 a′ orbital, which is shown to stabilize upon bending of the molecule, in agreement with Walsh's rules. The angles of nonlinear HBS range from 110° for 1 3 A′ to 146.4° for 2 1 A″, T e values from 3.71 to 4.87 eV, and R e(BS) values from 1.76 to 1.81 Å.

Energy surfaces for Si3 and C3: A comparative study.

Density-functional calculations have been performed for the energy surface of the $^{1}\mathrm{A}_{1}$ state of ${\mathrm{Si}}_{3}$ and for vertical excitation energies of low-lying excited states. In contrast to the results for ${\mathrm{C}}_{3}$ and the predictions of Walsh's rules for triatomic molecules with twelve valence electrons, the equilibrium geometry is found to be nonlinear (${\ensuremath{\alpha}}_{\mathrm{Si}\mathrm{?}(\mathrm{h}\mathrm{y}\mathrm{S}\mathrm{i}\mathrm{?}(\mathrm{h}\mathrm{y}\mathrm{S}\mathrm{i}\mathrm{\ensuremath{\sim}}85}$\ifmmode^\circ\else\textdegree\fi{}). The relative importance of d functions in silicon contributes to this and other differences between the energy surfaces of ${\mathrm{C}}_{3}$ and ${\mathrm{Si}}_{3}$. The trends in bond lengths and bond angles are discussed for dimers, trimers, and bulk systems of carbon and silicon. The energy surface for the lowest $^{3}\mathrm{B}_{2}$ state shows a minimum for \ensuremath{\alpha}=60\ifmmode^\circ\else\textdegree\fi{} which is almost degenerate with the $^{1}\mathrm{A}_{1}$ minimum.

Energy surfaces of low-lying states of C3

Density functional calculations have been performed for the energy surfaces of the ground state [1Σ+g(1A1)] and low-lying excited states [3Πu(3B1,3A1), 3Πg(3B2,3A2), 1Πu, 1Πg] of the C3 molecule. The experimental geometries and symmetric stretch frequencies of 1A1 and 1Πu states are reproduced well, and there is good agreement with CI calculations for the triplet states. The energy surface of the ground state is described qualitatively better than by CI calculations and does not show the unusual square-well form found in Hartree–Fock calculations. The splitting of the Born–Oppenheimer surfaces in the Π states (Renner–Teller effect) is discussed, and the qualitative features of the bonding presented in terms of the geometry dependence of the one-electron eigenvalues (Walsh diagrams). Together with earlier results for C2, the calculations provide insight into the unique features of the C–C bond.

Energy surfaces of low-lying states of O3 and SO2

Density functional calculations have been performed for the energy surfaces of the ground states (x 1A1) and low-lying excited states (1 3B1, 1 3B2, 1 1B1, 1 1B2) of O3 and SO2. Vertical excitation energies for the 1 3A2 and 1 1A2 states have also been calculated. The agreement with available experimental information is qualitatively better than for Hartree–Fock calculations and comparable to the predictions of configuration interaction calculations. Plots of the geometry dependence of the one-electron eigenvalues (Walsh diagrams) give insight into the similarities and differences between the bonds in O3 and SO2. Calculations have also been performed for the ground state of SO. Dissociation energies in O2, O3, SO, and SO2 are overestimated by ∼2 eV, a consequence of the local density approximation used for the exchange-correlation energy.

The graphite-to-diamond transformation

An orbital model for a solid state transformation, the graphite-to-diamond high-pressure reaction, is presented. Using solid state Walsh diagrams we relate this transformation to chemical reactions having orbital symmetry constraints. During the transformation the π-delocalization in the graphite planes is gradually lost, leading to buckling and in-plane bond length elongation as inter-plane bonds form. The pacing of the different components of the reaction coordinate is important. We show that the transformation passes through way points of metallic band structure, which may be related to symmetry dictated level crossings in the Walsh diagrams.

Density functional calculations for H2O, NH3, and CO2 using localized muffin-tin orbitals

Density functional calculations of forces and total energies have been performed for the ground states of H2O, NH3, and CO2 using the localized muffin-tin orbital (MTO) basis of Harris and Painter. Exchange-correlation effects are described using the local density (LD) approximation. It is shown that: (i) the localized MTO basis yields results of useful accuracy with a small number of functions; (ii) the LD approximation gives a remarkably accurate equilibrium geometry in each case; and (iii) details of the electronic structure, such as the inversion barrier in NH3, are reproduced with reasonable accuracy. The bonding in all three molecules is discussed in terms of the geometry dependence of the one-electron eigenvalues (Walsh diagrams).

Molecular inversion in the nπ* states: A theoretical investigation of some model systems in a semiempirical molecular orbital framework

AbstractThe considerations of Walsh rules are extended to rationalize the loss of planarity in the 1,3nπ* states of simple carbonyl and thiocarbonyl molecules. The role of Fermi correlation in shaping the differences between conformations in the singlet and the triplet state is emphasized. The role played by the π* orbital is also considered.

The non-planar structure of the triplet methyl cation

In accord with qualitative arguments based on Walsh diagrams, the equilibrium structure of the triplet methyl cation is found to be non-planar by ab initio molecular orbital theory. The inversion barrier is predicted to be 4.9kcal/mol and Δ H 0 f0 to be 346kcal/mol.

Theoretical studies on the geometric and electronic structure of substituted SCN isomers: Part 1. Non-empirical and MNDO results for some thiocyanates

Some well known thiocyanates have been studied by non-empirical and MNDO methods. The reliability of the adopted basis set and the unimportance of d orbitals on sulfur in describing thiocyanates have been tested on the HSCN molecule. The geometrical parameters computed at the STO—3G level are in good agreement with experimental data and indicate that thiocyanates are w shaped molecules with a high bending constant around the sulfur atom and quite important coupling between CSC and SCN angles. The MNDO method gives similar results, except for CS bond lengths, which are systematically underestimated. The correlation between geometry and electronic structure of thiocyanates is discussed, with special reference to cyanates, on the basis of PMO theory, Walsh diagrams and Mulliken population analysis.

Protonation and strong H-bonding as the factors controlling structural changes in excited azaaromatics

The relationship between the structure of a molecule and electron density distribution in excited states of protonated N-heteroaromatics has been discussed, basing on (1) Walsh rules (2) dihydroflavines as model compounds. Two selected examples of inter- and intramolecular proton transfer have been quoted, namely the net charge distribution in 7-azaindole and proton transfer kinetics in 2(2'-hydroxyphenyl) benzoxazole.

An ab initio reinvestigation of the geometric and electronic structure of boron trioxide

In an attempt to resolve the controversy over the structure of the boron trioxide (B 2O 3) molecule an ab initio molecular orbital study employing a minimal STO-3G basis set with complete geometry optimization is reported. Our results indicate that B 2O 3 is a planar “w” shaped molecule with a rather small inversion barrier around the central atom and a quite important coupling between BOB and OBO angles. The computed bond distances are consistent with previous electron diffraction results, whereas the apex angle is in better agreement with the most recent IR study. The results obtained by the MNDO method are in good agreement with the ab initio ones. The electronic structure of B 2O 3 is discussed by means of Walsh diagrams and Mulliken population analysis.

Walsh's Rules and the Small Bond Angle States of Triatomic Dihydride Molecules

AbstractA series of excited electronic states of AH2 molecules having extremely small bond angles has been discovered theoretically. Systems which have shown this characteristic to date include H2O+, NH2, CH2+, and NH2+. In the present research ab initio studies were carried out using a double zeta plus polarization basis set. Configuration interaction including all Hartree‐Fock interacting single and double excitations was performed. For the 2B2 state of CH2+, the predicted equilibrium geometry is θe(HCH) = 35.2°, re(C‐H) = 1.41 A. This state is bound by 20.3 kcal/mole relative to the separated C+ + H2 ground electronic state. The analogous state of BH2 is not substantially bound, but the neutral C + H2 system shows some very interesting features. All of these results may be qualitatively understood in the context of Walsh's rules.

A configuration interaction study of the water molecule and interpretation of the walsh diagram

Large scale ab initio SCF and CI calculations are used to investigate the bond angle dependence of the energy and one-electron properties of the water molecule. The SCF wave functions are used to reinvestigate the Hellmann-Feymann force interpretation of Walsh diagrams. The results are much closer to the ideas of Walsh than those obtained by Coulson and Deb.

ChemInform Abstract: A NEW LOOK AT STRUCTURE AND BONDING IN TRANSITION METAL COMPLEXES

Publisher Summary The construction of models of molecular geometry has been a popular exercise for many years. In the field of main-group stereochemistry the ideas of Sidgwick, Powell, Nyholm, and Gillespie have been successfully fused together into the VSEPR scheme, where the electron pairs around a central atom adopt the minimum energy consistent with their mutual electrostatic repulsion. The VSEPR rules have captured much of the essence of main-group stereochemistry and are unrivalled in their simplicity. In addition, Walsh diagrams quantified by the work of Gimarc and others, and the pseudo Jahn-Teller formalism introduced by Bartell (9) into the structural field and extended by Pearson (10, 11) have provided a molecular orbital interpretation of the wide range of available structural data. By way of contrast, fewer gas-phase structures of transition metal complexes are known: a few d0–d4 hexafluorides (all octahedral), do–d1 tetrachlorides (tetrahedral), and some 18-electron carbonyl and phosphine structures typified by tetrahedral Ni(CO)4 octahedral Cr(CO)6, and trigonal bipyramidal Fe(CO)5.

Geometry predictions for π-bonded molecules using simplified MO theory

A simplified version of Walsh's diagrams is proposed. Using this MO-based scheme, the angular geometry at dicoordinate and tricoordinate atoms in covalent molecules can be predicted, even when π bonding exists in the system. The basic “rule of thumb” developed in that distortion from the geometry of highest symmetry will occur only if the in-plane p orbital at the center of interest contains some antibonding, or appreciable nonbonding, electron density. These predictions are tested for a wide variety of molecules.

Structures and electronic properties of copper clusters and bulk; comments on Mulliken–Walsh diagrams and on criticisms of the extended Hückel procedure

Structures, energy levels, and binding energies of small copper clusters are determined using a two-step theory wherein (1) rigid atoms are superimposed giving rise to readily determined pairwise repulsion energies and (2) attractive energies due to electron delocalization are estimated with a molecular orbital theory derivable, with approximations, from the superimposed rigid atom Fock potentials. Optical spectra determined by Moskovits and Hulse for Ar matrix isolated Cu, Cu2, Cu3, Cu4, and Cu5 are interpreted in terms of molecular orbital energy levels. Matrix frequency shifts are seen to arise from antibonding interactions between Cu 4s and 4p orbitals with Ar matrix 3p orbitals. A fcc Cu13 cluster yields the major features of the Cu(100) surface photoemission spectrum due to Burkstrand et al. but not the lattice and force constants. The force constant is determined using a Poisson equation. It is suggested that small Cu microcrystals have structural and bond length disorder and may experience a phase transformation to fcc at a critical size. Less than bulk bond lengths in microcrystals are due to an absence of bulk coordination. It is suggested that the orbital energies, which are similar to extended Hückel ones, are obviously appropriate to Mulliken–Walsh diagrams and that past criticisms of extended Hückel orbital energy results have been premature.

The shapes of some excited states of acetylene

Parts of the potential surfaces for the ground and excited states (below 11 eV) of acetylene are computed with an ab initio frozen core method. Various planar and non-planar geometrics are investigated. Rydberg states, including the 1 1Σ + u V ππ * state, are found to be linear and to retain their Rydberg character upon bending. Valence ·(1π u) 3(1π * g) states are cis and trans bent if they result chiefly from excitation to the component of the 1π * g MO in the molecular plane. They are further distorted to gauche, non-planer, geometries if they arise from excitation to the out-of-plane component of the 1π * g MO. Walsh diagrams are used to rationalize these trends and the computed results are compared with the available experimental data.

Confirmation of the discrepancy between theory and experiment for the B̃ 1A″ state of HCN

Ab initio calculations have been carried out on the first and second 1A″ states of HCN using relatively large and flexible basis sets. The predicted geometries have been compared with the experimental results of Herzberg and Innes and with earlier calculations on HCN. These calculations concur with earlier theoretical results and the Walsh diagram prediction that Herzberg and Innes' assignment of the B̃ 1A″ state with bond angle 114.5° is incorrect.

The geometry of LiBO 2

Ab initio SCF calculations including different basis sets have been performed for the ground state of the LiBO 2 molecule. It is shown that the bent structure of the LiBO 2 molecule has a lower energy than the linear structure, which is in agreement with Walsh's rules. The calculations without polarization function failed to predict this result.

Vibrational Electronic Coupling and a Close Look at a Severe Case

AbstractElectronic spectroscopy, at once the oldest and most intricate branch of spectroscopy, has seen intense activity over the past decade. The difference between small‐molecule and large‐molecule spectroscopy is pointed out. The emphasis here is on larger polyatomics. Certain developments of note, especially of the interpretation of unresolved rotational fine structure, are mentioned. No point of principle has remained more tantalizing than the issue of the integrity of an electronic state: to what extent are electronic and nuclear motions really separable, in the Born‐Oppenheimer sense? There is much new theory, yet quantitative applications of theory to real cases are few, especially in polyatomic molecules. A straightforward computational approach to vibronic (= vibrational‐electronic) coupling in molecules such as naphthalene has proved to be quantitatively successful. Physical insight is harder to obtain, however, but a fairly straightforward explanation (based on a polyatomic version of Walsh's rules) can be offered for the presence of exceptionally strong vibronic coupling between two excited electronic states of azulene (C10H8). The effects of this coupling are so profound that the electronic spectrum is highly sensitive to such minor influences as partial deuteration or changes of solvent. These effects can be modelled rather successfully.