Molecular orbital calculations on transition metal complexes. Part IX

Potential energy curves for the ground and some low energy excited states of a number of complexes with a 3d ⁵ electronic configuration have been computed from INDO type SCF MO calculations. The results agree extremely well with the known ground states of the complex ions MnF ₆ ^4? , FeF ₆ ^3? , CoF ₆ ^2? , and Fe(CN) ₆ ^3? , in particular the crossover from high to low spin being obtained for changes in both central metal ion oxidation state and ligand. The calculated contraction in metal ligand distance on passing from the high spin to the low spin state is ～ 0.05 Å for each complex in very good agreement with the value indicated by pressure dependent magnetic measurements. Computed electronic transition energies involving bothd-d type and charge-transfer excitations compare favourably with observed spectroscopic values.     

An AB initio SCF MO CI study of the n → π* transition of methylenimine

The electron correlation energies of both the ground and n → π* excited states of methylenimine (CH₂NH) are investigated by means of ab initio SCF MO CI calculations. Then n → π* singlet and triplet state energies of methylenimine are obtained through 3461-dimensional CI including the singly, doubly and triply excited configurations. the excitation energy from the ground state to the ¹(n → π*) state nearly coincides with that obtained in the framework of the singly excited configuration interaction (SECI) procedure. This result suggests that there is good cancellation of the correlation energy between the ground and the excited singlet sates, proving the usefulness of the SECI method for the excitation energies.     

A SCF Xα MO study of the optical and Ti2p core photoemission spectra of TiCl4

SCF Xα MO calculations on the ground state and optical excitation transition states of TiCl₄ accurately predict the energies of its UV absorption peaks. Calculations on the Ti2p core ion state and associated transition states indicate that the recently observed low energy (4.0 eV) Ti2p satellite arises from ligand to metal charge transfer excitations while the satellite at high energy (9.4 eV), similar to those previously observed in Ti(IV) compounds, can be attributed to transitions from the highest filled orbitals to empty orbitals with Cl3pTi4s. 4p antibonding character.     

A multi-configuration LCAO–MO study for complex unsaturated molecules. I. General theory and its application to the benzene anion

A multi-configuration LCAO –MO approach using a π-bond order–bond length linear relation is introduced to predict the geometrical structures for the electronic ground and excited states of unsaturated hydrocarbons. The procedure is designed to include configuration interaction in each iterative computation where the π-electron approximation is employed under the Pariser–Parr type semi-empirical treatment. The π-bond order–bond length relation is determined as r_pq = 1.523 – 0.193P_pq, when the bond lengths of ethylene, benzene and naphthalene are used and the groundstate functions including the singly and doubly excited configurations are taken into account to obtain the bond orders P_pq. The iterative calculation is applied to the ground state and the two lowest excited states of the benzene anion in both D_6h and D_2h molecular geometries. The geometrical structures and the π-electron energies are computed for the ground and excited states of the anion; for the latter, two types of configuration species are used. It is found that the first lowest excited state is not subjected to the Jahn–Teller effect and the calculated excited state energies do not agree with the observed values (c. 1.0 ～ 2.5 eV higher than the observed values). The latter point is discussed in detail. It is also found that the resultant ground state energy depression due to configuration mixing is not very large and the two types of configuration species used give different CI effects on the energy levels of the two lowest excited states of the anion. Finally, the stabilization energy due to the Jahn–Teller distortion is estimated for the ground state of the anion.     

Spiro[4.4]nonatetraene and its Positive and Negative Radical Ions: Molectronic Structure Investigations

The electronic structure of spiro[4.4]nonatetraene 1 as well as that of its radical anion and cation were studied by different spectroscopies. The electron‐energy‐loss spectrum in the gas phase revealed the lowest triplet state at 2.98 eV and a group of three overlapping triplet states in the 4.5 – 5.0 eV range, as well as a number of valence and Rydberg singlet excited states. Electron‐impact excitation functions of pure vibrational and triplet states identified various states of the negative ion, in particular the ground state with an attachment energy of 0.8 eV, an excited state corresponding to a temporary electron attachment to the 2b₁ MO at an attachment energy of 2.7 eV, and a core excited state at 4.0 eV. Electronic‐absorption spectroscopy in cryogenic matrices revealed several states of the positive ion, in particular a richly structured first band at 1.27 eV, and the first electronic transition of the radical anion. Vibrations of the ground state of the cation were probed by IR spectroscopy in a cryogenic matrix. The results are discussed on the basis of density‐functional and CASSCF/CASPT2 quantum‐chemical calculations. In their various forms, the calculations successfully rationalized the triplet and the singlet (valence and Rydberg) excitation energies of the neutral molecule, the excitation energies of the radical cation, its IR spectrum, the vibrations excited in the first electronic absorption band, and the energies of the ground and the first excited states of the anion. The difference of the anion excitation energies in the gas and condensed phases was rationalized by a calculation of the Jahn‐Teller distortion of the anion ground state. Contrary to expectations based on a single‐configuration model for the electronic states of 1 , it is found that the gap between the first two excited states is different in the singlet and the triplet manifold. This finding can be traced to the different importance of configuration interaction in the two multiplicity manifolds.     

Theoretical study on the vertical electronic spectrum of carbonyl fluoride,F2CO

Ab initio self-consistent-field (SCF ) and configuration interaction (CI ) calculations on the ground and excited states of carbonyl fluoride (F₂CO) were carried out at its experimental ground-state equilibrium geometry. Vertical transition energies deduced from the CI results provide assignments for the electronic systems I–IV, experimentally observed by Workman and Duncan. The singlet excited state, ¹A₁ (π→π*), is found to be a mixed valence–Rydberg state and to he 1 to 1.2 eV above the suggested experimental value, irrespective of the choice of the basis used for the CI calculations.     

A multi-configuration LCAO–MO study for complex unsaturated molecules. II. Application to the benzene cation

The method of the MC –LCAO –MO approach, described in the preceding paper, is further applied to the benzene cation. Through the iteration process the π-electron energies and the molecular shapes are computed for the ground and two lowest excited states of the cation in both D_6h and D_2h geometries. A remarkable fact obtained is that a comparatively small variation of the geometrical structure (c. 0.010 – 0.013 Å bond length difference) brings about a considerable change of the energy value (c. 0.85 – 1.25 eV). The π-electronic excitation energies obtained from the iteration process are compared with the transition energies calculated from the usual method in which the structures of the excited states are assumed to be the same as the corresponding ground state structures. The difference in the excitation energy between the cation and the anion, and the CI effect on the excited states, are discussed. It is found that the doubly excited configurations play an important role in CI , which is somewhat different from that of the singly excited configurations. The stabilization energy due to the Jahn–Teller distortion is estimated for the ground state of the cation.     

The basis set dependence of structures and energies of various states of cyclodisiloxane

Several common basis sets, ranging from minimal to double-zeta, are applied to study the neutral singlet and triplet as well as positive- and negative-ion doublet states of cyclodisiloxane. The effect of d-polarization function exponents on the equilibrium geometries and energies is analyzed. The d-type functions seem to be essential in the basis set of silicon, whereas their presence on oxygen is less critical. The optimum exponents (with respect to SCF energy) are determined to be 0.45 for Si and 0.60 for O, very close to those recommended for the 6–31G^** basis set. The best structural predictions are obtained with the 6–31G(2d, p) basis set, which contains two sets of d functions on the heavy atoms. The predicted Si? O bond length is 166 pm; the Si? Si and O? O distances are 237 and 232 pm, respectively, which correspond to an O—Si? O angle of 88.6°. The ground state is found to be a singlet. All higher states have longer Si? O bonds and Si—Si distances, whereas O—O distances are shorter. The energy separation between the singlet and other states is modified by electron correlation (MP treatment) by only a few kcal/mol.     

Theoretical study of the electronic spectrum of diimide by AB initio methods

A series of ab initio calculations is reported for the ground and low-lying valence and Rydberg states of diimide N₂H₂. Symmetric bending potential curves for both the cis and trans forms of this system have been obtained at the SCF level of treatment. In addition Cl calculations have been carried out for the trans-diimide ground state equilibrium nuclear conformation, using a configuration selection procedure described elsewhere; an associated energy extrapolation scheme is also employed which enables the effective solution of secular equations with orders of up to 40000. The ensuing Cl wavefunctions are interpreted in the discussion and the corresponding calculated energy differences between the various electronic states are compared with experimental transition energy results for both diimide and for related systems such as trans-azomethane. A more detailed analysis of the observed absorption bands in the ¹B_g-X¹A_g transition in N₂H₂ is also given, making use of calculated potential curve data as well as the pertinent Cl vertical energy difference. The dipole-forbiddenness of the excitation process is thereupon concluded to result in a distinct non-verticality for this electronic band system, causing its absorption maximum to occur at a position some 0.6 eV to the blue of the so-called vertical transition, i.e., that for which maximum vibrational overlap is obtained.     

Absorption spectrum of manganian andalusite: Cluster calculation by an ab initio method

The ground state and the first few excited states of an MnO₆^9? cluster are calculated in the unrestricted Hartree–Fock model. The state ordering is ⁵B_{1 g}, ⁵A_{1 g}, ⁵B_{2 g}, and ⁵E_g as can be expected from simpler models. Consistent with the results by the same method for copper complexes, we obtain d–d transition energies about one half or less of the experimental energies. The charge transfer spectrum is subject to a large spin polarization in the sense that the lowest charge transfer state (⁵E_u) has five unpaired spins on Mn.     

Density functional calculations of optical excitation energies by a transition-state method

Optical excitation energies of MnO⁻₄, CrO²⁻₄, and RuO₄ are calculated using the density functional methodology. A short outline of some important developments in this theory for the determination of excited-state properties is given. A practical working procedure for the calculation of transition energies including multiplet splitting is described. This method is based on a transition-state approach which is connected, as will be shown, to Slater's transition-state concept. Results obtained by this working procedure are compared to the energy differences between separately converged configurations of ground and excited states and the corresponding multiplet structure, denoted as the ΔSCF calculation in the following. © 1997 John Wiley & Sons, Inc.     

Structure and spectra of the molecules of manganese, iron, and cobalt trifluorides: A CCSD(T) study in the complete basis set

The coupled-cluster singles and doubles with perturbative triples (CCSD(T)) method in triple-, quadruple-, and quintuple-zeta basis sets with extrapolation to the complete basis set limit is used to analyze the properties of MnF₃, FeF₃, and CoF₃ molecules. The relative energies of low-lying electronic states are determined. The Jahn-Teller effect is investigated in the ground electronic state ⁵ E?? of the MnF₃ molecule and the first excited electronic state ⁵ E?? of the CoF₃ molecule. Geometric parameters, atomization enthalpies, vibrational frequencies, intensities in the infrared and Raman spectra are found with high accuracy. The assignment of the bands observed in the low-frequency region of the IR and Raman spectra of MnF₃ and CoF₃ molecules are revised.     

Applications of the model potential method to transition metal compounds

Model potential parameters and basis sets, presented previously for the transition metal atoms Sc through Hg, are tested in calculations of the transition metal compounds (CuF, CuCl, Cu₂, TiCl₄, ZrCl₄, CoF₆^3?, CoF₆^2?, AgH, AuH, CrF₆, ScO, ZrO, Cr₂, Mo₂). Calculated values of the bond distances, vibrational frequencies, and some transition energies (for Cu₂ and CoF₆^2?) are compared with those given by all-electron calculations with basis sets of high quality. Singlet-triplet splittings in Cu₂ and correlation energies in CrF₆^n? (n = 0, 1, and 2) are also examined. The satisfactory results obtained by these calculations strongly support the contention that the model potential method is a reliable and economical alternative to the ab initio Hartree-Fock-Roothaan method.     

Ab initio quantum chemical calculation of the electronic structure of the chelate complex Ni(S2C2H2)2

The electronic structures and equilibrium geometries of the square-planar Ni(S₂C₂H₂)₂ complex and its dianion are calculated at the MP2 level of theory by the ab initio SCF MO LCAO method in the split-valence Gaussian basis set. The calculated two-electron affinity is 57 kJ/mole. In the ground state, the complex has a d⁸ configuration of Ni(II). The square-pyramidal structure of the complex is also considered. The transformation of the complex structure from square-planar to square-pyramidal involves the two-electron d-d transition. Based on the calculated electronic structure of the complex and on the experimental data on its stable dimers, we assumed an unusual valent state of nickel, Ni(IV), in the complex with the d⁶ electronic configuration. Institute of Catalysis, Siberian Branch, Russian Academy of Sciences. Translated fromZhurnal Strukturnoi Khimii, Vol. 37, No. 2, pp. 231–236, March–April, 1996. Translated by I. Izvekova     

Electronic structure and the hydrogen-shift isomerization of hydrogen nitryl HNO2

Summary Electronic structure of hydrogen nitryl HNO₂, a yet not identified entity, and the path of its possible isomerization totrans-HONO have been investigated byab initio SCF and MRD-CI computations using the 6-31G** basis set. HNO₂ isC _2v -symmetric and its ground state (¹ A ₁) is less stable thantrans-HONO by 66 kJ/mol (with the SCF vibrational zero-point energy correction). The lowest two excited singlet states (¹ A ₂ and¹ B ₁) are nearly degenerate, their vertical excitation energies being predicted to be 4.8 eV. The isomerization path is traced by the CASSCF procedure and the activation barrier height is evaluated by the CI treatment. HNO₂ in its ground state isomerizes totrans-HONO by maintaining the planar (C _s-symmetric) structure. The activation energy is calculated to be 171 kJ/mol, which is clearly lower than the calculated H-N bond energy (253 kJ/mol). The transition state seems to be more adequately described as an interacting system of proton and the nitrite anion rather than as a pair of two fragment radicals.     

Electronic structure of small copper clusters

An all-electron ab initio LCAO -MO SCF calculation has been carried out for the electronic structure of small copper clusters (Cu_n, n = 2–6). The basis set superposition error occurring in the calculation, the equilibrium configuration of Cu₃, the bond energy in the clusters, and the localized d-hole in excited and ionized states of Cu₂ are closely examined.     

Theoretical studies on structures and electronic spectra of linear carbon chains C2nH+ (n = 1−5)

The density functional theory (DFT) and the complete active space self‐consistent‐field (CASSCF) method have been used for full geometry optimization of carbon chains C_2nH⁺ (n = 1–5) in their ground states and selected excited states, respectively. Calculations show that C_2nH⁺ (n = 1–5) have stable linear structures with the ground state of X³Π for C₂H⁺ or X³Σ^? for other species. The excited‐state properties of C_2nH⁺ have been investigated by the multiconfigurational second‐order perturbation theory (CASPT2), and predicted vertical excitation energies show good agreement with the available experimental values. On the basis of our calculations, the unsolved observed bands in previous experiments have been interpreted. CASSCF/CASPT2 calculations also have been used to explore the vertical emission energy of selected low‐lying states in C_2nH⁺ (n = 1–5). Present results indicate that the predicted vertical excitation and emission energies of C_2nH⁺ have similar size dependences, and they gradually decrease as the chain size increases. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Theoretical study of degree of covalency in some CoF6(n-) complexes (n = 4, 3, and 2)

On the basis of a high-quality LCAO MO SCF calculation, covalency versus ionicity of a Co–F bond in the CoF₆(n-) complexes, where n = 4, 3, and 2, is discussed. The overlap and gross atomic populations, delocalization of certain MOS, and the charge densities in the bond region as well as around F's all indicate that the covalency increases as n decreases or the valency of Co increases in these complexes.     

SCF?CI and SCF open-shell studies of the base components of the nucleic acids

The π-electron structure of adenine, guanine, cytosine, thymine and uracil in their ground, ionized, singlet and triplet excited states are investigated by means of the SCF ? CI and SCF open-shell methods. The calculations for singlets fit the maxima of the absorption bands well. The energy difference between the first and the second singlet states of adenine is found to be very small. The open-shell method leads to the same relative ionization potential as does the SCF (with the integrals empirically corrected). The calculated energies of the triplet states almost coincide in the SCF open-shell and the SCF ? CI approximation. The calculated transition energies to the first triplet state of the pyrimidines are higher than in the case of the purines. The value of the singlet–triplet separation energy of purines is in agreement with experimental data.     

Wellenmechanische Absolutrechnungen an Molekülen und Atomsystemen mit der SCF?MO?LC(LCGO) Methode. IX. Das System (Li2H)−

The system (Li₂H)^? has been investigated ab initio for several nuclear positions, taking all eight electrons into account, using the Allgemeines Programmsystem/SCF ? MO ? LC (LCGO ) Verfahren. A stable molecule was found for the linear symmetric configuration with a bond distance of R_LiH = 3.41 a.u., and a total energy of ?15.3874 a.u., which is about 0.0114 a.u. (0.311 eV, 7.61 kcal/mole) lower than the sum of the comparable SCF energies of the systems LiH and Li^?. The force constant of the symmetric vibration was estimated to be k = 1.64722 × 10⁶ dyn/cm and the frequency to be ω = 1998.9 cm^?1. The results are discussed.