On the geometrical structure and UV spectrum of the truncated icosahedral C60, molecule

The PPP CI molecular-orbital theory for three-dimensional systems has been applied to study the UV spectrum of the truncated icosahedral C₆₀ molecule. We have found that only the one-electron transitions to T_1u symmetry (4.2270,4.7498 and 6.5182 eV) have oscillator strengths different from zero. Using a bond-order-bond-length relation in SCF iteration connected to the PPP method, we have obtained two kinds of bond lengths r₁ = 1.439 Å and r₂ = 1.398 Å, which correspond to the edges of the regular pentagon and the edge of a hexagon not lying on a pentagon.     

The electronic states of icosahedral molecules

After a brief discussion of progress in the theory of icosahedral molecules, the terms arising from simple electronic configurations are deduced from tables of symmetrized powers of representations previously published by the author.     

Pauling's criterion of bond strength and the relative bond lengths in molecule MLk

In this paper, the bond strengths, defined by Pauling, for a series of molecules in the type of ML_k have been calculated by using the generalized method obtained from the maximum overlap method in a preceding paper and by using Pauling's pair–defect–sum approximation. A number of geometrical bonding situations are investigated. It is demonstrated why a previous study purporting to use of Pauling's criterion of bond strength to find that the axial bonds in trigonal bipyramidal ML₅ are stronger than the equatorial bonds is incorrect. The results obtained from the two methods approach each other and are in good agreement with the experimental bond lengths, which show that Pauling's criterion is viable and that the pair–defect–sum approximation is indeed an excellent one that agrees with the maximum overlap method.     

Expanded electronic states of the fluorine molecule

Potential curves of electronically excited states of F₂ with an expanded outer orbital have been calculated using a modified frozen core technique: The ionic core has been described with a two-determinant wave function and for the excited states a mixing of configurations with different cores has been employed. An investigation of the valence shell states of F₂ is presented and potential curves for a singly excited as well as a doubly excited V-state of ¹Σ_u⁺ symmetry have been calculated. Further a low lying two-configuration state resulting from simultaneous excitation to a valence and a Rydberg orbital is predicted.     

Two icosahedral structures for the C60 cluster

Two icosahedral structures, a truncated icosahedron and a truncated dodecahedron, have been examined for the C₆₀ cluster. Optimized geometries by INDO calculations are: in the former, 1.449 Å (for pentagonal edges) and 1.397 Å; in the latter, 1.41 Å (for triangular edges) and 1.345 Å. At these geometries, HOMO-LUMO gaps are 9.23 and 8.86 eV, respectively.     

On the lowest electronic states of the C2F radical

The adiabatic energy surfaces of the lowest three electronic states [²(²A′ and ²A′)] and ²Σ⁺[²A′] of the C₂F radical were investigated by the Hartree-Fock multiconfiguration self-consistent field (HF—MCSCF) ab initio method using a large set of atomic natural orbitals (ANO) and an extended configuration space, and the results were shown to be in agreement with the predictions of valence theory for this radical. The electronic ground state was found to have a bent equilibrium structure, hence contradicting the Walsh rule which predicts for the isoelectronic molecules a ² linear state. The three states were found to be nearly degenerate and the potential energy surfaces of the two lowest electronic states exhibit an avoided crossing at an energy ∼2000 cm⁻¹ above the ground-state minimum, lower than the highest vibrational fundamental. The strong adiabatic interaction which is responsible for the ordering of the electronic states and their equilibrium geometry involves not only the bending coordinate as normally found for Renner-Teller pairs of states, but also the C—C stretching coordinate, due to the near degeneracy of the ²Σ⁺ and the ² lowest electronic states at linear geometries. © 1996 John Wiley & Sons, Inc.     

Influence of bond lengths between substituents and mother molecule on spectral properties of pyrazoloquinolines

Absorption and luminescent spectra of several new synthesized pyrazolo-quinoline possessing different substituents are studied. Absorption spectra of all the considered compounds possess five relatively strong absorption bands at about 430, 320, 270, 253 and about 230 nm. A correlation between the bond lengths between the substituent molecule and mother molecule with the observed spectral shifts was found. Theoretical spectra obtained within semi-empirical quantum chemical AM1 calculation methods seem to be more widened compared to the experimental ones due to electron-vibration interactions. However generally a good coincidence between spectral positions between experimental and calculated spectral peak positions was achieved. The corresponding experimental spectra have an absorption edges situated at about 430 nm which appears in fairly good agreement with quantum chemical simulations, namely for absorption spectra calculated by semi-empirical AM1-method. The red shifts in the experimental luminescence spectra are a consequence of electron-vibration interactions which increase with the effective radius and polarizabilities of the particular substituents.     

Theoretical electronic structure of the lowest-lying states of the YI molecule

CAS-SCF/MRCI calculations have been performed for 15 molecular states in the representation ^2S+1Λ^(+/−) (neglecting spin–orbit effects) for the molecule YI. The corresponding 33 molecular states in the representation Ω^(+/−) (including spin–orbit effects) have been calculated using a semi-empirical spin–orbit pseudopotential built up for yttrium. Calculated potential energy curves and spectroscopic constants are reported, to the best of our knowledge they are the first ones from ab initio methods for this molecule. Present results are compared to experimental accurate data available for the ground X¹Σ⁺ and 3 excited states (1)¹Π, (2)¹Σ⁺ and (2)¹Π.     

Theoretical investigation on icosahedral C60(FeCp)12: A hybrid of C60 and ferrocene

A perfect hybrid complex C₆₀(FeCp)₁₂ is predicted using density functional theory method_. This fullerene derivative could be view as a C₆₀ cage of which each C₅ ring coordinates a (FeCp) ligand. Theoretical calculation reveals that it has a large lowest unoccupied molecular orbital–highest unoccupied molecular orbital gap (2.53 eV) and keeps the I_h symmetry of C₆₀. But the C? C bond length of its inner C₆₀ cage trends to be uniform, which is quite different from the bonding character of C₆₀ fullerene. Further investigation reveals that the chemical bonding, TDOS and the aromaticity of the (C₅FeCp) unit in C₆₀(FeCp)₁₂ are similar as those of ferrocene molecule, which indicates the similarity of their electronic properties. So, this compound could be viewed as the combination of ferrocene molecules. Thus, its unconventional formation process from 12 Fe(Cp)₂ is proposed and the reaction energy is calculated. As the C₆₀(FeCp)₁₂ compound has the geometry framework as C₆₀ and the electronic characters as ferrocene, it would inherit the outstanding properties from both two molecules and have wild potential applications in nanochemistry. We hope our study could give some references for the further investigation and experimental synthesis research of the C₆₀(FeCp)₁₂ compound. © 2015 Wiley Periodicals, Inc.     

Theoretical calculation of the low-lying sextet electronic states of CrF molecule

The potential energy curves have been investigated for the 12 lowest sextet electronic states in the ^2s+1Λ^(±)${}^{2s+1}{\mathrm{\Lambda }}^{(\pm )}$ representation below 53,000 cm⁻¹ of the molecule CrF via CASSCF and MRCI (single and double excitation with Davidson correction) calculations. Seven electronic states have been studied theoretically for the first time. The harmonic frequency ω_e, the internuclear distance R_e, the rotational constant B_e, the electronic energy with respect to the ground state T_e, and the permanent dipole moment μ have been calculated. By using the canonical functions approach, the eigenvalues E_v, the rotational constant B_v and the abscissas of the turning points R_min and R_max have been calculated for the considered electronic states up to the vibrational level v = 39. The comparison of these values to the theoretical and experimental results available in the literature shows a good agreement.     

Theoretical reinvestigation of opposite electronic effects on bond lengths in thiophenols and thiophenolic radicals

Our previous study has revealed that para-substituents have opposite electronic effects on the C-S bond lengths of thiophenols and thiophenolic radicals. Although a theoretical elucidation has been given, it has not been supported by theoretically calculated atomic charges. To give an alternative explanation, we calculated the C-S bond lengths, C-S bond electron densities, and Mulliken charges on the carbon and sulfur atoms for thiophenols, thiophenolic radicals, and thiophenolic radical cations by means of the B3LYP density functional theory method using the 6-31G(d, p) basis set. It was revealed that the C-S bond length is adequately defined in terms of C-S bond electron density. The distinct electronic effects on the C-S bond lengths of thiophenols, thiophenolic radicals and thiophenolic radical cations are well elucidated by the different electronic states (electron-deficient or-rich) of the phenyl ring and SH group.     

酞菁铜分子的电子态和反饱和吸收

用ROHF-INDO/SDCI方法结合实验研究了酞菁铜分子的电子的电子结构.紫外-可见光谱.激发态分子动态学和反饱和吸收的微观机制.对酞菁铜实现反饱和吸收的必要条件是最低四重态对激光的吸收截面必须大于基态对激光的吸收截面. 在波长为532nm的激光作用下.该条件得到了满足,故Cupc呈现反饱和吸收特征.理论分析与实验结果一致.     

On the low-lying electronic states of BiF

Relativistic CI calculations on the low-lying states of BiF(0⁺, 1, 2, 0⁺(II)) arising from the σ²π² configuration are carried out. Comparison calculations of the λ-s states without spin-orbit interaction (³Σ⁻, ¹Σ⁺ and ¹Δ) are also presented. These calculations enable the assignment of three experimentally observed low-lying states. In addition, the properties of a new state (2) are calculated (yet to be observed). The calculated dissociation energy of the ground state is 2.63 eV. The potential energy surfaces of the low-lying electronic states of BiF reveal interesting avoided crossings. Our calculations clarify the earlier assignment of the electronic transitions of BiF.     

Excited electronic states of a hydrogen bond: Bifluoride ion

We report here a summary of a limited CI calculation carried out on the C_∞v and D_∞h electronically excited states of bifluoride ion. This species is interesting as the prototype of a hydrogen-bonded system. It is determined that the lowest-lying excited states of the system are dissociative and/or autoionizing.     

Ab initio study of low-lying electronic states of the FNO2 molecule

Ab initio electronic structure calculations are reported for low-lying electronic states, ¹A₁, ¹A₂, ³A₂, ¹B₁, ³B₁, ¹B₂, and ³B₂ of the FNO₂ molecule. Geometric parameters for the ground state ¹A₁ are predicted by MRSDCI calculations with a double-zeta plus polarization basis set. The vertical excitation energies for these electronic states are determined using MRSDCI/DZ+P calculations at the ground-state equilibrium conformation. The oscillator strengths and radiative lifetimes for some electronic states are calculated based on the MRSDCI wave functions. © 1993 John Wiley & Sons, Inc.     

Calculation of low-lying electronic states of the MgN molecule in the effective-core-potential approximation

Plots of the potential energy and the dipole moment of four low-lying electronic states of the MgN molecule have been calculated by the self-consistent-field and configuration-interaction methods in the effective-core-potential approximation. The ground state of the molecule is not bound and has^4– symmetry. The lowest bound states,² and^2–, are practically degenerate; the values of the equilibrium internuclear distances (1.91 and 1.98 Å) and the vibrational constants (637 and 519 cm^–1, respectively) have been found for them. The vertical energy of the transition from these states to the ground state amounts to about 0.5 eV.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 21, No. 2, pp. 217–220, March–April, 1985.     

All electron ab initio investigations of the electronic states of the MoN molecule

The low lying electronic states of the molecule MoN were investigated by performing all electron ab initio multi-configuration self-consistent-field (CASSCF) calculations. The relativistic corrections for the one electron Darwin contact term and the relativistic mass-velocity correction were determined in perturbation calculations. The electronic ground state is confirmed as being ⁴∑⁻. The chemical bond of MoN has a triple bond character because of the approximately fully occupied delocalized bonding π and σ orbitals. The spectroscopic constants for the ground state and ten excited states were derived. The excited doublet states ²∑⁻, ²Γ, ²Δ, and ²∑⁺ are found to be lower lying than the ⁴Π state that was investigated experimentally. Elaborate multi-configuration configuration-interaction (MRCI) calculations were carried out for the states ⁴∑⁻ and ⁴∏ using various basis sets. The spectroscopic constants for the ⁴∑⁻ ground state were determined as r_e=1.636 Å and ω_e=1109 cm⁻¹, and for the ⁴∏ state as r_e=1.662 Å and ω_e=941 cm⁻¹. The values for the ground state are in excellent agreement with available experimental data. The MoN molecule is polar with a charge transfer from Mo to N. The dipole moment was determined as 2.11 D in the ⁴∑⁻ state and as 4.60 D in the ⁴∏ state. These values agree well with the revised experimental values determined from molecular Stark spectroscopic measurements. The dissociation energy, D_e, is determined as 5.17 eV, and D₀ as 5.10 eV.