Thermodynamic functions for vibronic systems

A method is introduced which simplifies the derivation of equations for the calculation of statistical sums for vibronic systems. Within the “independent ordering approximation” analytical expressions are found for thermodynamic functions for molecules with degenerate electronic ground state (E?β and E ? e types of degeneracies). Vibronic interactions are shown to yield an additional thermodynamic stabilization. The computations were carried out for VCl₄ and VBr₄ with doubly degenerate electronic ground states. For these molecules the effect is shown to be small.     

Effect of the orientation of coordinated water molecules on the electronic structure of trans halo-aquo complexes: application to TiCl2(H2O) 4 + and VCl2(H2O) 4 +

The X method has been utilized to calculate the electronic structure of trans-TiCl₂(H₂O) ₄ ⁺ and trans VCl₂(H₂O) ₄ ⁺ ions. Different conformations of coordinated water molecules have been considered. It has been found that the most stable configuration in both cases is the one with the plane of the water molecules parallel to the Cl-metal-Cl axis. The nature of the tetragonally distorted ground state has been found to depend on the orientation of the water molecules in these systems.     

Time‐dependent density functional calculations on the electronic spectra of the neutral nickel complex [Ni(LISQ)2] (LISQ = 3,5‐di‐tert‐butyl‐o‐diiminobenzosemiquinonate(1−)) and its monoanion and dication

The electronic spectrum of the neutral nickel complex [Ni(L^ISQ)₂] (L^ISQ = 3,5‐di‐tert‐butyl‐o‐diiminobenzosemiquinonate(1^?)) and the spectra of its anion and dication have been calculated by means of time‐dependent density functional theory. The electronic ground state of the neutral complex exhibits an open shell singlet diradical character. The mandatory multireference problem for this electronic ground state has been treated approximately by using the unrestricted and spin symmetry broken Kohn‐Sham Slater determinant as the wave function for the noninteracting reference system in the time‐dependent density functional calculations. A reasonable agreement with observed transition energies and band intensities has been achieved. This holds also for the long wavelength transitions that are shown to be of charge transfer type. The charge distributions in the electronic ground state and the corresponding low lying excited states, however, are rather similar. Thus, the known failure of standard time‐dependent density functional theory to describe improperly long range charge transfer transitions is absent in this work. The applied computational scheme might be adequate for calculating electronic spectra of transition metal complexes with noninnocent ligands. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

Semiempirical INDO/S calculations on the absorption spectrum of mono‐ and trinuclear vanadium(II) complexes

This work is concerned with prospective starting materials for the synthesis of larger molecules used as functional models of the substrate binding and reducing site of the vanadium nitrogenase. It is well known that the mononuclear adduct of vanadium(II) chloride with N,N,N′,N′‐tetramethylethylenediamine, henceforth referred to as [VCl₂(tmeda)₂], is a good starting material for the synthesis of trinuclear vanadium complexes. We now report the results of semiempirical calculations on the spectroscopy of [VCl₂(tmeda)₂] using the intermediate neglect of differential overlap (INDO) method. For the mononuclear complex, the ground state was calculated to be a quartet, about 45 kcal/mol below the doublet. For the positively charged trinuclear vanadium complex, [V₃(μ‐Cl)₃(μ₃‐Cl)₂(tmeda)₃]⁺, the ground state was calculated to be a decatet, about 47 kcal/mol below the octet. For both complexes the frontier orbitals are dominated by the vanadium 3d manifold, and accordingly the electronic spectra are dominated by d‐d* excitations within this manifold. The INDO/S‐calculated spectra are in good agreement with the observed UV‐visible spectra in both cases. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem 88: 245–251, 2002     

Plasma diagnostics of barrier-torch discharge in argon flow in a capillary by cross-correlation spectroscopy

The radiation kinetics of the plasma of barrier-torch disrcharge in argon flow in a capillary has been studied by cross-correlation spectroscopy. It was established that the discharge emission spectrum consists of peaks of electronically excited states of argon, bands of hydroxyl radicals, and a second positive system of nitrogen. An analysis of the spatio-temporal distributions of emission intensity for the selected spectral indicators showed that the causes of the torch are ionization waves that extend through the capillary from the electrode system with a speed of 10⁵ m/s and project up to 3–4 mm. It was established that the formation of electronically excited molecules of nitrogen N₂(C ³Π _u ) in the torch of discharge occurs mainly on the reaction between metastable electronically excited atoms of argon and molecules of nitrogen in the electronic ground state.     

Ir absorption spectrum of CrO2Cl2 molecules for high-lying states of the vibrational quasi-continuum

A new approach to the spectroscopy of highly excited vibrational states of polyatomic molecules has been elaborated. The molecules of CrO₂Cl₂ were prepared in states with a vibrational energy of the ground electronic term A₁ of ≈ 19000 cm⁻¹ by means of internal conversion of electronic energy from the electronic state B₁ excited by laser radiation. The spectroscopy of the vibrationally excited molecules has been carried out in the region of the ν₆ and ν₁ bands with diode and CO₂ lasers. The fwhm of the obtained spectrum was ≈ 15 cm⁻¹. The intermode interaction in CrO₂Cl₂ has been theoretically analyzed, and the calculated spectrum compared with that measured experimentally. The time evolution of the spectrum of vibrationally excited CrO₂Cl₂ molecules has been studied. The average energy transferred per one collision with unexcited CrO₂Cl₂ molecules was equal to 〈δE〉 ≈ 1200 cm⁻¹.     

Bromokomplexe von Mn(II) und V(III) in Acetonitril,Propandiol-1,2-carbonat und Trimethylphosphat

Zusammenfassung Die Bromokomplexe von Mn(II) und V(III) inAN, PDC undTMP wurden auf spektrophotometrischem, potentiometrischem und konduktometrischem Wege untersucht. Folgende Koordinationsformen dürften vorliegen: [MnBr]⁺ (inAN), MnBr₂ (tetraedrisch inAN), [MnBr₃]^– (tetraedrisch inAN), [MnBr₄]^2– (tetraedrisch inAN undPDC); [VBr]²⁺ (oktaedrisch inTMP), [VBr₂]⁺ (oktaedrisch inAN), VBr₃ (oktaedrisch inAN), [VBr₄]^– (oktaedrisch inAN undPDC).

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Bromocomplexes of Mn(II) and V(III) were investigated inAN, PDC andTMP by spectrophotometric, potentiometric and conductometric methods. The presence of the following species is indicated: [MnBr]⁺ (inAN), MnBr₂ (tetrahedral inAN), MnBr₃]^– (tetrahedral inAN), [MnBr₄]^2– (tetrahedral inAN) andPDC); [VBr]²⁺ (octahedral inTMP), [VBr₂]⁺ (octahedral inAN), VBr₃ (octahedral inAN), [VBr₄]^– (octahedral inAN andPDC).

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Mit 5 Abbildungen     

tBuN = VCl2 · 1,2-Dimethoxoethan,eine Schlüsselverbindung zur Darstellung von zweikernigen,diamagnetischen tert-Butylimidovanadium(IV)-Verbindungen

^tBuN = VCl₂ · 1,2-Dimethoxoethane, a Precursor in the Synthesis of Binuclear Diamagnetic tert -Butylimidovanadium(IV) Compounds Syntheses of the paramagnetic tert-butylimidovanadium(IV) complexes ^tBuN = VCl₂ · DME ( 7 ), ^tBuN = VCl₂ · 2 L (L = 1,4-dioxane, thf, PMe₃, PEt₃, pyridine) and ^tBuN = VBr₂ · DME are described; the free Lewis acids has been found by mass spectroscopy to be the binuclear compounds [(μ-N^tBu)₂V₂Cl₄] und [(μ-N^tBu)₂V₂Br₄]. 7 reacts with LiOR, LiOAr and LiNR₂ forming binuclear diamagnetic tert-butylimidovanadium(IV) compounds: [(μ-N^tBu)₂V₂Cl₂(OⁱPr)₂] ( 18 ), [(μ-N^tBu)₂V₂(OR)₄], [(μ-N^tBu)₂V₂Cl₂(OAr)₂], [(μ-N^tBu)₂V₂(OAr)₄] and [(μ-N^tBu)₂V₂Cl₂(NR₂)₂]. In additional experiments the complexes [(μ-N^tBu)₂V₂(CH₂CMe₃)₂(OAr)₂], [(μ-N^tBu)₂V₂Me₂(NR₂)₂], [(μ-N^tBu)₂V₂Cl₄] and ^tBuN = V(OAr)₃ has been prepared. All compounds obtained are characterized by spectroscopic methods (MS; ¹H, ¹³C, ⁵¹V NMR), [(μ-N^tBu)₂V₂Cl₂(N^tBuSiMe₃)₂] ( 21 ) by single crystal x-ray diffraction. For 18 the presence of cis/trans isomeres was shown by NMR spectroscopy. The ⁵¹V NMR spectra of the binuclear diamagnetic vanadium (IV) compounds are discussed.     

Intrakonfigurations‐, Trip‐Multiplett‐ sowie anomal polarisierte A1gund A2g‐Übergänge in elektronischen und vibratorischen Resonanz‐Raman‐Spektren von (spinentarteten) trans‐Di(cyano)phthalocyaninatorhenaten

Intraconfigurational, Trip‐Multiplet, and Anomalously Polarised A_1g and A_2g Transitions in Electronic and Vibrational Resonance Raman Spectra of (Spin‐Degenerate) trans ‐Di(cyano)phthalocyaninatorhenates Brown bis(tetra(n‐butyl)ammonium) trans‐di(cyano)phthalocyaninato(2‐)rhenate(II) ( 1 ) is prepared by melting bis(phthalocyaninato(2‐)rhenium(II)) with tetra(n‐butyl)ammonium cyanide. According to electrochemical data, 1 is oxidised by iodine to yield blue tetra(n‐butyl)ammonium trans‐di(cyano)phthalocyaninato(2‐)rhenate(III) ( 2 ), whose cation exchange in the presence of bis(triphenylphosphine)iminium salts has been confirmed by x‐ray structure determination. 1 and 2 dissolve without dissociation of the cyano ligands in conc. sulfuric acid. Dilution with cold water precipitates blue trans‐di(cyano)phthalocyaninato(2‐)rhenium(III) acid. 1 and 2 are oxidised by bromine yielding violet trans‐di(cyano)phthalocyaninato(1‐)rhenium(III). Oxidation of 2 with dibenzoylperoxide and N‐chlorsuccinimide is described. 1 and 2 are characterised by polarised resonance Raman(RR) spectra, FIR/MIR spectra, and UV‐Vis‐NIR spectra. Due to a Kramers degenerate ground electronic state of low‐spin Re^II, a polarisation anomaly of the totally symmetric vibrations a_1g at 598 and 672 cm^–1 with depolarisation ratios ρ_l > 3 is observed in the RR spectra of 1 . Weak bands in the unusual UV‐Vis‐NIR spectrum of 1 , starting at 10200 cm^–1, are attributed to trip‐multiplet (TM) transitions. An electronic RR effect is detected for 2 . The selectively enhanced anomalously polarised line at 1009 cm^–1 with ρ_l ≈ 15 and the (de)polarised lines between 1688 and 2229 cm^–1 are attributed to intraconfigurational transitions A_1g → A_2g > A_1g, B_1g, B_2g, E_g arising from the ³T_1g ground electronic state of low‐spin Re^III split by spin‐orbit coupling and low symmetry (D ). Some of their vibronic bands are detected in the IR spectrum between 1900 and 4000 cm^–1. B and Q transitions of 2 at 16700 and 31900 cm^–1, respectively, as well as eight weak TM transitions are observed between 5050 and 26100 cm^–1.     

An SCF-MS-Xα study of the bonding and nuclear quadrupole coupling in diatomic halogens and interhalogens in the ground X Σ and B Π 0 excited states

SCF-MS-Xα calculations of the electronic structure of diatomic halogens and interhalogens XY (X = I, Br, Cl; Y = I, Br, Cl, F) have been used to investigate the bonding and nuclear quadrupole coupling in these molecules. Calculations have been carried out for the ground X ¹ Σ electronic state, and for the excited B ³ Π₀ state in the case of I₂, Br₂, ICl and IBr. Good agreement (to within 10% in most cases) is obtained between the calculated and observed nuclear quadrupole coupling constants for the molecules in the ground state. For the excited state the agreement is not as good, but the calculation does reproduce the observed decrease in the coupling constants to less than one quarter of their ground state values, and analysis of the contributions to the field gradients clearly shows the reasons for this. The electric dipole moments and electric quadrupole moments of the molecules have also been calculated. However, these prove to be much more strongly dependent on the variables used in the calculation (atomic sphere radii, inclusion of d orbitals). The results of the calculations have also been used to test some of the assumptions made in the Townes and Dailey method of analysis of nuclear quadrupole coupling data.     

The He I photoelectron spectrum of TeO

The photoelectron spectrum of a molecular beam produced by heating a sample of “TeO₂” is consistent with the presence of TeO as the predominant species. It indicates that as expected the electronic structure is closely related to that of other group VI diatomic molecules. The ground state of the ion differs however from the X ²II states of lighter diatomics of this series exhibiting Hund's case c coupling as has been observed for the ground state of the Te⁺₂ ion.     

Author index to volume 59

Expansion of tetracene vapour with excess argon carrier gas through a nozzle of a supersonic jet apparatus permits the controlled formation of (C₁₈H₁₂)Ar_n molecules. These have been studied by laser fluorescence techniques in the 450 nm region of the spectrum corresponding to excitation of the parent tetracene molecules to the ¹B_1u electronic state. We have been able to observe up to the n = 10 complex and have identified three different binding sites on the tetracene framework. From the resolved fluorescence spectra of these species one obtains an upper limit of the van der Waals binding energy of 314 cm^?1 in the upper electronic states and 274 cm^?1 in the ground state. These resolved spectra also exhibit features identified as due to the tetracene-argon stretching vibration giving a value of 36.5 ± 2 cm^?1 for the lowest transition in the ground state of (C₁₈H₁₂)Ar.     

Theoretical calculations and vibrational spectra of 1,4-benzodioxan in its S(1)(pi, pi*) electronic excited state

The structure and vibrational frequencies of 1,4-benzodioxan in its S₁(π, π^*) electronic state have been calculated using the GAUSSIAN 03 and TURBOMOLE programs. The results have been compared to experimental data and also to the ground state. Structural data for the T₁(π, π^*) state have also been calculated. The theoretical frequencies agree very well with the experimental values for the S₀ electronic ground state but are less accurate for the S₁ excited state. Nonetheless, they provide valuable guidance for excited state calculations.     

A CNDO-MO calculation of VCl4

The electronic structure of the tetrahedral molecule VCL₄ is investigated within the CNDO-MO approximations. The metal and ligand valence orbitals, 3d, 4s, 4p; and 3s, 3p; respectively, have been systematically varied in an attempt to minimize the total energy; “optimum” V 4s(χ₄ = 1.10) and 4p(d ³ p ²) orbitals have been established, but V 3d(d ⁿ ) and Cl(-δ) valence orbitals are only seen to favor lower energy for expanded orbitals. Since determining the one-electron molecular orbital level which is occupied by the vanadium lone electron is a major aspect of this investigation, all calculations have been performed in triplicate: calculations assuming the unpaired electron occupies the 3a ₁, 2 _e and 4t ₂ molecular orbital (ground state electronic configurations² A ₁,² E, and² T ₂, respectively). The Hartree-Fock equations have been solved by Roothaan's SCF method for open shells, but off-diagonal multipliers between filled and partly filled molecular orbitals of the same symmetry have been neglected. As a qualitative estimate of the error introduced by this simplification, the pertinent overlap integrals between the eigenfunctions from calculations for the three possible configurations,² A ₁,² E, and² T ₂, are investigated as functions of the component 3d(d ⁿ ) and Cl(-δ) valence orbitals. The overlap integrals from the relevant² A ₁ and² T ₂ calculations are reasonably small, but the neglect of off-diagonal multipliers in calculations on the² E state is found to be a poor approximation. An ordering of the non-filled molecular orbitals in VCl₄ of 4t ₂ < 3a ₁ < 2e < 5t ₂ seems most consistent with the numerous calculations. This suggested ground state electronic configuration of² T ₂ introduces new aspects to the consideration of a (dynamic) Jahn-Teller effect in VCl₄. Experimental data pertinent to the electronic structure of VCl₄ has been briefly summarized, but unfortunately it is inadequate to confirm or deny the present calculations.     

S1←S0 Vibronic spectrum and structure of 2,2-difluoroethanal in the S1 state

The vibronic spectrum of the 2,2-difluoroethanal vapor was recorded using a multipass optical cell with an optical length of at least 140 m. The spectrum in the region of 300—364 nm was assigned to the S₁S₀ electronic transition (from the ground S₀ to the first excited singlet S₁ electronic state); the vibrational structure of the spectrum was analyzed. The spectrum bands were assigned to two systems of vibronic transitions, namely, transitions between the levels of the cis-conformer (S₀) and of the S₁ conformers, with the origins (0₀ ⁰ transitions between the zero vibrational levels of conformers) at 29192 and 29087 cm^–1, respectively. Analysis of the spectrum showed that the S₁S₀ electronic excitation of the cis-conformer was followed by rotation of the CHF₂ top and pyramidal distortion of the carbonyl fragment. A number of fundamental frequencies were found for S₁ conformers, in particular, torsion and inversion energy levels. The experimental data are in satisfactory agreement with the results of quantum-chemical calculations for the 2,2-difluoroethanal molecule in the S₀ and S₁ states.     

Theoretical study of the electronic spectra ofcis-1,3,5-hexatriene andcis-1,3-butadiene

Summary The electronic spectra forcis-1,3-butadiene andcis-1,3,5-hexatriene have been studied using multiconfiguration second-order perturbation theory (CASPT2) and extended ANO basis sets. The calculations comprise all singlet valence excited states below 8.0 eV, the first 3s, 3p, 3d Rydberg states, and the second 3s state. The four lowest triplet states were also studied. The resulting excitation energies forcis-hexatriene have been used in an assignment of the experimental spectrum, leading to a maximum deviation of 0.13 eV for the vertical transition energies. The calculations place the 1¹ B ₂ state 0.04 eV below the 2¹ A ₁ state. 16 excited states were studied incis-butadiene, using a CASPT2 optimized ground state geometry. The 1¹ B ₂ state was located at 5.58 eV, 0.46 eV below the 2¹ A ₁ state and 0.09 eV above the experimental value. No experimental assignments are available for the 15 other transitions. On leave from: Departmento de Quimica Física, Universidad de Valencia, Dr. Moliner 50, Burjassot, E-46100-Valencia, Spain     

Theoretical investigations of the electronic states of porphyrins. II. Normal and hyper phosphorus porphyrins

Ab initio methods have been used to calculate the ground and excited states of “normal” and “hyper” porphyrins. Perturbation theory and CI methods were used to determine differential ground and excited-state correlation effects for [P^v(P)F₂]⁺ and [P^III(P)]⁺. A comparison is made to the INDO /S /CI predicted wavefunctions and spectra and to the experimental spectra of closely related molecules. The “hyper” [P^III(P)]⁺ calculations show some very low energy electronic transitions which provide an explanation for an anomalous “red” band in the spectrum and for the lack of fluorescence. Ab initio calculations also predict that (1) the lowest energy ¹A₁ state is a two-configuration wavefunction which can be described as a diradical, (2) the two lowest-energy singlet excited states are double excitations from the closed shell SCF configuration, and (3) a ³B₂ state is very close in energy to the lowest ¹A₁ state.     

Optical Spectroscopy of the Au4+ Cluster: The Resolved Vibronic Structure Indicates an Unexpected Isomer

Knowledge of the geometric and electronic structure of gold clusters and nanoparticles is vital for understanding their catalytic and photochemical properties at the molecular level. In this study, we report the vibronic optical photodissociation spectrum of cold and mass‐selected Au₄⁺ clusters measured at a resolution high enough to allow for comparison with Franck–Condon simulations of the excited state transitions based on time‐dependent density functional theory calculations. The three vibrational frequencies identified for the lowest‐lying optically accessible excited state at 2.17 eV stem from the Y‐shaped isomer (C_2v) and not from the rhombic isomer (D_2h) considered to be the ground state structure of Au₄⁺. This study demonstrates that an analysis of low‐resolution electronic spectra by calculations of vertical transitions alone is not sufficient for a reliable isomer assignment of such metal clusters.     

Darstellung und Eigenschaften von trans-Di(fluoro)phthalocyaninato(2–)-rhenat(III); Kristallstruktur des linear-Bis(triphenylphosphin)iminium-Doppelsalzes l(PNP)trans[Re(F)2pc2–] · 0,33l(PNP)F · 2 H2O

Synthesis and Properties of trans -Di(fluoro)phthalocyaninatorhenate(III); Crystal Structure of the linear -Bis(triphenylphosphine)iminium Double Salt ^l (PNP) ^trans[Re(F)₂pc^2–] · 0.33^l (PNP)F · 2 H₂O trans-Bis(triphenylphosphine)phthalocyaninato(2–)rhenium(II) reacts with (ⁿBu₄N)F · 3 H₂O in acetone on air yielding trans-di(fluoro)phthalocyaninato(2–)rhenate(III), ^trans[Re(F)₂pc^2–]^–. The complex anion is precipitated as tetra(n-butyl)ammonium (ⁿBu₄N), or after addition of (PNP)HSO₄ as linear-bis(triphenylphosphine)iminium (^l(PNP)) salt. The latter crystallizes as a double salt of formula ^l(PNP)^trans[Re(F)₂pc^2–] · 0.33^l(PNP)F · 2 H₂O in the cubic space group I23 (no. 197) with the cell parameter a = 21.836(2) Å; V = 10412(2) ų; Z = 6. The Re atom is located in the centre of the (N_iso)₄ plane (N_iso: isoindole-N atom) and coordinates axially two fluorine atoms in a mutual trans position. The Re–N and Re–F distance is 2.035(6) and 1.798(7) Å, respectively. According to the short Re–F distance the asymmetric Re–F stretching vibration is observed in the MIR spectrum at 746 cm^–1. Obviously due to a large spin-orbit coupling, the complex salt with an electronic low-spin d⁴ ground state of Re^III (S = 1) is diamagnetic. Hence a sharp signal is observed at –126.1 ppm in the ¹⁹F NMR spectrum. The UV-VIS-NIR spectrum shows the typical π-π* transitions at 15000 (B), 29500 (Q) and 36900 cm^–1 (N) and trip-multiplet transitions at 9500/10500 cm^–1 and 13200/14100 cm^–1.     

Theoretical electronic studies of aluminum monobromide and aluminum monoiodide

By using CASSCF/MRCI methods, theoretical molecular calculations have been performed for 12 electronic states for AlBr molecule and 12 electronic states for AlI molecule in the representation ^2s+1Λ (neglecting spin‐orbit effects). Calculated potential energy curves are displayed. Spectroscopic constants including the harmonic vibrational wave number ω_e, the electronic energy T_e referred to the ground state and the equilibrium internuclear distance R_e are predicted for these singlet and triplet electronic states for both AlBr and AlI molecules. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010