A study of electron scattering from benzene: excitation of the 1B1u, 3E2g, and 1E1u electronic states

We report results from measurements for differential and integral cross sections of the unresolved (1)B(1u) and (3)E(2g) electronic states and the (1)E(1u) electronic state in benzene. The energy range of this work was 10-200 eV, while the angular range of the differential cross sections was ～3°-130°. To the best of our knowledge there are no other corresponding theoretical or experimental data against which we can compare the present results. A generalized oscillator strength analysis was applied to our 100 and 200 eV differential cross section data, for both the (1)B(1u) and (1)E(1u) states, with optical oscillator strengths being derived in each case. The respective optical oscillator strengths were found to be consistent with many, but not all, of the earlier theoretical and experimental determinations. Finally, we present theoretical integral cross sections for both the (1)B(1u) and (1)E(1u) electronic states, as calculated within the BEf-scaling formalism, and compare them against relevant results from our measurements. From that comparison, an integral cross section for the optically forbidden (3)E(2g) state is also derived.     

Spectroscopic constants and molecular properties of A3Σu+, B3Πg,W3Δu,and B′3Σu− electronic states of the N2 molecule

The potential energy curves (PECs) of A³Σ, B³Π_g, W³Δ_u, and B^′3Σ electronic states of the N₂ molecule have been studied for internuclear separations from 0.05 to 2.0 nm using the full valence complete active space self‐consistent‐field method followed by the highly accurate valence internally contracted multireference configuration interaction (MRCI) approach in conjunction with the correlation‐consistent basis sets. Effects on the PECs by the core–valence correlation and relativistic corrections are taken into account. The way to consider the relativistic correction is to use the second‐order Douglas‐Kroll Hamiltonian approximation. The core–valence correlation correction is made with the cc‐pCV5Z basis set. And the relativistic correction is performed at the level of cc‐pV5Z basis set. To obtain more reliable results, the PECs determined by the MRCI calculations are also corrected for size‐extensivity errors by the Davidson modification (MRCI+Q). These PECs are extrapolated to the complete basis set limit. The spectroscopic parameters of ¹⁴N₂, ¹⁴N¹⁵N, and ¹⁵N₂ isotopologs have been evaluated and compared with those reported in the literature. Excellent agreement has been found between the present results and the Rydberg‐Klein‐Rees (RKR) data. With the PECs obtained by the MRCI+Q/CV+DK+56 calculations, the first 30 vibrational states for three species are computed for each electronic state. And for each electronic state of each species, the vibrational level G(ν), inertial rotation constant B_ν, and centrifugal distortion constant D_ν have been determined, which agree well with the RKR data. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Franck-Condon Factors for the Transitions N2, C 3πu → B 3πg and CN,B 2 Σ + → X 2 Σ +

Franck-Condon factors for the transitions N₂, C ³π_u→ B ³π_g and CN, B ² Σ ⁺ → X ² Σ ⁺ have been calculated by the method of Chang and Karplus.     

Theoretical study of spectroscopic constants and molecular properties of diatomic anions using B3LYP method

Structure, spectroscopic constants and molecular properties of selected diatomic anions in their ground states have been studied in detail using HF/DF B3LYP method. The consistency of the calculated values of spectroscopic constants and molecular properties has been tested using four basis sets with improved quality. The spectroscopic constants and molecular properties of these diatomic ions agree well with the experimental and theoretical values wherever available. Most of the spectroscopic constants and molecular properties of these ions, in particular the spectroscopic constants of SiO⁻, CS⁻ and the molecular properties of SiN⁻, CP⁻, SiO⁻ are first reported.     

Electric-field-induced g/u mixing of the E0g+(3P2) and D0u+(3P2) ion-pair states of jet-cooled I2 observed using optical triple resonance

Electric-field-induced electronic state g/u mixing of nearly isoenergetic rovibrational levels of the E0g+(3P2) and D0u+(3P2) ion-pair states of I2 has been observed using optical triple resonance combined with resonance ionization. Detectable mixing with applied fields of 1 kV/cm occurs over a range of energy level separations of < or = 0.3 cm(-1).     

A MINDO/3 harmonic force field for pyrazine. In-plane Ag and B3u vibrations

A general Quadratic Force Fields has been computes in the MINDO/3 approximation by calculating analytical first derivatives and numerical second derivatives of the energy in a 3N cartesian space. Force constants are transformed to the space of independent symmetry co-ordinates and then a refinement has been carried out to fit frequencies of pyrazine-h₄, -d₄ and cis-d₂, corresponding to in-plane vibrations. Results concerning A_g and B_3u species are presented here.     

A laser spectroscopic study of the X2pi(g), A2pi(u), and B2sigma+ states of BS2: Renner-Teller, spin-orbit, and K-resonance effects

The lowest-lying vibronic levels of the X, A, and B states of BS2 have been investigated at high resolution using a combination of room-temperature absorption and supersonic jet data. In both cases, the BS2 radical was prepared in an electric discharge using a precursor gas mixture of BCl3,CS2, and either helium or argon. Extensive absorption spectra were obtained for the 0(0)0 and 2(1)1 bands of the A2pi(u)-X2pi(g) electronic transition in the visible. The A-X 2(1)1 and B2sigma(u)(+)-X2pi(g) 2(1) bands of jet-cooled BS2 were also studied with laser-induced fluorescence techniques. By fitting the 0(0) bands of both electronic transitions simultaneously, we were able to precisely determine the spin-orbit splittings in both the A and X states. Similarly, the 21 bands were fitted in a merged analysis in order to determine the relative separations of the vibronic components of the ground and first excited state bending levels as accurately as possible. Due to a large spin-orbit splitting and small Renner-Teller interaction, the A state bending level shows small but definite K-resonance effects, which were fitted using a full matrix for the four components of upsilon2' = 1. The resulting parameters were used along with previously published data to refine the Renner-Teller analyses in both the A2pi(u), and X2pi(g) electronic states. Where possible, the fitted constants and observed boron isotope splittings have been shown to be in accord with theoretical estimates of their sign and magnitude.     

Photoactive liquid crystalline polymers: A comprehensive study of linear and hyperbranched polymers synthesized by A2B2, A2B3, A3B2, and A3B3 approaches

A series of linear and hyperbranched polyester epoxies, with varied structural parameters such as kinked structure and different dendritic architectures, were synthesized by A₂ + B₂, A₂ + B₃, A₃ + B₂, and A₃ + B₃ approaches. The structures of synthesized monomers and polymers were confirmed by Fourier transform infrared, ¹H NMR, and ¹³C NMR spectroscopic techniques. The effect of varied structural parameters on phase behavior and photoresponsive properties was investigated by using differential scanning calorimeter, thermal optical polarized microscope, UV–visible spectroscopy, photoviscosity, and refractive index studies. The transition temperatures of hyperbranched polymers were higher than that of the corresponding linear analogues. All the polymers showed nematic phase (nematic droplets) over a broad temperature range. The effect of kinked structural unit on photoresponsive property is less in both linear and hyperbranched architectures. Although the effect of architectural nature is highly considerable within the hyperbranched architectures, the polymer (HPE–33) synthesized by A₃ + B₃ approach showed highest rate of photocrosslinking, followed by HPE–I 32; HPE–T 32, and HPE–23, which were synthesized by A₃ + B₂ and A₂ + B₃ approaches, respectively. The findings in photoresponsive properties were further supported by molecular modeling studies. Substantial variation of refractive index (0.015–0.024) indicates that these polymers could be used for optical recording. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Fluorescence and laser properties of D2-, C2- and D3 symmetry series oligophenylenes

The fluorescence and laser properties of ten aromatic compounds, specially chosen from the p-oligophenylenes (D(2) symmetry) or m-oligophenylenes (C(2) or D(3) symmetry) are studied experimentally (at 293 K) and quantum chemically. The quantum yields, gamma and the decay times, tau(f) of fluorescence are measured for deaerated and non-deaerated cyclohexane solutions. The oscillator strengths, f(e) of the S(0)-->S(p) (1A-->(1)L(a)) and S(0)-->S(alpha) (1A-->(1)L(b)) transitions, fluorescence, k(f) and intersystem crossing, k(ST), rate constants, and natural lifetimes, tau(0)(T) are calculated. The lowest 1L(b), 1L(a) and 3L(b) (77 K) levels are determined. It is found that all p-oligophenylenes from p-terphenyl onwards are excellent, photochemically stable laser dyes although the solubility in this series decreases dramatically. On the basis of trends observed in p-oligophenylenes (D(2)-series) and on the properties of the experimentally studied m-oligophenylenes of the C(2)- and D(3)-series, the fluorescence and laser properties of other compounds from these series are estimated/predicted. It is shown, for the first time, that m-oligophenylenes of the C(2)-series, from 1,3-di(p-terphenyl)benzene will acquire fluorescence of 1L(a)-->(1)A nature and could be extremely effective laser dyes. It is also shown that m-oligophenylenes of the D(3)-series, from 1,3,5-tri(p-quaterphenyl)benzene will also acquire 1L(a)-->(1)A nature fluorescence and laser ability, although this would not be as good as that of compounds in the C(2)-series. It is concluded that m-oligophenylenes can be used not only for passive mode locking but some may also be used as laser dyes and scintillators. The results obtained are important for various practical purposes and theoretical considerations.     

Kinetic study of N2(B3Πg, υ) quenching by laser-induced fluorescence

The quenching kinetics of N₂(B³Π_g, υ) have been determined in a low-pressure flow system in the absence of N atoms. Individual vibrational levels of the B state were populated by laser pumping (first-positive bands) of N₂(A³Σ_u⁺) molecules. The latter were created upstream by energy transfer from Ar metastable atoms.     

Lifetime of the B3Σ−u state of S2

Using the single-photon time correlation method, we have determined the lifetime of the S₂(B³Σ^?_u) state from the decay rate of the fluorescence at 370 nm. A lifetime of 45.0 ± 0.6 ns was measured, and the cross section for fluorescence quenching by S₂ as found to be 81.3 ± 4.7 A². A slight dependence of the lifetime on the wavelength of the excitation source over the range of 280 to 337 nm was observed.     

Linear dependency in the refinement of force constants with the Jacobian method

The Jacobian method in the refinement of force constants is studied. Theoretical and experimental frequencies and other observables, ν_s, are matched by minimizing Σ_sW_s(ν – ν)², where s = 1, 2, 3,…, proceeds over all normal modes and isotopes, and W_s are weighting factors. Modification of the theoretical frequencies is accomplished with the Jacobian matrix, J , with elements J_si = ?ν_s/?k_i involving each force constant or associated parameter, k_i, i = 1, 2, 3,…, by Δν = J Δ k . The parameters are adjusted directly with Δ k = ( J ^T WJ )^?1( JW ) Δν, where W is a diagonal matrix which weights the frequencies. The linear dependence problem must be addressed prior to inversion of J ^T WJ . The approach entails diagonalization of J ^T WJ , analysis of the components of the eigenvectors associated with zero and small eigenvalues, identification of the linearly dependent parameters, successive elimination of selective parameters, and a repeat of this procedure until linear dependency is removed. The Jacobian matrices are obtained by differencing the frequencies when the parameters are varied and by numerical and analytical evaluation of the derivative of the potential. The unitary transformation, U , used to calculate J = U ^T (? F /? k ) U or J = U ^T (Δ F /Δ k ) U , is obtained from the diagonalization of the Hessian, F_mn = ?²ν/?p_m?q_n, where p, q = x, y, z are the Cartesian coordinates for atoms m, n = 1, 2, 3,…, at the initial value of k_i, i = 1, 2, 3, ? The accuracy of and the ability to evaluate the Jacobian matrix by these methods are discussed. Applications to CH₄, H₂CO, C₂H₄, and C₂H₆ are presented. Linearly dependent and ill-conditioned parameters are identified and removed. The procedure is general for any observable quantity. © 1994 by John Wiley & Sons, Inc.     

Calculation of the in-plane force constants and vibrational spectra of pyridine and its deuterated derivatives by the CNDO/2 force method

The in-plane vibrations of pyridine and its deuterated derivatives (4-d₁, 2,6-d₂, 3,5-d₂, and d₅) have been studied with the CNDO/2 force method. The calculated values of the force field scaled by five empirical parameters yield good agreement with the experimental spectra. The results seem to permit the reassignment of some bands.     

Generation of potential energy curves for the X1Sigma(+)g, B1Delta(+)g, and B'1Sigma(+)g states of C2 using the effective valence shell Hamiltonian method

Calculations of the ground and excited state potential energy curves of C2 using the third-order effective valence Hamiltonian (Hv3rd) method are benchmarked against full configuration interaction and other correlated single-reference perturbative and nonperturbative theories. The large nonparallelity errors (NPEs) exhibited even by state-of-art coupled cluster calculations through perturbative triples indicate a serious deficiency of these single-reference theories. The Hv method, on the other hand, produces a much reduced NPE, rendering it a viable approximate many-body method for accurately determining global ground and excited state potential energy curvessurfaces.     

Multireference coupled-cluster study of the symmetry breaking in the C2B radical

The potential energy surfaces (PESs) for both the ground and the excited electronic states of the C(2)B radical are investigated using various multireference (MR) coupled-cluster (CC) approaches. In the ground state case we employ the reduced MR (RMR) CC approach with singles (S) and doubles (D), the RMR CCSD method, as well as its RMR CCSD(T) version corrected for secondary triples, relying on various model spaces and basis sets. The reliability of this approach is also tested against the benchmark full configuration interaction results obtained for a small Dunning-Hay (DH) basis set. The results imply a clear preference for a cyclic structure which, however, breaks the C(2v) symmetry. This symmetry breaking manifests itself strongly at the level of the independent particle model, as represented by the restricted open-shell Hartree-Fock approximation, but the tendency toward symmetry breaking diminishes with the increasing size of the basis set employed as well as with the enhanced account of the correlation effects. It is likely to disappear in the complete basis set limit. The general model space CCSD method is then used to compute vertical excitation energies for a number of excited states as well as the cuts of the PES as the boron atom moves around the C(2) fragment. These results also explain why no symmetry breaking is found when relying on a spin contaminated unrestricted Hartree-Fock reference, as in the UMP2 method.     

Observation and calculation of the Cs2 2 3Delta(1g) and b 3Pi(0u) states

The Cs(2) 2 (3)Delta(1g) and b (3)Pi(0u) states have been observed by infrared-infrared double resonance spectroscopy for the first time. 221 2 (3)Delta(1g)<--A (1)Sigma(u) (+)<--X (1)Sigma(g) (+) double resonance lines have been assigned to transitions into the 2 (3)Delta(1g) v=6-13 vibrational levels. Resolved fluorescence into the b (3)Pi(0u) v(')=0-48 levels has been recorded. Molecular constants and potential energy curves are determined by the global fit of the entire set of the experimental data. Theoretical potential energy curves of the 2 (3)Delta(g) and b (3)Pi(u) states have been determined in the framework of the pseudopotential method and are compared with the experimental results.     

A new method for the calculation of vibrational force constants. Application to H2

A new method for the quantum mechanical calculation of vibrational force constants is presented. This method is applied to the calculation of the vibrational force constant of H₂, using a completely optimized wavefunction constructed from a single gaussian orbital. The value of the force constant obtained using this method is k₀ = 0.422341088751 au (= 6.5754 × 10⁵ dyne/cm), compared to the value of k₀ = 0.42234079S380 au (= 6.5754 × 10⁵ dyne/cm) obtained using an analytic method, and the experimental value of k_e = 0.3692 au (= 5.748 × 10⁵ dyne/cm).