Relativistic corrections in a series of helium excited states

Relativistic corrections to order (υ/c)² are applied to the helium excited states 2 ^1,3P, 3 ^1,3D,…, 8 ^1,3K. Simple correlated open-shell wavefunctions are employed and the Breit operators H₁ through H₅ treated as perturbations. Account is also taken of mass polarization and lowest-order one electron Lamb shift. The energies thus calculated agree with experiment to within 2.2 cm^?1 or better.     

Two-photon properties of the La and Lb bands of substituted benzenes computed from CNDO/S

Two-photon tensor invariants proportional to two-photon absorptivities are calculated from CNDO/S CI wavefunctions for a variety of substituted benzenes for transitions to the two lowest singlet states, L_b^? (B_2u^?) and L₃⁺ (B_1u⁺). Providing hexagonal geometry is used, the results demonstrate considerable effectiveness by this method for predicting the relative sensitivity of these bands to vibronic, inductive and conjugative effects, including the intensity ratios for multiple substitutions by aza, methyl and amino. The method fails for fluorobenzene.     

Visualization of electron correlation in ground states of He and H−

For the ground states of He and H^?, conditional probability densities d(r₂,θ₁₂r₁) for finding two electrons in different relative positions have been calculated for several wavefunctions including simple one-configuration wavefunctions and Hylleraas—Kinoshita type functions. The calculations, including graphing, were all carried out on a desktop computing calculator.     

The relaxation of HCl(ν = 1) and DCl(ν = 1) by O atoms between 196 and 400 K

The rates of relaxation of HCl(ν = 1) and DCl(ν = 1) by atomic oxygen have been determined between 196 and 400 K using the laser induced vibrational fluorescence method. The values of the rate constants, κ_1,H and κ_1,D, can be matched quite well by Arrhenius expressions: κ_1,H = 6.2 × 10^?12 exp (?1.0₅ kcal mole^?1/RT) cm³ molecule^?1 s^?1 and κ_1,D = 2.9 × 10^?12 exp (?0.5 kcal mole^?1/RT) cm³ molecule^?1 s^?1. The most likely explanation of the absolute and relative magnitudes of these rate constants appears to be that relaxation occurs as a result of non-adiabatic vibronic transitions during collisions.     

Time-dependent close coupling for vibrational excitation in three dimensions: Application to H+ - H2

Impact parameter calculations for the non-reactive H⁺ + H₂ (n_i = 0) → H⁺ + H₂ (n_f) collision are reported for energies 10 eV ? E_cm ? 200 eV describing the rotational motion of the molecule in the sudden limit. The time-dependent Schrödinger equation for the vibrational motion has been solved by close coupling techniques expanding the vibrational wavefunction into both harmonic and numerically exact H₂ bound states. The convergence in vibrational basis sets, where up to six vibrational levels are considered, becomes worse with decreasing energy and increasing inelasticity. Furthermore, the harmonic wavefunctions are not suitable over a large range of energies to calculate proper cross sections. The various integral and differential cross sections have been compared with the classical results of Giese and Gentry.     

Lifetimes of the vibronic Ã2A1 states of H2S+

Lifetimes have been measured for the Σ and Π vibronic òA₁ states of H₂S⁺ by studying the decay curves of the òA₁ (0, υ′₂, 0) → X? ²B₁ (0, υ″₂, 0) emission bands. The vibronic òA₁ states are produced via excitation of H₂S molecules by 150 eV electrons. The Σ sublevels 1 ? υ′₂ ? 7 and the Π sublevels 3 ? υ′₂ ? 6 have been considered. Predissociation occurs in the Σ sublevels for υ′₂ ? 7 and in the Π sublevels for υ′₂ ? 6. The obtained radiative lifetimes for the non-predissociated Σ and Π sublevels are around 4.2(±0.4) × 10^?6 s and 5.6(±0.5) × 10^?6 s respectively. For the predissociated Σ(0, 7, 0) and Π(0, 6, 0) levels the corresponding lifetimes are 2.3(±0.3) × 10^?6 s and 1.6(±0.3) × 10^?6 s respectively. The rate constant for collisional deactivation (quenching) of the vibronic òA₁ states by H₂S molecules was found to equal 2.3(±0.3) × 10^?9 cm³ mol^?1 s^?1.     

Polarization and assignment of the two-photon excitation spectrum of benzene vapor

The two-photon excitation (TPE) of benzene fluorescence in the vapor phase at 60 torr is reported for the total-energy region from 38 086 cm^?1 to 42 441 cm^?1 using both circular and linear polarized light from a nitrogen-pumped dye-laser. The theory of the polarization dependence of the vibronic transitions in benzene is briefly reviewed, and it is seen how transitions involving vibrations of b_1u symmetry are expressly forbidden for this type of TPE experiment in which the two photons are identical. Five vibronic origins with distinctive rotational contours and polarization dependence are identified in the TPE spectrum. The υ₁₄(b_2u) vibronic origin at 1570 cm^?1 (above the electronic origin of the ^IB_2u state) stands out very prominently in the linear polarized spectrum, but nearly disappears in the circular polarized spectrum. This striking polarization dependence indicates a significant contribution of A_2u electronic states to the intermediate states of this TPE vibronic transition. The relatively great strength of the υ₁₄ band may be due to vibronic borrowing by the b_2u mode from the ground electronic state (A_1g).     

Intramolecular vibrational state mixing in glyoxal by stimulated emission pumping spectroscopy

Stimulated emission pumping spectra of glyoxal in a supersonic jet were recorded up to 7000 cm⁻¹ above the ground vibrational state employing X̃(¹A_g) ← Ã(¹A_u)2¹₀ vibronic transitions. At low energies, only isolated states were observed. However, at high energies, clumps of eigenstates were observed, which suggests extensive vibrational state mixing with dense bath states.     

Quantum chemical ab initio calculations for excited states of F IV

Quantum chemical ab initio calculations have been performed for the ground state and for several excited states of the F³⁺ ion (F IV). Three levels of accuracy have been used: Frozen-core SCF calculations (FRC-SCF) to determine orbital energies ε _nl and quantum defects δ _l for excited Rydberg orbitalsnl; frozen-core SCF followed by CI calculations (FRC-CI) which account for multiplet splittings and configuration mixings, and multi-configuration coupled-electron-pair approximation (MC-CEPA) calculations which include dynamic correlation effects. The accuracy of the calculated excitation energies is in the order of 5000 cm^?1 at the FRC-CI level and in the order of 500 cm^?1 at the MC-CEPA level. This latter error amounts to about 0.1% for excitation energies in the range of 400000 to 600000 cm^?1. The MC-CEPA calculations have been performed for 17 experimentally known states and for 14 experimentally unknown states, in particular for the configurations 2s2p ² (² D)3s, 2s 2p ²(² S)3s, 2s ² 2p 4p, and 2s ² 2p 5p.     

Analysis of pseudo jahn–teller distortion based on natural bond orbital theory: Case study for silicene

Ground state (GS) instability of nondegenerate molecules in high symmetric structures is understood through Pseudo Jahn–Teller mixing of the electronic states through the vibronic coupling. The general approach involves setting up of a Pseudo Jahn–Teller (PJT) problem wherein one or more symmetry allowed excited states couple to the GS to create vibrational instability along a normal mode. This faces two major complications namely (1) estimating the adiabatic potential energy surfaces for the excited states which are often difficult to describe in case the excited states have charge-transfer or multi-excitonic (ME) character and (2) finding out how many such excited states (all satisfying the symmetry requirements for vibronic coupling) of increasing energies need to be coupled with the GS for a particular PJT problem. An analogous alternative approach presented here for the well-known case of symmetry breaking of planar (D_6h) hexasilabenzene (Si₆H₆) to the buckled (D_3d) structure involves identifying the second-order donor–acceptor, hyperconjugative interactions (E²_{i → j}) that stabilize the distorted structure. Following the recent work of Nori-Shargh and Weinhold, one observes that the orbitals involved in the vibronic coupling between the S₀/S_n states and those for the donor (filled)–acceptor (empty) interactions are identical. In fact, deletion of any particular pair of E²_{i → j} interaction creates vibrational instability in the buckled structure and as a corollary, deleting it for the planar structure removes its instability. The one-to-one correlation between the natural bond orbital theory and PJT theory assists in an intuitive identification of the relevant (few) excited states from a manifold of computed ones that cause symmetry breaking by vibronic coupling. © 2019 Wiley Periodicals, Inc.     

Theoretical DFT study of phosphorescence from porphyrins

Geometrical structure of free-base porphin (H₂P) and Mg- and Zn-porphyrins together with their vibrational frequencies and vibronic intensities in phosphorescence are investigated by density functions theory (DFT) with the standard B3LYP functional. These molecules have a closed-shell singlet ground state (S₀) and low-lying triplet (T₁) excited states of ππ* type. The S₀–T₁ transition probability and radiative lifetime of phosphorescence (τ_p) of these molecules are calculated by time-dependent DFT utilizing quadratic response functions for account of spin–orbit coupling (SOC) and electric-dipole transition moments including displacements along active vibrational modes. The infrared and Raman spectra in the ground singlet and first excited triplet states are also studied for proper assignment of vibronic patterns. The long radiative lifetime of free-base porphin phosphorescence (τ_p ∼ 360 s at low temperature limit, 4.2 K) gets considerably shorter for the metalloporphyrins. An order of magnitude reduction of τ_p is predicted for Mg-porphyrin but no change of phosphorescence polarization is found. A forty times enhancement of the radiative phosphorescence rate constant is obtained for Zn-porphyrin in comparison with the H₂P molecule which is accompanied by a strong change of polarization and spin-sublevel radiative activity. A strong vibronic activity of free-base porphin phosphorescence is found for the b_2g mode at 430 cm⁻¹, while the 679 and 715 cm⁻¹ vibronic bands of b_3g symmetry are less active. These and other out-of-plane vibrations produce considerable changes in the radiative constants of different spin sublevels of the triplet state; they also promote the S₁ → T₁ intersystem crossing. Among the in-plane vibrations the a_g mode at 1614 cm⁻¹ is found very active; it produces a long progression in the phosphorescence spectrum. The time-dependent DFT calculations explain the effects of the transition metal atom on phosphorescence of porphyrins and reproduce differences in their phosphorescence and EPR spectra.     

High temperature collisional energy transfer in highly vibrationally excited molecules: Isotope effects in tert-butyl chloride systems

The average downward collisional energy transfer (<ΔE_down>) is obtained for highly vibrationally excited tert-butyl chloride, both undeuterated and per-deuterated, with Kr, N₂, CO₂, and C₂H₄ bath gases, at ca. 760 K. Data are obtained using the technique of pressure-dependent very low-pressure pyrolysis. Reactant internal energies to which the data are sensitive are in the range 200–250 kJ mol^?1. For C₄H₉Cl, the <ΔE_down> values (cm^?1) are 255 (Kr), 265 (N₂), 440 (CO₂), and 585 (C₂H₄), and for C₄D₉Cl, 245 (N₂), 370 (CO₂), and 540 (C₂H₄). The uncertainties in these values are ca. 20% (40% for Kr); the uncertainties in the deuteration ratios are 10–15%. The value for Kr is in agreement with theoretical predictions of a biased random walk model for internal energy change in monatomic/substrate collisions. The effect of deuteration of <ΔE_down> is also in accord with that predicted by a modification of the theory. Extrapolated highpressure rate coefficients for the thermal decomposition of reactant are 10^13.6 exp(-187 kJ mol^?1/RT) s^?1 (C₄H₉Cl) and 10^14.2 exp(?196 kJ mol^?1/RT) s^?1 (C₄D₉Cl), in accord with other studies and the expected isotope effect.     

Ab initio chemical kinetics for the NH2 + HNOx reactions,part II: Kinetics and mechanism for NH2 + HONO

The kinetics and mechanism for the reaction of NH₂ with HONO have been investigated by ab initio calculations with rate constant prediction. The potential energy surface of this reaction has been computed by single‐point calculations at the CCSD(T)/6‐311+G(3df, 2p) level based on geometries optimized at the CCSD/6‐311++G(d, p) level. The reaction producing the primary products, NH₃ + NO₂, takes place via precomplexes, H₂N???c‐HONO or H₂N???t‐HONO with binding energies, 5.0 or 5.9 kcal/mol, respectively. The rate constants for the major reaction channels in the temperature range of 300–3000 K are predicted by variational transition state theory or Rice–Ramsperger–Kassel–Marcus theory depending on the mechanism involved. The total rate constant can be represented by k_total = 1.69 × 10^?20 × T^2.34 exp(1612/T) cm³ molecule^?1 s^?1 at T = 300–650 K and 8.04 × 10^?22 × T^3.36 exp(2303/T) cm³ molecule^?1 s^?1 at T = 650–3000 K. The branching ratios of the major channels are predicted: k₁ + k₃ producing NH₃ + NO₂ accounts for 1.00–0.98 in the temperature range 300–3000 K and k₂ producing OH + H₂NNO accounts for 0.02 at T > 2500 K. The predicted rate constant for the reverse reaction, NH₃ + NO₂ → NH₂ + HONO represented by 8.00 × 10^?26 × T^4.25 exp(?11,560/T) cm³ molecule^?1 s^?1, is in good agreement with the experimental data. © 2009 Wiley Periodicals, Inc. Int J Chem Kinet 41: 678–688, 2009     

Dipole‐bound anions supported by charge–transfer interaction: Anionic states of HnF3−nN → BH3 and H3N → BHnF3−n (n = 0, 1, 2, 3)

The possibility of electron binding to five molecules (i.e., F₃N → BH₃, H₂FN → BH₃, HF₂N → BH₃, H₃N → BH₂F, H₃N → BHF₂) was studied at the coupled cluster level of theory with single, double, and noniterative triple excitations and compared to earlier results for H₃N → BH₃ and H₃N → BF₃. All these neutral complexes involve dative bonds that are responsible for significant polarization of these species that generates large dipole moments. As a consequence, all of the neutral systems studied, except F₃N → BH₃, support electronically stable dipole‐bound anionic states whose calculated vertical electron detachment energies are 648 cm^?1 ([H₂FN → BH₃]^?), 234 cm^?1 ([HF₂N → BH₃]^?), 1207 cm^?1 ([H₃N → BH₂F]^?), and 1484 cm^?1 ([H₃N → BHF₂]^?). In addition, we present numerical results for a model designed to mimic charge–transfer (CT) and show that the electron binding energy correlates with the magnitude of the charge flow in the CT complex. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

Data on the thermochemistry of azoalkanes

The rate constant of the primary decomposition step was determined for four symmetrical and four unsymmetrical azoalkanes. From the experimental activation energies and some literature enthalpy data, the following enthalpies of formation of radicals and group contributions were calculated: ΔH_? (CH₃N₂) = 51.5 ± 1.8 kcal mol^?1, ΔH_? (C₂H₅N₂) = 44.8 ± 2.5 kcal mol^?1, ΔH_? (2?C₃H₇N₂) = 37.9 ± 2.2 kcal mol^?1, [N_A-(C)] = 27.6 ± 3.7 kcal mol^?1, [N_A-(?_A) (C)] = 61.2 ± 3.1 kcal mol^?1.     

Structure of small molecular hydrogen clusters

The ground state energies and structural properties of small (H₂) _N ,N=2?7, are calculated using the variational Monte Carlo method. These wavefunctions include both short- and long-range correlation effects that are important in the binding of van der Waals clusters. We have investigated these clusters using shadow wavefunctions and found that the coupling to shadow variables raises the energy in all cases, implying that the ground states of these small clusters are properly described as quantum liquids rather than solid structures.     

AB initio SCF study of the electronic structure and spectrum of CuF2

MC SCF and contracted CI calculations have been performed for the three ligand-field states of CuF₂ and also for two charge-transfer states. With the most extensive basis set the calculated d-d transition energies, including a Davidson correctior for cluster effects, are 4150 cm^?1 (²11g) and 10560 cm^?1 (²Δg). These calculations were made with 98 basis functions, including of orbitals on Cu and d orbitals on F. To check the charge distribution in the molecule, calculations of the ESR g factors were also made at the SCF and CI levels of approximation. Resulting CI values are g_| = 1.93 (1.91) and g₁ = 2.76 (2.60). with corresponding experimental numbers in parentheses.     

Experimental and quantum-chemical study of complexation of carbene analogs with dinitrogen. Direct IR-spectroscopic observation of Cl2Si·N2 complexes in low-temperature argon-nitrogen matrices

Interaction of dichlorosilylene with dinitrogen in mixed Ar—N₂ matrices at 9 - 10 K was studied by IR spectroscopy. A donor-acceptor complex Cl₂Si·N₂ was found and characterized by six bands of symmetric (at 511.2, 508.9, and 506.5 cm^–1) and antisymmetric (at 500.1, 496.9, and 495.1 cm^–1) stretching vibrations of Si—Cl bonds in the most abundant isotopomers. Two bands at 498.7 and 493.5 cm^–1 observed in mixed matrices were tentatively assigned to Cl₂Si·(N₂)₂ complex. Several stretching vibration bands of minor isotopomers of SiCl₂ were detected for the first time in argon matrices. Assignment has been done for the isotopic structure of SiCl₂ associates with dinitrogen observed in N₂ matrices. Dimerization of SiCl₂ and its complexation with one and two N₂ molecules were studied by quantum-chemical DFT calculations (PBE and B3LYP functionals). The structures, energies, and vibrational frequencies of the Cl₂Si·N₂ and Cl₂Si·(N₂)₂ complexes and the Si₂Cl₄ dimer were determined. The energies of SiCl₂ complexation with one and two N₂ molecules obtained from PBE and B3LYP calculations are 0.3 and 0.6 kcal mol^–1, respectively. More accurate G2(MP2,SVP) calculations using the B3LYP geometries have predicted a higher stability of the Cl₂Si·N₂ complex (1.2 kcal mol^–1). The calculated and experimental vibrational frequencies of reagents and complexes are in good agreement. A correlation has been established between the PBE calculated energies of complexation of EHal₂ (E = Si, Ge, Sn, Pb) with N₂ and the experimentally observed shifts of E—Hal stretching vibrations in EHal₂ upon complexation. The strength of the complexes with N₂ increases on going from dihalosilylenes to dihaloplumbylenes.     

Interaction of the Benzenium Ion with Inert Ligands: IR Spectra of C6H7+?Ln Cluster Cations (L=Ar,N2, CH4, H2O)

IR photodissociation spectra of mass‐selected clusters composed of protonated benzene (C₆H₇⁺) and several ligands L are analyzed in the range of the C? H stretch fundamentals. The investigated systems include C₆H₇⁺? Ar, C₆H₇⁺? (N₂)_n (n=1–4), C₆H₇⁺? (CH₄)_n (n=1–4), and C₆H₇⁺? H₂O. The complexes are produced in a supersonic plasma expansion using chemical ionization. The IR spectra display absorptions near 2800 and 3100 cm^?1, which are attributed to the aliphatic and aromatic C? H stretch vibrations, respectively, of the benzenium ion, that is, the σ complex of C₆H₇⁺. The C₆H₇⁺? (CH₄)_n clusters show additional C? H stretch bands of the CH₄ ligands. Both the frequencies and the relative intensities of the C₆H₇⁺ absorptions are nearly independent of the choice and number of ligands, suggesting that the benzenium ion in the detected C₆H₇⁺? L_n clusters is only weakly perturbed by the microsolvation process. Analysis of photofragmentation branching ratios yield estimated ligand binding energies of the order of 800 and 950 cm^?1 (≈9.5 and 11.5 kJ mol^?1) for N₂ and CH₄, respectively. The interpretation of the experimental data is supported by ab initio calculations for C₆H₇⁺? Ar and C₆H₇⁺? N₂ at the MP 2/6‐311 G(2df,2pd) level. Both the calculations and the spectra are consistent with weak intermolecular π bonds of Ar and N₂ to the C₆H₇⁺ ring. The astrophysical implications of the deduced IR spectrum of C₆H₇⁺ are briefly discussed.     

An ab initio calculation of symmetric bending and stretching vibrational states of the H3O+ and D3O+ ions

Calculations are reported for the symmetric bending and stretching vibrational states of H₃O⁺ and D₃O⁺ including coupling between these two modes. The calculations were carried out by using a potential surface calculated by the SCF CI method and expressed in terms of symmetric internal coordinates. The transition energy of the ν₂ (1^? ← 0⁺) inversion mode is found to be 985 cm^?1, which is comparable to the experimental value of 954.417 cm^?1 observed by Haese and Oka. The calculated inversion doubling of the lowest state is 51 cm^?1.