Index of content:
Volume 62, Issue 9, 01 May 1975

MCSCF calculations for six states of NaH
View Description Hide DescriptionA b i n i t i o multiconfiguration self‐consisting‐field calculations are reported for the energies, electronic wavefunctions, and one‐electron properties of the X ^{1}Σ^{+}, A ^{1}Σ^{+}, B ^{1}Π, a ^{3}Σ^{+}, b ^{3}Π, and c ^{3}Σ^{+} states of NaH over a wide range of internuclear distances. In these calculations, only the two valence electrons are correlated. Three states (X ^{1}Σ^{+}, A ^{1}Σ^{+}, and b ^{3}Π) were found to be bound, with the following dissociation energies and internuclear separations (with known experimental values in parentheses): D _{ e } (X ^{1}Σ^{+}) = 1.878 (2.12±0.20) eV, R _{min} (X ^{1}Σ^{+}) = 3.609 (3.566) bohr; D _{ e } (A ^{1}Σ^{+}) = 1.203 (1.41±0.20) eV, R _{min} (A ^{1}Σ^{+}) = 6.186 (6.062) bohr; and D _{ e } (b ^{3}Π) = 0.109 eV, R _{min} (b ^{3}Π) = 4.458 bohr.

Rotation–vibrational analysis for three states of NaH and NaD
View Description Hide DescriptionWe have carried out a rotation–vibrational analysis for the X ^{1}Σ^{+}, A ^{1}Σ^{+}, and b ^{3}Π states of NaH and NaD using accurate a b i n i t i o calculated potential curves. The calculated values of B _{ e }, α_{ e }, R _{ e }, ω_{ e }, and ω_{ e } x _{ e } (with known experimental values in parentheses) are NaH X ^{1}Σ^{+} : B _{ e } = 4.748 (4.886) cm^{−1}, α_{ e } = 0.126 (0.129) cm^{−1}, R _{ e } = 3.625 (3.562) bohr, ω_{ e } = 1183.17 (1172.2) cm^{−1}, and ω_{ e } x _{ e } = 21.23 (19.72) cm^{−1}; NaD X ^{1}Σ^{+} : B _{ e } = 2.475 (2.5575) cm^{−1}, α_{ e } = 0.0474 (0.0520) cm^{−1}, R _{ e } = 3.624 (3.565) bohr, ω_{ e } = 826.60 (826.10) cm^{−1} and ω_{ e } x _{ e } = 9.44 cm^{−1}; NaH b ^{3}Π : B _{ e } = 3.533 cm^{−1}, α_{ e } = 0.853 cm^{−1}, R _{ e } = 4.202 bohr, ω_{ e } = 419.39 cm^{−1} and ω_{ e } x _{ e } = 50.25 cm^{−1}; NaD b ^{3}Π: B _{ e } = 1.763 cm^{−1}, α_{ e } = 0.265 cm^{−1}, R _{ e } = 4.294 bohr, ω_{ e } = 311.95 cm^{−1} and ω_{ e } x _{ e } = 28.68 cm^{−1}. The anomalous behavior of the B _{ v }′s and ΔG _{ v+1/2}′s of the A ^{1}Σ^{+} state is satisfactorily reproduced by these calculations: for NaH, B _{ v } (max ) = 1.9717 (1.941) cm^{−1} at v = 6 (6) and ΔG _{ v+1/2} (max) = 381.37 (360.3) cm^{−1} at v = 9 (8); for NaD, B _{ v } (max) = 1.0274 (1.012) cm^{−1} at v = 8 (8) and ΔG _{ v+1/2} (max) = 275.34 (260.22) cm^{−1} at v = 13 (12). The wavefunctions obtained were also used to calculate average electric dipole moments resulting in the following values (for the lowest rotation–vibrational states): for NaH, μ_{ e } (X ^{1}Σ^{+}) = 2.674 a.u., μ_{ e } (A ^{1}Σ^{+}) = 0.189 a.u., and μ_{ e } (b ^{3}Π) = 0.158 a.u., for NaD, μ_{ e } (X ^{1}Σ^{+}) = 2.668 a.u., μ_{ e } (A ^{1}Σ^{+}) = 0.178 a.u., and μ_{ e } (b ^{3}Π) = 0.163 a.u.

Transition moments, band strengths, and line strengths for NaH
View Description Hide DescriptionElectronic transition moments, as functions of internuclear separation, are calculated for the A ^{1}Σ^{+} → X ^{1}Σ^{+}, B ^{1}Π → X ^{1}Σ^{+}, B ^{1}Π → A ^{1}Σ^{+}, c ^{3}Σ^{+} → a ^{3}Σ^{+}, b ^{3}Π → a ^{3}Σ^{+}, and b ^{3}Π → c ^{3}Σ^{+} transitions in NaH from a b i n i t i o molecular wavefunctions. Reduced line strengths, band strengths, band oscillator strengths, and band Einstein coefficients are calculated for the observed A ^{1}Σ^{+} → X ^{1}Σ^{+} transition, and are compared to experimental band intensities. Also calculated are Franck–Condon factors and R centroids, and the effects of various approximations used in treating experimental data are analyzed.

Calculation of the far‐wing line broadening of the sodium D line induced by collisions with hydrogen atoms
View Description Hide DescriptionUsing a b i n i t i o potential curves and electronic transition moments we have calculated the far wings of the sodiumD line emission spectrum broadened by collisions with hydrogen atoms. A classical–statistical model was used for this calculation. The calculated spectrum has two satellite peaks, one at 9683 cm^{−1}, whose intensity diminishes with increasing temperature, and one at 21 641 cm^{−1}, whose intensity increases with increasing temperature.

Frozen core approximation, a pseudopotential method tested on six states of NaH
View Description Hide DescriptionA pseudopotential formulation, more appropriately called the frozen core approximation (FCA), is presented in detail. This FCA is tested by performing MCSCF calculations on the six low lying states, X ^{1}Σ^{+}, A ^{1}Σ^{+}, a ^{3}Σ^{+}, c ^{3}Σ^{+}, B ^{1}Π, and b ^{3}Π of NaH. The results obtained are compared with those of an analogous previous MCSCF calculation on these states without the use of FCA, i.e., with all orbitals optimized. It is found that energies are obtained rather accurately with FCA; however, calculated molecular properties are affected more strongly and the shapes of the potential curves appear to be distorted somewhat by FCA. It is argued that no pseudo‐ or model‐potential calculation can give errors less than FCA unless the potential is made valence shell dependent. This, however, would be analogous to a full calculation, and the savings due to a pseudopotential approximation would be lost.

Graph theory and molecular orbitals. XII. Acyclic polyenes
View Description Hide DescriptionA graph‐theoretical study of acyclic polyenes is carried out with an emphasis on the influence of branching on several molecular properties. A definition of branching is given and several branching indices are analyzed. The case of polyenes without a Kekulé structure is discussed briefly. The main conclusions are: (a) thermodynamic stability of conjugated polyenes decreases with branching, but (b) reactivity, in general, increases with branching.

Normal coordinate analysis of the optically active vibrations (k=0) of crystalline magnesium orthosilicate Mg_{2}SiO_{4} (forsterite)
View Description Hide DescriptionA normal coordinate analysis for the vibrations of the olivine type crystal Mg_{2}SiO_{4} (forsterite) in the limit k=0 has been carried out to investigate the group behavior of the SiO_{4} ion and also to identify the ’’external’’ modes. The crystal FG matrix method of Shimanouchi e t a l. is used with a potential function which combines general valence and short range force constants. Calculations have also been done for the ^{26}Mgisotope. A dipole–dipole interaction model has been introduced through stretch–stretch interaction to account for the correlation field splitting of ν_{3b } of the SiO_{4} group. Conclusions are also drawn about the nature of different vibrational modes.

Statistical mechanics of interfacial properties of polyatomic fluids. I. Surface tension
View Description Hide DescriptionGeneral expressions for the surface tension and bulk pressure are derived for a semiclassical polyatomic fluid. The Fowler–Kirkwood–Buff approximation is used to reduce the general surface tension formula to a simple form and to show that the dipole–dipole interactions account for about half of the surface tension of low vapor pressure water.

EPR investigation of Eu^{2+} in orthorhombic sites of RbBr
View Description Hide DescriptionAccurate spin‐Hamiltonian parameters describing the electron paramagnetic resonance spectra of Eu^{2+} in orthorhombic sites of RbBr single crystals have been determined at 77 and 300 K for the first time. Absolute signs of the spin‐Hamiltonian parameters were determined for sample temperatures less than 4.2 K. The sign of the spin‐Hamiltonian parameter b _{2} ^{0} was found to be positive and therefore the same as that previously found for the same impurity in the isomorphic hosts of NaBr and KBr. We present a plot of the b _{2} ^{0} term vs lattice parameter for Eu^{2+} ions in the alkali bromide series with results which should be noted in attempts to calculate theoretical^{8} S _{7/2} ground state splittings.

EPR discharge‐flow kinetics: The H + ClF_{3} reaction
View Description Hide DescriptionThe reaction of hydrogen atoms and chlorine trifluoride is studied directly by the discharge‐flowEPR technique over the temperature range of 243–313 K and total pressure range of 4–8 torr. Hydrogen atoms are produced by dissociation of molecular hydrogen in a microwavedischarge. Absolute rate constant data from 43 experiments at four temperatures yield the Arrhenius equation, log(k _{ex}/cm^{3} mol^{−1}⋅sec^{−1}) = (11.9±0.1) − (1470±560)/ϑ, where ϑ = 2.303 R T/J mol^{−1}. The experimental rate constant,k _{ex}, is interpreted as a lower bound for the reaction H+ClF_{3}→HF+ClF_{2}.

Electronic spectroscopy of t r a n s‐azomethane by electron impact
View Description Hide DescriptionThe electron impact excitation of t r a n s‐azomethane (i.e., t r a n s‐dimethyl diazine CH_{3}–N–N–CH_{3}) has been studied by both trapped electron (TE) and differential electron scattering (DES) techniques. The nature of the excited state in each of several transitions has been identified by the energy and angular dependences of the excitation cross section. Two previously unreported singlet→triplet transitions are observed with maxima at 2.75 and 4.8_{4} eV. Theoretical calculations on the parent compound, t r a n s‐diimide (H–N=N–H), suggest that these are the ? ^{1} A _{ g }→1 ^{3} B _{ g } (produced by excitation of an electron from an n _{+} molecular orbital to a π* molecular orbital) and the ? ^{1} A _{ g }→1 ^{3} B _{ u } (π→π*) transitions, respectively. The ? ^{1} A _{ g }→1 ^{1} B _{ g } (n _{+}→π*) transition is observed with a peak at 3.50 eV in the DES studies. A strong peak at 6.01 eV in the TE spectra appears as a weak shoulder in the DES studies and is interpreted as either a symmetry‐forbidden or Rydberg‐like singlet→singlet transition. Allowed singlet→singlet features overlap each other in the transition energy range from 6 to 10 eV. Peaks are seen in the DES spectra at 6.71, 7.8, and 9.5 eV and in the TE spectrum at 8.0 eV. Several significant differences between the TE and the DES spectra are analyzed on the basis of the different nature of the two experiments.

Shift of the emission band upon excitation at the long wavelength absorption edge. II. Importance of the solute–solvent interaction and the solvent reorientation relaxation process
View Description Hide DescriptionFluorescence and phosphorescence of quinine and its related compounds such as 6‐methoxyquinoline are found to exhibit a red shift when excitation is achieved at the long wavelength edge of the first absorption band, and this anomalous shift is investigated in detail. The anomalous shift is observed not only in room temperature fluorescence, but also in low temperature fluorescence and phophorescence. The term e d g e e x c i t a t i o n r e d s h i f t (EERS) is introduced. After various plausible interpretations we have suggested a logical mechanism for EERS. In the suggested mechanism, EERS is observed if the solvent reorientation relaxation rate is small compared with the emission rate, and the Franck–Condon solvation energy is reasonably large with respect to solvent orientation. All the experimental observations are satisfactorily interpreted within the framework of the suggested mechanism.

Breakdown of selection rules in the Raman spectra of KDP
View Description Hide DescriptionRaman spectra of A _{1} and B _{1} modes of KH_{2}PO_{4}single crystal are studied experimentally by varying the orientation of the crystal axes relative to the incident and scattered light directions. It has been found that the scattering intensities depend on the k vector of the scatteringphonons, thus invalidating the selection rules in the first order Raman scattering.

Angular distributions, kinetic energy distributions, and excitation functions of fast metastable oxygen fragments following electron impact on CO_{2}
View Description Hide DescriptionDissociative excitation of CO_{2} by electron impact has been studied using the methods of translational spectroscopy and an angular distributionanalysis. Earlier time‐of‐flight studies revealed two overlapping spectra, the slower of which has been attributed to metastable CO(a ^{3}π) fragments. The fast peak is the focus of the present study. Threshold energy,angular distribution, and improved time‐of‐flight measurements indicate that the fast peak actually consists of five overlapping features. The slowest of the five features (1) is found to consist of the metastable O(^{5} S) produced by predissociation of a Σ_{ u } ^{+} state of CO_{2} into O(^{5} S) + CO(a ^{3}π). Oxygen Rydberg fragments originating directly from a different Σ_{ u } ^{+} state are believed to make up the next fastest feature (2). Mechanisms for producing the three remaining features are discussed.

Computation of atomic many‐electron integrals using a Markov chain generated Monte Carlo method
View Description Hide DescriptionA Monte Carlo method for evaluating complicated many‐electron integrals is described. The process utilizes a Markov chain which properly chooses configurations of electrons in accordance with the form of Ψ chosen. The method inherently reduces the variance compared to the classical Monte Carlo method. Some explicit examples are shown for a four electron system.

Coherence in multilevel systems. I. Coherence in excited states and its application to optically detected magnetic resonance in phosphorescent triplet states
View Description Hide DescriptionA method for monitoring the time development of the coherent components in a multilevel system using an observable which can measure only the relative populations in the levels is presented. Using standard density matrix formulation, expressions are obtained for the conventional and this new ’’probe’’ pulse method. For several of the more common coherence experiments, optically detected magnetic resonance of molecular excited triplet states is used to illustrate the principles. The effect of coherent averaging of relaxation terms in the spin Hamiltonian is discussed and specifically applied to excited triplet states in zero field. Finally, experimental results of coherence measurements are presented along with a detailed description of the apparatus and methods used.

The reduction of nucleotides by ionizing radiation: Uridine 5′ phosphate and cytidine 3′ phosphate
View Description Hide DescriptionAnions formed by the addition of an electron to the uracil base were observed in single crystals of the barium salt of uridine 5′ phosphate x‐irradiated at 4.2 °K. The hyperfine coupling tensor for the C_{6}–H proton was deduced from ENDOR measurements; the principal values are −59.12, −32.92, and −16.24 MHz. Similar measurements were made on single crystals of cytidine 3′ phosphate. The principal values for the C_{6}–H proton hyperfine coupling in the anion formed on the cytosine base are −59.26, −33.98, and −14.68 MHz.

The statistical treatment of the dielectric constant of a nonpolar gas
View Description Hide DescriptionIt is shown that the statistical treatment of Isihara for the dielectric second virial coefficient B of nonpolar gases is equivalent to that of Buckingham and Pople. The negative value of B for helium, determined theoretically by Isihara, is due to an error in his calculation.

Interpretation of c i s‐hexatriene absorption spectrum. The Duschinsky effect
View Description Hide DescriptionThe differences between the uv absorption spectra of t r a n s‐ and c i s‐hexatriene are interpreted in terms of the coupling between the ground statenormal modes in the electronic excited state, i.e., the Duschinsky effect. The model Hamiltonian is derived and its eigenvalues and eigenvectors are found by means of the standard perturbation theory. The spectra of both molecules are simulated at the computer. A good agreement with experiment is found. Some approximations involved are discussed and the possibilities of further experimental verification are pointed out.

Potential energy surfaces for H + Li_{2} → LiH + Li ground state surface from large scale configuration interaction
View Description Hide DescriptionA b i n i t i oelectronic structure calculations have been performed to determine the HLi_{2}potential energy surface. A contracted Gaussian basis set was employed: H(5s 1p/3s 1p), Li(8s 3p/4s 3p). In addition to selfconsistent‐field (SCF) wavefunctions, full configuration interaction (CI) was carried out for the three valence electrons. For general geometry (point group C _{ s }), the CI included 5175 configurations. For the diatomic molecules Li_{2} and LiH, these methods yield dissociation energies within 5 kcal/mole of experiment, and accurate spectroscopic constants are also predicted. The minimum on the HLi_{2} CI potential surface occurs for an isosceles triangle structure with r (H–Li) = 1.72 Å and on LiHLi bond angle of 95°. This minimum lies 22.4 kcal/mole below the separated products LiH + Li. The linear HLiLi minimum is much shallower, lying only 4.2 kcal/mole below the products. The much simpler single configuration SCF calculations yield qualitatively similar results. Furthermore, these features of the surface are quite analogous to those predicted for F + Li_{2} by Pearson and coworkers. The angular dependence of the surface between the C _{2v } and C _{∞v } extremes is discussed. The ’’electron jump’’ from covalent HLi_{2} to ionic H^{−}Li_{2} ^{+} is seen to be much more gradual than was the case for FLi_{2}. The electronic structure is described using a natural orbital analysis of the most important configurations in the wavefunction.