Volume 103, Issue 5, 01 August 1995
Index of content:

Identification of the 4pσ_{ u } ^{1}Π_{ u } Rydberg state of O_{2}
View Description Hide DescriptionNew high‐resolution measurements of the O_{2}photoabsorption cross section in the 1147–1155 Å region are presented. The observation of three previously‐unreported narrow lines in a band near 1148 Å has enabled unambiguous assignment of the band to a ^{1}Π_{ u }←X ^{3}Σ_{ g } ^{−} transition which gains strength through a spin‐orbit interaction with the upper state of a ^{3}Π_{ u }←X ^{3}Σ_{ g } ^{−} transition appearing at 1153 Å. Other lines in the 1148 Å band are broadened by predissociation through a heterogeneous interaction with a nearly energetically coincident ^{1}Δ_{ u } level. The states, labelled h ^{1}Π_{ u }, F ^{3}Π_{ u } and i ^{1}Δ_{ u }, are predominantly of 4pλ Rydberg molecular orbital configurations although there are indications that the Π_{ u } states interact strongly with valence states of the same symmetry.

The visible excitation spectrum of jet cooled NO_{2}: The chaotic behavior of a set of ^{2} B _{2} vibronic levels
View Description Hide DescriptionWe have observed a set of 350 ^{2} B _{2} vibronic levels of NO_{2} in the 16 000–19 360 cm^{−1}energy range by the laser induced fluorescence(LIF) technique combined with a supersonic jet. This work extends (i.e., a larger energy range) and improves (i.e., a better detection threshold) our previous study [J. Chem. Phys. 95, 5701 (1991)]. 42 new ^{2} B _{2} vibronic levels have been detected in this range where 159 vibronic levels were previously observed. In the 16 580–19 360 cm^{−1}energy range we estimate that the 315 observed levels represent 96% of the existing ^{2} B _{2} levels. The correlation properties of this large and almost complete set of 315 ^{2} B _{2} vibronic levels have been analyzed. We present the next neighbor distribution, the Σ^{2}(L), and Δ_{3}(L) statistics, the Fourier transform (FT) of the stick spectrum with constant intensities (‖FT‖^{2}), and the intensity distribution. The results of these analyses confirm the chaotic behavior of the ^{2} B _{2} vibronic levels in this energy range: there are strong level repulsion, long range correlations and a Porter–Thomas intensity distribution. The correlation ‘‘hole’’ observed in the ‖FT‖^{2} of the stick vibronic spectrum is close to the one of the Gaussian orthogonal ensemble (GOE). However we have found a significant deviation from completely chaotic behavior (GOE type). Two peaks in the FT indicate recurrences (periods of 50 and 150 fs) i.e., periodic motions. We conclude that chaos is established within the ^{2} B _{2} vibronic levels of NO_{2}, after few hundred femtoseconds.

Imaging of wave functions and potentials from time‐resolved and frequency‐resolved fluorescence data
View Description Hide DescriptionImaging of the amplitude and phase of time‐evolving wave functions and excited‐state potentials, using fluorescence data, is performed. The method relies on the use of both frequency‐resolved and time‐resolved fluorescence to reduce the problem of wave function imaging to a solvable set of linear algebraic equations. The potential inversion is performed by a new formula which expresses an excited state potential in terms of the ground state potential, the transition frequencies, and the transition‐dipole matrix elements, whose sign is shown to be derivable from the spectral line strengths.

The vibrational spectra of molecular ions isolated in solid neon. XII. HCl^{+}, (HCl)^{+} _{2}, ClHCl^{−}, and O_{2}⋅⋅HCl^{+}
View Description Hide DescriptionWhen a Ne:HCl or a Ne:DCl sample is codeposited at approximately 5 K with a beam of neon atoms that have been excited in a microwavedischarge, the infrared spectrum of the solid deposit includes the fundamental absorption of HCl^{+} or DCl^{+}, which appears about 1% below the corresponding gas‐phase band center. Another absorption, intermediate between the fundamentals of HCl and of HCl^{+}, is contributed by an HCl‐stretching fundamental of (HCl)^{+} _{2}. Among the important anion species present in the solid is ClHCl^{−}, infrared absorptions of which are identified. Charge delocalization is sufficiently reduced in solid neon, compared to the heavier rare gases, that ion production from HCl does not occur at or below 10.2 eV. The electric field of the ions trapped in solid neon inhibits the rotation of HCl and leads to the appearance of a prominent HCl Q‐branch absorption. In the presence of traces of oxygen, the O_{2}⋅⋅HCl^{+} complex is stabilized, as evidenced by the appearance of the OO‐ and HCl‐stretching absorptions of that species. The two O atoms are equivalent or nearly equivalent in the complex. It is suggested that photoexcitation of O_{2}⋅⋅HCl^{+} leads to charge exchange, producing O^{+} _{2} and HCl, with a threshold near 370 nm.

The permanent electric dipole moment of PtO, PtS, PtN, and PtC
View Description Hide DescriptionThe permanent electric dipole moments of the ground, and the low‐lying excited electronic states of platinum monocarbide, PtC, platinum monoxide, PtO, and platinum monosulfide, PtS, were measured using a molecular beam optical Stark spectroscopic scheme. The determined values were (in Debye): PtO(X ^{3}Σ^{−}) 2.77(2); PtO(A ^{1}Σ^{+}) 1.15(4); PtS[X(Ω=0)] 1.78(2); PtS[B(Ω=0)] 0.54(6); PtC(X ^{1}Σ^{+}) 0.99(5); and PtC(A ^{1}Π) 2.454(3). These results, along with the previous results for PtN(X ^{2}Π_{1/2}) 1.977(9); PtN(d ^{4}Π_{1/2}) 1.05(9) [J. Chem. Phys. 102, 643 (1995)], are used as a basis for a discussion of the nature of the electronic states.

Photoion rotational distributions from near‐threshold to deep in the continuum
View Description Hide DescriptionWe present the first measurements of ion rotational distributions for photoionization over an extended range [0≤E _{ K }≤200 eV for N_{2} (2σ^{−1} _{ u }) and 3≤E _{ K }≤125 eV for CO (4σ^{−1})]. The N_{2} ion rotational distributions are seen to change dramatically over this energy range, indicating that characteristically molecular behavior of the photoelectron persists far from ionization threshold. In addition, the N_{2} and CO results show a strikingly different dependence on energy. Although differences are expected due to the absence of a center of symmetry in CO, detailed calculations reveal that this behavior arises from the presence of Cooper minima in the 2σ_{ u }→kσ_{ g } continuum in the case of N_{2} and from an f‐wave shape resonance in the 4σ→kσ channel in CO. Agreement between measured and calculated ion rotational distributions is excellent. The N_{2} results are also compared with electron bombardment ionization data. This comparison demonstrates that previous interpretations of electron bombardment data are prone to errors.

A modification of the Gaussian‐2 approach using density functional theory
View Description Hide DescriptionThe quadratic configuration interaction calculation in the Gaussian‐2 second‐order Mo/ller–Plesset perturbation theory approach, G2(MP2), is replaced by a coupled‐cluster (CC) singles and doubles calculation including a perturbational estimate of the triples excitations. In addition, the self‐consistent‐field (SCF) and MP2 geometry optimizations and SCF frequency calculation in the G2(MP2) approach are replaced by a density functional theory geometry optimization and frequency calculation [using the Becke three parameter hybrid functional with the Lee–Yang–Parr non‐local correlation functional (B3LYP)] in the proposed G2(B3LYP/MP2/CC) approach. This simplification does not affect the average absolute deviation from experiment, but decreases the maximum error compared with the G2(MP2) approach. The G2(B3LYP/MP2/CC) atomization energies are compared with those obtained using the B3LYP approach, and the G2(B3LYP/MP2/CC) model is found to be more reliable, even if the B3LYP calculations are performed using a large basis set.

Nonadiabatic energies of the ground state of the hydrogen molecule
View Description Hide DescriptionPossible sources of residual errors in the theoretical energies of the hydrogen molecule are investigated. Nonadiabatic corrections are computed for all bound, J≤10 X ^{1}Σ_{ g } ^{+} ro‐vibrational states of the six isotopic hydrogen molecules. The new results improve significantly the overall agreement with accurate experimental transition frequencies. In order to estimate the convergence errors of the Born–Oppenheimer energies generalized James–Coolidge functions with powers of the interelectronic distance, r _{12}, up to 6 are used and the precision of the computations is increased. Except for the equilibrium separation, R=1.4011 bohr, the obtained potential energy curve is lower by a few thousandths of a wave number than any other reported variational result. This lowers the v=0 vibrational levels by 0.009 cm^{−1} and results in a dissociation energy of H_{2}, D _{0}=36118.069 cm^{−1}.

Molecular dynamics simulation of the zero‐field splitting fluctuations in aqueous Ni(II)
View Description Hide DescriptionThe fluctuations in the zero‐field splitting (ZFS) of the electronic ground state of the Ni(II) ion in aqueous solution have been studied through a combination of ab initio quantum chemistry calculations, including spin–orbit coupling, and molecular dynamics (MD) simulations. The ab initio calculations for the hexa‐aquo Ni(II) complex have been used to generate an expression for the ZFS as a function of the distortions of the idealized T _{ h } symmetry of the complex along the normal modes of E _{ g } and T _{2g } symmetries. The MD simulations provide a 200 ps trajectory of motions in the system consisting of a Ni(II) ion and 255 water molecules, which is analyzed in detail in terms of both the structure and the dynamics in the solvation sphere around the ion. The time correlation function (TCF) for the ZFS interaction has been computed and analyzed. It is found that the mean square amplitude of the ZFS is about 5.2 cm^{−1}, which is about twice the estimates based on the model‐dependent analysis of the proton spin relaxation in the aqueous Ni(II) solution. The decay of the ZFS TCF is found to occur on a subpicosecond time scale, which is much faster than earlier proposals. It is also interesting to note, for comparison with theoretical models, that the ZFS tensor is far from cylindrical and that the normal modes of E _{ g } och T _{2g } symmetry both contribute to its fluctuations.

Variational discrete variable representation
View Description Hide DescriptionIn developing a pseudospectral transform between a nondirect product basis of spherical harmonics and a direct product grid, Corey and Lemoine [J. Chem. Phys. 97, 4115 (1992)] generalized the Fourier method of Kosloff and the discrete variable representation (DVR) of Light by introducing more grid points than spectral basis functions. Assuming that the potential energy matrix is diagonal on the grid destroys the variational principle in the Fourier and DVR methods. In the present article we (1) demonstrate that the extra grid points in the generalized discrete variable representation (GDVR) act as dealiasing functions that restore the variational principle and make a pseudospectral calculation equivalent to a purely spectral one, (2) describe the general principles for extending the GDVR to other nondirect product spectral bases of orthogonal polynomials, and (3) establish the relation between the GDVR and the least squares method exploited in the pseudospectral electronic structure and adiabatic pseudospectral bound state calculations of Friesner and collaborators.

Estimating full configuration interaction limits from a Monte Carlo selection of the expansion space
View Description Hide DescriptionFull configuration interaction (FCI) calculations are useful as benchmarks for approximate techniques used in quantum chemistry: they are indeed the desired goal for all energy and wave function calculations in that they are the best solution to the Schrödinger equation within a finite basis Ansatz. Application of the method is limited due to the rapid increase in the number of configurations as the basis set size is increased. Many means have been applied to limit the number of terms in the expansion with the best known method being the singles and doubles expansion CI(SD). A Monte Carlo algorithm is proposed here whereby a CI expansion is allowed to expand by randomly including new terms which interact with those terms already present in the expansion. Solution of the variational problem is then performed for these randomly chosen configurations and a selection criterium for the resulting CI coefficients is applied. Repeated application of this method allows for estimates of the FCI energy. Calculations for the water molecule are performed to demonstrate the method.

Isomer dependence of HF vibrational frequency shift for Ar_{ n }HF (n=4–14) van der Waals clusters: Quantum five‐dimensional bound state calculations
View Description Hide DescriptionThe HF vibrational frequency shifts for Ar_{ n }HF van der Waals (vdW) clusters with n=4–14 are predicted to be strongly isomer‐specific, providing distinct spectroscopic signatures for different cluster isomers. This represents an extension of our recent studies of the size dependence of the vibrational frequency shift for Ar_{ n }HF clusters [J. Chem. Phys. 101, 6359, 10 181 (1994)]. The HF vibrational frequency shifts calculated for the two or three lowest‐energy isomers of each cluster size considered differ by at least a couple of wave numbers. Their relative magnitudes directly reflect the number of Ar atoms that each Ar_{ n }HF isomer has in the first solvation shell around HF. The calculations are performed on pairwise additive intermolecular potential energy surfaces constructed from spectroscopically accurate Ar–Ar and anisotropic Ar–HF potentials. In the frequency shift calculations, the Ar_{ n } subunit is treated as rigid, frozen in the geometry of one of the global or local Ar_{ n }HF minima found previously by simulated annealing [J. Chem. Phys. 100, 7166 (1994)]. The 5D coupled intermolecular vibrational levels of what is now effectively a floppy Ar_{ n }–HF dimer, are calculated highly accurately by the quantum 5D bound state methodology which is described in detail. The 5D vdW vibrational zero‐point energy of the Ar_{ n }HF cluster affects significantly the energy gap between various isomers.

Density‐functional calculation of core‐electron binding energies of C, N, O, and F
View Description Hide DescriptionThe unrestricted generalized transition‐state model using B88/P86 functional with Dunning’s cc‐pV5Z basis set, found to be an excellent method of calculating core‐electron binding energies (CEBEs), was further applied to many more molecules, some of which contain atoms from the third period. Estimation of relativistic corrections has also been refined. The average absolute deviation of over 50 calculated CEBEs from experiment is 0.30 eV before inclusion of approximate relativistic corrections (C _{rel}), and 0.23 eV after adding C _{rel}. Those molecules with observed CEBEs served to confirm our procedure, whereas the other cases provided our prediction of CEBEs.

Computation of interior eigenstates of large matrices using the quasiadiabatic evolution of instantaneous eigenvectors
View Description Hide DescriptionA two‐stage iterative scheme is proposed to handle a central problem of molecular dynamics, the computation of interior eigenvalues of large Hamiltonian matrices. The proposed method involves an initial propagation process for a time‐dependent wave operator which is then inserted in an iterative process (recursive distorted wave approximation or single cycle method) to yield the exact stationary wave operator. The merits of the wave operator formalism for quasiadiabatic propagation are analyzed, and possible improvements such as the use of partial adiabatic representations and spectral filters, are outlined. The proposed algorithm is applied to the test case of two coupled oscillators with variable coupling strength, and yields accurate results even with small switching times.

Conditions for invariance of molecular magnetic properties in Landau gauge transformations
View Description Hide DescriptionGeneral constraints for invariance of magnetic properties in a gauge transformation are analyzed. Sum rules relative to the transformation from Coulomb to Landau gauges are examined in particular. Numerical tests for hydrogen fluoride, water, ammonia, and methane molecule have been carried out in large basis set calculations, using random‐phase approximation. The conditions for invariance are severe conditions for accuracy of variational molecular wave functions.

Theoretical study of the Cu(H_{2}O) and Cu(NH_{3}) complexes and their photolysis products
View Description Hide DescriptionEquilibrium geometries, binding energies, harmonic vibrational frequencies, infrared intensities, and isotopic shifts have been calculated for the Cu(H_{2}O) and Cu(NH_{3}) complexes and their photolysis products [HCuOH, CuOH, HCu(NH_{2}), and Cu(NH_{2})] using Kohn–Sham theory with a gradient‐corrected nonlocal potential. Cu(H_{2}O) and Cu(NH_{3}) are weakly bound systems, their binding energies are estimated to be 3.7 and 12.0 kcal/mol, respectively. The HCuOH and HCu(NH_{2}) insertion products are 2.4 and 6.3 kcal/mol less stable than Cu(H_{2}O) and Cu(NH_{3}), whereas H+CuOH and H+Cu(NH_{2}) lie 49.7 and 58.0 kcal/mol above Cu(H_{2}O) and Cu(NH_{3}), respectively. The calculated harmonic frequencies agree remarkably well with matrix‐isolation infrared data; the agreement is always within 50 cm^{−1} (30 cm^{−1} on average) and the mean relative deviation from the experimental frequencies is 2.8%. The calculated isotopic frequency shifts are in close agreement with experiment, except for normal modes, where two or more types of vibrations are coupled. For these modes, the sum of the isotopic shifts is accurately reproduced. The sensitivity of the calculated properties to the numerical integration grid has been investigated and it is found that the grid usually used for main‐group molecules has to be extended to obtain numerically stable vibrational properties for transition metal‐ligand systems.

Electronic structures of new π‐conjugated cyclic polymers with quinoid structures
View Description Hide DescriptionGeometrical and electronic structures of new π‐conjugated five‐membered ring polymers were theoretically investigated. These polymers are analogous to heterocyclic polymers, but adopt as bridging groups ≳CH_{2}, ≳CF_{2}, ≳SiH_{2}, ≳SiF_{2}, ≳C=CH_{2}, ≳C=O and ≳C=S moieties instead of heteroatoms. The ground‐state geometries of the polymers were predicted to be quinoid from semiempirical band calculations with AM1 Hamiltonian. The electronic properties of these systems were obtained using the modified extended Hückel method. The calculated band gaps (E _{ g }) were analyzed in terms of geometrical relaxations and electronic effect of the bridging groups using the equation of E _{ g }=ΔE ^{δr }+ΔE ^{1–4}+ΔE ^{el}. The effect of bond‐length alternation (ΔE ^{δr }) amounts to 1.1–1.4 eV for the aromatic forms and 1.8–1.9 eV for the quinoid forms of the polymers. The interactions (ΔE ^{1–4}) between C1 and C4 atoms of the cis‐PA type backbone tend to decrease the band gaps of the aromatic forms and to increase the gaps of the quinoid forms as much as 0.2–0.5 eV, depending on the size of a bridging atom. It is found that the electronic effect (ΔE ^{el}) of these bridging groups is quite small compared to that found in heterocyclic polymers such as polythiophene, polypyrrole, and polyfuran. ΔE ^{el} of ≳CF_{2}, ≳SiH_{2}, and ≳SiF_{2} bridging groups are negligible and that of the other groups amounts to 0.3–1.0 eV. Therefore, the band gaps of these systems almost correspond to the ΔE ^{δr } values which arise from the bond‐length alternations, except the case of the polymers with ≳C=O and ≳C=S bridging groups whose π* orbitals strongly interact with the π system of the polymeric backbone.

Extension of Gaussian‐2 (G2) theory to bromine‐ and iodine‐containing molecules: Use of effective core potentials
View Description Hide DescriptionBasis sets have been developed for carrying out G2 calculations on bromine‐ and iodine‐containing molecules using all‐electron (AE) calculations and quasirelativistic energy‐adjusted spin–orbit‐averaged seven‐valence–electron effective core potentials (ECPs). Our recommended procedure for calculating G2[ECP] energies for such systems involves the standard G2 steps introduced by Pople and co‐workers, together with the following modifications: (i) second‐order Mo/ller–Plesset (MP2) geometry optimizations use polarized split‐valence [31,31,1] basis sets for bromine and iodine together with 6‐31G(d) for first‐ and second‐row atoms; (ii) single‐point higher‐level energies are calculated for these geometries using our new supplemented bromine and iodine valence basis sets along with supplemented 6‐311G and McLean–Chandler 6‐311G bases for first‐ and second‐row atoms, respectively; and (iii) first‐order spin–orbit corrections are explicitly taken into account. An assessment of the results obtained using such a procedure is presented. The results are also compared with corresponding all‐electron calculations. We find that the G2[ECP] calculations give results which are generally comparable in accuracy to those of the G2[AE] calculations but which involve considerably lower computational cost. They are therefore potentially useful for larger bromine‐ and iodine‐containing molecules for which G2[AE] calculations would not be feasible.

Structural characterization of an electrolytic aqueous solution, LiCl⋅6H_{2}O, in the glass, supercooled liquid, and liquid states
View Description Hide DescriptionUsing the technique of hydrogen and deuterium substitution, the structure of water in concentrated lithium chloride aqueous solutions (LiCl⋅6H_{2}O) is explored for the liquid, supercooled liquid, and glass states. It is found that changes in structure between the glass and supercooled states are minor, but that a major change in water structure occurs as the supercooled liquid is heated above the temperature of peritexy of the penta‐hydrate (T _{ p }=207 K). In particular the 4.4 Å peak in the OO pair correlation function of pure water, which is normally viewed as indicating tetrahedral short range coordination in water, is absent in the LiCl solution at the same temperature, but reappears strongly in the glass and supercooled states. Corresponding changes occur in the HH and OH correlation functions. In addition, correlations appear to extend nearly twice as far in the glass and supercooled liquid, compared to the room temperature liquid.

Medium and long range correlations in the electrolyte LiCl⋅4H_{2}O: Transition to the glass regime
View Description Hide DescriptionNew data on the structure of water in the aqueous system LiCl⋅RH_{2}O, with R=4, are presented for the liquid, supercooled liquid, and glass states. The results are compared to an earlier study of the system LiCl⋅6H_{2}O [J. Chem. Phys. 103, 1886 (1995)]. Many of the qualitative trends seen for R=6 are similar for R=4, but there is evidence that the water structure is even more severely disrupted than for R=6. In the liquid state the distribution functions appear to be dominated by the packing of hydrated ions, rather than by hydrogen bonding forces. The latter partly reassert themselves in the supercooled and glass states. H/D isotope substitution throws some light on the first structure diffraction peak (FSDP) at 0.5 Å^{−1} which is correlated with the nonhydrogenated components. This peak is not therefore the signature of long range water concentration fluctuations, but must be due to some weak periodicity in the underlying longer range order.