State Potential Energy Curves Research Articles

Vibronic structure in the optical absorption spectra of phenylene vinylene oligomers: a joint experimental and theoretical study

We present a joint experimental and theoretical investigation of the optical absorption spectra of phenylene vinylene oligomers. The vibronic structure, which is clearly observed in the experimental spectra, is well described by a simple model based on the Frank-Condon approximation but requires the use of at least two effective modes coupled to the electronic states. Using a fitting procedure, we deduce the displacement of the 1Bu excited state potential energy curve relative to that of the ground state and compare it to the results of recent Hartree-Fock semi-empirical calculations. Such information is of prime importance in the description of the frequency-dependent linear as well as nonlinear optical responses.

Vibronic structure in the optical absorption spectra of phenylene vinylene oligomers: a joint experimental and theoretical study

We present a joint experimental and theoretical investigation of the optical absorption spectra of phenylene vinylene oligomers. The vibronic structure, which is clearly observed in the experimental spectra, is well described by a simple model based on the Frank-Condon approximation but requires the use of at least two effective modes coupled to the electronic states. Using a fitting procedure, we deduce the displacement of the 1B u excited state potential energy curve relative to that of the ground state and compare it to the results of recent Hartree-Fock semi-empirical calculations. Such information is of prime importance in the description of the frequency-dependent linear as well as nonlinear optical responses.

Valence states and a universal potential energy curve for covalent and ionic bonds

The relations between the diatomic spectroscopic constants and a novel parameter D VS, the valence state dissociation energy, are investigated. An energy scaling by D VS, instead of the spectroscopic D e, allows the formulation of a universal three-parameter valence state potential energy curve (VS-PEC). The second and higher derivatives at the equilibrium distance, R e, are simple functions of a valence state parameter z = k e R e 2/ D VS. The analysis of the VS-PECs of 25 single and multiple bonded molecules covering the whole range of polarity reveals a far greater similarity near the minimum than previously reported. In comparison with the Morse and Rydberg potentials, the accuracy of the calculated vibration-rotation coupling and anharmonicity constants is improved by an order of magnitude.

A comparison of finite difference and finite basis set Hartree-Fock calculations for the ground state potential energy curve of CO

The Hartree-Fock ground state potential energy curve for the carbon monoxide molecule is calculated using both the finite difference and the finite basis set methods. The results of calculations performed at ten internuclear separations are reported and a comparision is made of the calculated potential energy curves over the range of internuclear separations, 1.970-2.330 a0, around the experimental equilibrium value. Potential energy curve constants and spectroscopic constants are determined.

Multiphoton studies of jet-cooled Xe2 near the Xe*5d[5/2]3 state: Characterization of the ground and excited state potential curves

The two-photon resonant, three-photon (2+1) ionization spectra of jet-cooled mXenXe, at energies near the Xe* 5d[5/2]03 state, are reported. A new progression has been observed and is attributed to transitions from the van der Waals ground state, X 1Σ+g(0+g), through bound vibrational levels of an excited state of gerade symmetry. The analysis of some 26 closely spaced vibronic bands and isotope effects provides information on the excited and ground state potential energy curves. The vibrational quantum number of the lowest frequency band near 82 539.1 cm−1 is assigned to v′=6±1. For v′=6 this leads to molecular constants Te′ ≂ 82 514.9 cm−1, ωe′ ≂ 5.7955 cm−1, and ωexe′ ≂ 0.07491 cm−1. The upper state can be described by a Morse potential with dissociation energy De′ ≂ 112.10 ± 0.05 cm−1 and internuclear separation Re′ ≂ 5.51 ± 0.03 Å. This is consistent with assignment to a Rydberg molecular state of either the B 2Π1/2g or D 2Σ+1/2g ion core. At the Xe 1S0+Xe* 5d[5/2]03 threshold the molecular spectrum terminates and continuum absorption is evidenced by a rise and fall in the fragment ion yield. The direct determination of the dissociation limit for the excited state is used to derive the ground state dissociation energy De″≂ 196.32 ± 0.05 cm−1.

A study of the chemiionization reactions of Ca, Sr and Ba with O 2(X 3Σ −g)

Chemielectron and chemiion spectra resulting from the reactions of effusive beams of Ca, and Sr and Ba (in their ground 1S states) with ground state molecular oxygen O 2(X 3Σ − g) have been recorded using electron spectroscopy and mass spectrometry. The chemielectron spectra are similar for all three reactions exhibiting a strong near-zero energy band and another band at higher electron energies. The chemiion spectra show O + 2, M + and M 2O + 2 as the major ions. The total ion current as well as the individual ion intensities, have been recorded as a function of the extraction potential on the reaction cell. The results obtained indicate that the metal oxide dimer ion is the primary chemiion, formed via an associative ionization reaction of a metal atom with a long-lived metal superoxide intermediate MO* 2. A two state potential energy curve model is proposed for the M+MO* 2 reaction to explain the shape of the experimental electron distribution.

Collision-induced dissociation of oriented CO + ions. Probing potential energy curves by ion collision spectrometry

Translational energy spectra of C + and O + fragments produced in the collision-induced dissociation of ground state CO + ions have yielded kinetic energy release distribution functions. These are compared with theoretical simulations that have been carried out by reflecting the probability distribution of the zeroth vibrational state of the 2Σ state onto various low-lying excited state potential energy curves of the CO + molecular ion which have been computed using contemporary ab initio molecular orbital techniques.

Optical control of molecular dynamics: Molecular cannons, reflectrons, and wave-packet focusers

We consider the control of molecular dynamics using tailored light fields, based on a phase space theory of control [Y. J. Yan et al., J. Phys. Chem. 97, 2320 (1993)]. This theory enables us to calculate, in the weak field (one-photon) limit, the globally optimal light field that produces the best overlap for a given phase space target. We present as an illustrative example the use of quantum control to overcome the natural tendency of quantum wave packets to delocalize on excited state potential energy curves. Three cases are studied: (i) a ‘‘molecular cannon’’ in which we focus an outgoing continuum wave packet of I2 in both position and momentum, (ii) a ‘‘reflectron’’ in which we focus an incoming bound wave packet of I2, and (iii) the focusing of a bound wave packet of Na2 at a turning point on the excited state potential using multiple light pulses to create a localized wave packet with zero momentum. For each case, we compute the globally optimal light field and also how well the wave packet produced by this light field achieves the desired target. These globally optimal fields are quite simple and robust. While our theory provides the globally optimal light field in the linear, weak field regime, experiment can in reality only provide a restricted universe of possible light fields. We therefore also consider the control of molecular quantum dynamics using light fields restricted to a parametrized functional form which spans a set of fields that can be experimentally realized. We fit the globally optimal electric field with a functional form consisting of a superposition of subpulses with variable parameters of amplitude, center time, center frequency, temporal width, relative phase, and linear and quadratic chirp. The best fit light fields produce excellent quantum control and are within the range of experimental possibility. We discuss relevant experiments such as ultrafast spectroscopy and ultrafast electron and x-ray diffraction which can in principle detect these focused wave packets.

Ground and excited states of benzil: A theoretical study

The ground and low-lying excited state potential energy curves of benzil have been studied. The ground state geometry is fully optimized by the AM1 method. The excited states are calculated by using the CNDO/S-CI method. The calculations confirm that benzil in the ground state has a skewed conformation whereas the first excited singlet and triplet states of this molecule are trans-planar. The geometry relaxation in the excited states of benzil agrees well with the experimental findings. The absorption and emission bands of benzil have been compared with the observed bands. The dipole moments of the ground and excited states at some conformations are also reported. The effect of solvents on the electronic states of benzil has been studied using the continuum dielectric model.

Spectroscopy of the indium argon van der Waals complex: A high resolution study of the B 2Σ1/2←X2 2Π3/2 system

The InAr van der Waals complex has been characterized by high resolution laser induced fluorescence excitation spectroscopy. Six vibronic bands of the B 2Σ1/2←X2 2Π3/2 transition have been observed and five of these (v′,0), where v′=1–5, have been rotationally analyzed. Rydberg–Klein–Rees potential curves were constructed for the B 2Σ1/2 state using the rotational and vibrational constants determined from these spectra. Equilibrium bond lengths were determined for the B and X2 states and a dissociation energy was determined for the B state. The stronger bonding present in the B state is rationalized in terms of penetration of the argon atom into the diffuse 6s orbital of indium. Evidence is presented that the B state potential energy curve has a barrier at long range, due to Pauli repulsion, of ∼60 cm−1. An analysis of the hyperfine structure involving the 115In nucleus was made. It is concluded that the X2 state conforms to Hund’s coupling case aβ, whereas the B state conforms to case bβs. The extent of 6s–6p hybridization in the upper state was measured from hyperfine splittings and was used in conjunction with a simple electrostatic model to estimate the polarizability of the indium atom in the 6s 2S1/2 state. A value of 68(4) Å3 was obtained (1σ error).

All-electron Dirac—Fock—Slater SCF calculations of the Au 2 molecule

All-electron Dirac—Fock—Slater SCF clculations of the Au 2 molecule have been carried out using relativistic numerical atomic basis functions. In order to get a numerically accurate potential energy curve an improved calculation of the direct Coulomb potential has been taken into account. The relativistic effect inthe binding energy, the bond distance and the vibration frequency of the ground state potential energy curve have been studied in comparison with consistent non-relativistic results.

Ab initio effective Hamiltonian calculations on the valence states of SH and SH +

The second-order ab initio effective valence shell Hamiltonian of quasi-degenerate many-body perturbation theory has been used to determine the valence state potential energy curves of SH and SH +. The calculated spectroscopic constants of various valence states are in good agreement with those of experiments or configuration interaction calculations. The experimentally known B 2Σ state has been closely examined. And it is confirmed that the B 2Σ state be the Rydberg 2Σ − state as suggested by Hirst and Guest. This conclusion is readily drawn from the unique nature of the effective valence shell Hamiltonian, which can simultaneously determine the valence states of a molecule and its ions.

Potential curves and predissociation rates for the heavy species HBr 2+ and DBr 2+

Potential energy curves for states of HBr 2+ which correlate with the first six dissociation limits are calculated employing multi-reference configuration-interaction (MRD-CI) treatments in a Gaussian AO basis. Tunneling rates for the X 3Σ −, a 1Δ and b 1Σ + vibrational levels in HBr 2+ and DBr 2+ are calculated as well as predissociation rates for vibrational levels of the a 1Δ and b 1Σ + states resulting from spin-orbit interaction with the repulsive 3Π state. The spin-orbit coupling elements are evaluated explicitly by employing the Breit-Pauli operator and the MRD-CI wavefunctions.

An examination of a b i n i t i o results for the helium potential energy curve

Obtaining a ground state potential energy curve for helium has been the subject of much research involving empirical, semiempirical, and ab initio methods. In this work, we examine critically recent ab initio potentials proposed for this interaction with respect to their ability to predict certain accurate experimental data. To accomplish this analysis, potentials with a modified HFD-B form were fit to the recent theoretical work of van Duijneveldt and co-workers [Vos, van Lenthe, and van Duijneveldt, J. Chem. Phys. 93, 643 (1990) and Vos, van Mourik, van Lenthe, and van Duijneveldt (to be published)] and Liu and McLean (LM-2) [J. Chem. Phys. 91, 2348 (1989)]. A well depth (ε/k=10.92 K) and a separation at the minimum (rm=2.9702 A) consistent with both determinations were chosen and the properties of helium were calculated based on these potentials. These ‘‘mimic’’ potentials fail to predict the very low temperature 4He and 3He virials and one of them [Vos, van Maurik, van Lenthe, and van Duijneveldt (to be published)] also fails to predict the very accurate room temperature viscosity of Vogel [Ber. Bunsenges. Phys. Chem. 88, 997 (1984)]. For a potential which was fit as closely as possible to the LM-2 potential at its maximum suggested depth (ε/k=10.97 K), the virials are satisfactorily predicted. This compromise potential appears to be the best characterization of the He–He interaction in its ability to predict a variety of experimental data as well as being consistent with ab initio results.

Improved potential energy curves and dissociation energies for HF, DF and TF

We have constructed new hybrid potential energy curves for the ground states of HF, DF and TF based primarily on the experimentally based potentials of Coxon and Hajigeorgiou which include the isotopic dependence of the Born-Oppenheimer breakdown. For observed and unobserved quasibound states of HF and DF, we used these potentials and calculated quasibound energies and linewidths for various dissociation energies D e. Based on a comparison of calculated and observed line positions and widths, we determined improved D e values: for HF, D e = 49362 ± 5 cm −1 ( D 0 = 47311 cm −1); for DF, D e = 49346 ± 8 cm −1 ( D 0 = 47856 cm −1); for TF, D e = 49341 ± 9 cm −1 ( D 0 = 48093 cm −1.

Scattering of magnetically analyzed F (2P) atoms and their interactions with He, Ne, H2 and CH4

An improved source of a beam of fluorine atoms has been characterized by magnetic analysis of sublevels for F(2P). Ground state and lower lying excited state potential energy curves for the interaction of fluorine atoms with He, Ne, H2 and CH4 have been obtained from measurements of integral scattering cross sections at thermal energies. The results for the rare gas systems are discussed in connection with previous work on Ar, Kr, and Xe fluorides; those for the H2 and CH4 systems provide information of fine structure effects on the long range pan of entrance channels for reactive potential energy surfaces.

On the origin of metastable decay in Ar+2

Metastable Ar+2 (Ar+2 →Ar++Ar) has been observed in a double-focusing mass spectrometer from ions created by 70 eV electron bombardment of an Ar cluster beam. New ground and excited state potential energy curves have been calculated for Ar+2, and these have been used to show that metastability is due to radiative decay from the II(1/2)u state of the ion. It is shown that vertical (FC) ionization from neutral Ar2, with a vibrational temperature of approximately 30 K, results in a significant fraction of the ions occupying the II(1/2)u state. Detailed pressure dependent measurements show that collision-induced dissociation does not contribute to the observed Ar+ signal. The mean kinetic energy released to the Ar+ has been measured as 44 cm−1 in the center-of-mass frame, and calculations show that this value is consistent with the proposed mechanism.

Spectroscopy of the AlAr van der Waals complex: Rotationally resolved B 2Σ+←X 2Π1/2 electronic transitions

Rotationally resolved spectra were recorded for six bands of the AlAr B 2Σ+←X 2Π1/2 transition. Vibrational and rotational constants derived from these spectra were used to determine the upper and lower state potential energy curves. The accuracy of these potentials was assessed through calculations of the spectroscopic constants and Franck–Condon factors. Dissociation energies of D′e=440+35−8 cm−1 and D′e=180+40−10 cm−1 were obtained for the B and X states, respectively. The interaction between X 2Π1/2 and the low-lying A 2Σ+ state has been characterized by analysis of the ground-state lambda doublet splitting.

Potential energy surfaces for NbH+2 and MoH+2

Electronic structures, potential energy surfaces (PES), and some one-electron properties of 12 electronic states of the NbH+2 and MoH+2 ions are studied using the complete active space MCSCF (CASSCF) followed by multireference singles plus doubles configuration interaction (MRSDCI) calculations. The 3B2 ground state of NbH+2 (re =1.687 Å, θe =105.2°) is formed by the spontaneous insertion of Nb+(a3F, 4d35s1) into H2 while the lowest a 5F(4d35s1) state of the Nb+ ion has to surmount a barrier to 56 kcal/mol to insert into H2. The ground state (4B2) potential energy curve of MoH+2 contains two minima with geometries: re =1.637 Å, θe =37° and re =1.626 Å, θe =115.7°. The a4G state of Mo+ inserts spontaneously into H2 to form the 4B2 state of MoH+2, while the ground state (a 6S, 4d5) of the Mo+ ion has to overcome a barrier of 74 kcal/mol to form the linear 6Πu state of the MoH+2 ion. In the collinear mode of interaction, the ground state of Mo+ forms a van der Waals complex which is only 1.2 kcal/mol more stable than Mo++H2. In general, all the low-lying states of NbH+2 and MoH+2 are formed from the excited low-spin states of the metal ions. The PES of NbH+2 were found to be similar to the neutral surfaces confirming Smalley and coworkers experimental findings. The addition of f-type diffuse functions does not alter the geometries much. The vertical ionization potentials of NbH2 and MoH2 are calculated as 7.57 and 8.04 eV, respectively.

Pseudopotential investigation of some alkali metal molecules

AbstractThe effect of electron correlation on the results of pseudopotential calculations was examined using a simple analytical semiempirical pseudopotential and a correlated floating‐type one‐center wave function. Investigations were performed for the XH alkali metal hydride molecules (X  Na, K, Rb, Cs). The inclusion of the electron correlation in the ground state proved important for the calculation of the dissociation and ionization energies, but it is less significant for the determination of the equilibrium nuclear distances. The ground state potential energy curves are also determined.