Ground State Potential Energy Curves Research Articles

Ab initio and molecular-dynamics studies on rare gas hydrides: Potential-energy curves, isotropic hyperfine properties, and matrix cage trapping of atomic hydrogen

Ground-state potential-energy curves and distance dependent isotropic hyperfine coupling (IHC) constants for ground-state H–RG (=Ne, Ar, Kr, Xe) are obtained at CCSD(T) (coupled-cluster single double triple) and MP4(SDQ) (fourth-order Moller–Plesset single double quadruple) levels, respectively, with an augmented basis set aug-Stuttgart (RG)/aug-cc-pVQZ (H). The obtained Rm and ε are for NeH: 3.45 Å and −1.36 meV; ArH: 3.65 Å and −3.48 meV; KrH: 3.75 Å and −4.32 meV; XeH: 3.90 Å and −5.22 meV. The computed pair potentials are utilized in classical molecular-dynamics simulations of H–RG lattices. Along the classical trajectory, the many-body perturbation on the H atom hyperfine coupling constant is computed by pair-wise addition of the individual RG–H contributions obtained from the present quantum-chemical calculations. The computed IHC shifts are compared with electron paramagnetic resonance (EPR) spectra obtained in low-temperature matrix isolation experiments. For most cases this theoretical treatment agrees very well with the experiment and confirms the previous site assignments. However, for H–Xe, the theory would suggest stability of both interstitial Oh and substitutional sites, whereas only one site is observed in the experiment. Based on the present calculations this site can be assigned as a nearly undistorted substitutional site.

Relativistic all-electron ab initio calculations of CsHg potential energy curves including spin-orbit effects

We report a relativistic all electron ab initio calculation of the ground and excited state potential energy curves of the CsHg molecule along with a determination of the spectroscopic parameters. Spin-orbit and kinematical relativistic effects were taken into account using the Douglas–Kroll-transformed no-pair Hamiltonian.

Separability of spin–orbit and correlation energies for the sixth-row main group hydride ground states

The spin–orbit energy contributions to the ground state potential energy curves for the main group hydrides, TIH through AtH are estimated by differencing multireference, single promotion, configuration interaction (MRS-CI) energies with and without the spin–orbit operator. The spin–orbit contributions are then summed into the energies determined at the λ−s MRSD-CI level (both single and double promotions). The agreement between the resultant curves and those obtained using intermediate coupling MRSD-CI is within 1.2 kcal/mol over a range of internuclear separations. This suggests that, contrary to previous arguments, spin–orbit coupling and correlation energies are very nearly separable for the main group hydride ground states. Furthermore, the computational effort expended by this separate evaluation is up to 12 times less than that for a comparable intermediate coupling CI. The analysis of some properties of these hydrides indicates that bond length shifts due to spin–orbit coupling are small (0.03 Å) while harmonic vibrational frequencies decrease by up to 9%. Dissociation energies are predicted to change considerably in the presence of the operator in agreement with previous findings.

Erratum to “Accurately solving the electronic Schrödinger equation of atoms and molecules using explicitly correlated ( r12-) MR-CI: the ground state potential energy curve of N 2” : [Chem. Phys. Lett. 283 (1998) 253

Erratum to “Accurately solving the electronic Schrödinger equation of atoms and molecules using explicitly correlated ( r12-) MR-CI: the ground state potential energy curve of N 2” : [Chem. Phys. Lett. 283 (1998) 253

Valence and excited states ofLiH−

Valence and excited dipole-bound states of the ${\mathrm{LiH}}^{\mathrm{\ensuremath{-}}}$ anion are calculated with the recently developed electron-attachment equation-of-motion coupled-cluster technique. It is found that the first dipole-bound state of ${\mathrm{LiH}}^{\mathrm{\ensuremath{-}}}$ corresponds to the second dissociation channel ${\mathrm{LiH}}^{\mathrm{\ensuremath{-}}}{\ensuremath{\rightarrow}\mathrm{Li}}^{\mathrm{\ensuremath{-}}}{(}^{1}S)+\mathrm{H}{(}^{2}S).$ The second (excited) dipole-bound state of ${\mathrm{LiH}}^{\mathrm{\ensuremath{-}}}$ is below the neutral ground-state potential energy curve only for some range of the Li-H internuclear distance. This state appears at bond lengths larger than $\ensuremath{\approx}2.0\AA{}$ and decays at Li-H distances longer than \ensuremath{\approx}4.2 \AA{}, where the dipole moment of LiH becomes smaller than the critical value of 2.5 D. The adiabatic electron affinity of LiH calculated at the coupled-cluster level with the iterative inclusion of all single, double, and triple excitations and a large atomic natural orbital basis set is 0.327 eV, almost matching the recently obtained experimental value of $0.342\ifmmode\pm\else\textpm\fi{}0.012\mathrm{eV}.$

Accurately solving the electronic Schrödinger equation of atoms and molecules using explicitly correlated ( r12-)MR-CI: the ground state potential energy curve of N 2

The recently proposed MR-CI ansatz which contains terms linear in the interelectronic distances ( r 12) is used to compute the potential energy curve of N 2 by means of r 12-MR-ACPF. The computed spectroscopic constants with the respective errors, e.g. Δ D e (−0.2 kcal/mol), Δ R e (+1×10 −4 Å) and Δ ω e (+2 cm −1), are found to be in excellent agreement with values derived from experimental spectra. With only a moderate computational effort, we reach accuracies which are probably out of reach of present day (traditional) CI-methods and computers.

Epstein-Nesbet second-order perturbation treatment of dynamical electron correlation and ground state potential energy curve of Cr 2

The Cr 2 potential energy curve is obtained by treating the dynamical correlation energy terms using a CI procedure based on determinants, equivalent to multi-reference second-order perturbation theory with the Epstein-Nesbet partition of the Hamiltonian. One of the advantages of this treatment is that the level shifts required for the equivalent Møller-Plesset type of treatment to eliminate intruder states and avoid divergences in the ground state second-order energy expression, are not required. Moreover, by truncating the reference space, the dynamical and the non-dynamical correlation energy is included also for the 3s, 3p electrons. The potentials are compared to experiment and to the most accurate theoretical potential curves in the literature.

TheG0u+(61P1)–X0G+Excitation and Fluorescence Spectra of Hg2Excited in a Supersonic Jet

TheG0u+(61P1)–X0G+excitation and fluorescence spectra of Hg2van der Waals molecules, produced in a pulsed free-jet supersonic expansion beam crossed with a pulsed dye-laser beam, were studied using Ar as the carrier gas. A well-resolved vibrational structure of theG0u+←X0g+excitation spectrum was recorded, as well as the isotopic structures of the vibrational components. A Condon internal diffraction pattern in theG0u+→X0g+fluorescence band, emitted upon the selective excitation of the v′ = 39 vibrational component, was also observed and confirmed the assignments derived from the analysis of the isotopic structure. Analyses of the spectra yielded molecular constants for both states, as well as information on the ground state potential energy curve. The results are compared with those obtained from other experiments and from theoretical calculations.

All-electronXαself-consistent-field calculations of relativistic effects in the molecular properties ofTl2,fPb2, andBi2molecules

Relativistic effects in the binding energy, the bond length, and vibrational frequencies of ground-state potential-energy curves are investigated for ${\mathrm{Tl}}_{2}$,${\mathrm{Pb}}_{2}$, and ${\mathrm{Bi}}_{2}$ by performing relativistic and nonrelativistic all-electron Dirac-Fock-Slater ${\mathrm{X}}_{\mathrm{\ensuremath{\alpha}}}$ calculations. Wave functions from numerical solutions of Dirac(Hartree)-Fock-Slater equations for atoms are taken as basis sets. A variationally consistent approximation for the direct Coulomb potential has been used for efficiently obtaining accurate potential energy curves. Our calculations confirm that the spin-orbit effect weakens the binding of the 6p-element molecules ${\mathrm{Tl}}_{2}$,${\mathrm{fPb}}_{2}$, and ${\mathrm{Bi}}_{2}$.

Ground- and excited-state properties of neutral and anionic selenium dimers and trimers.

Ab initio molecular-orbital methods using a newly constructed large, flexible basis set of the atomic-natural-orbital type and extensive treatments of electron correlation were used to accurately predict the ground-state potential-energy curves of ${\mathrm{Se}}_{2}$ and ${\mathrm{Se}}_{2}^{\phantom{\rule{0ex}{0ex}}\mathrm{\ensuremath{-}}}$. In addition, the potential curves of low-lying electronically excited states of the ${\mathrm{Se}}_{2}^{\phantom{\rule{0ex}{0ex}}\mathrm{\ensuremath{-}}}$ anion, which are coupled to the ground state through the electronic dipole operator, are determined. Calibration of the accuracy expected for the employed theoretical models is achieved by calculations on electronically excited states of neutral ${\mathrm{Se}}_{2}$, for which accurate experimental data are available. Besides reporting accurate predictions for spectroscopic constants, electron affinities, and transition matrix elements, particular emphasis is laid on the use of the computed dimer potential-energy curves for interpreting the recently investigated peculiar optical properties of diatomic selenium species embedded in solid host matrices. Further, the equilibrium geometries and relative stabilities of the ${\mathit{C}}_{2\mathit{v}}$ and ${\mathit{D}}_{3\mathit{h}}$ forms of the neutral ${\mathrm{Se}}_{3}$ cluster, the electron affinity of ${\mathrm{Se}}_{3}$, and the low-lying electronic states of ${\mathrm{Se}}_{3}^{\mathrm{\ensuremath{-}}}$ have been investigated theoretically.

Photodissociation mechanism of MgN 2+ ion-molecule complex. An ab initio MO study

Potential energy curves (PECs) for the dissociation of the MgN 2 + complex have been calculated by means of the ab initio MO method for the ground (X 2∑) and low-lying excited ( 2 Π and 2 2∑) states. The PECs for the ground and the first excited states were bound with respect to both dissociation limits, Mg +( 2S) + N 2 and Mg +( 2P) + N 2 , respectively. A linear structure was obtained as the most stable form of the complex on the ground state PEC. The CI calculations showed that the first excitation energy ( 2 Π ← X 2∑) was red-shifted relative to that for free Mg +( 1P ← 2 S ) transition owing to the formation of an excited state complex with a π interaction between Mg +(3p) and N 2( π NN ). The PEC for the second excited state (2 2∑) has a strongly repulsive shape because of a σ ∗ interaction between Mg +(3p) and N 2(nσ). The photodissociation and NN bond activation mechanisms of the MgN 2 + complex are discussed on the basis of the PEC characteristics.

Ground State Properties of Hg2. 2. A Quantum Monte Carlo Study

We have carried out variational and pure diffusion quantum Monte Carlo calculations for the Hg atom and the Hg2 molecule. In the case of the Hg atom we have calculated valence correlation energies for relativistic and nonrelativistic 20-valence-electron pseudopotentials. The results are compared with those of conventional ab initio methods. For the Hg2 molecule we have used a 2-valence-electron pseudopotential together with a core-polarization potential. The resulting ground state potential energy curve agrees well with curves derived from configuration interaction calculations. Jastrow factors were found to be an efficient method to describe electron correlation in these systems.

Cr 2 in density-functional theory: approximate spin projection

The ground-state potential energy curve of Cr 2 is examined using three density-functional exchange-correlation approximations: the local spin-density approximation (LSDA), the gradient-corrected BLYP approximation, and the recent B3P86 approximation incorporating a small admixture of exact exchange. An attempt is made in this work to project, at least approximately, the pure singlet energy from the usual Cr 2 antiferromagnetic broken-symmetry state. The effect of this approximate spin projection is significant. Only the B3P86 functional is found to give good agreement with experiment after spin projection. Moreover, we obtain a double-well potential energy curve which has been suggested by other theoretical (non-DFT) studies and even by experiment.

Reaction-path potential and vibrational frequencies in terms of curvilinear internal coordinates

We present a general formulation that allows physically intuitive curvilinear internal coordinates to be used for the calculation of potential energy expansions and generalized normal-mode vibrational frequencies in reaction-path calculations. The reaction path is defined, as usual, as the minimum-energy path in the mass-scaled Cartesian coordinate system, and curvilinear coordinates are used for vibrational frequency calculations at nonstationary points. The method is well adapted for use in variational transition state theory with semiclassical multidimensional tunneling (VTST/MT) approximations to calculate thermal rate constants. We present VTST/MT calculations for five reactions, H+H2→H2+H, O+H2→OH+H, CH3+H2→CH4+H, H+O2→HO2, and Cl+HBr→HCl+Br, to illustrate the use of the new curvilinear coordinates, and we compare the results to calculations employing rectilinear coordinates. We make detailed comparisons not only of the calculated rate constants but also of the vibrationally adiabatic ground-state potential energy curves and bound-state vibrational frequencies as functions of the reaction coordinate.

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.

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.

Observation of a “new” quadrupole transition at 7.7 eV in CF 3Cl by momentum-transfer-resolved electron energy loss spectroscopy

A “new” non-dipole electronic transition at 7.7 eV in CF 3Cl has been observed using momentum-transfer-resolved electron energy loss spectroscopy at 2.5 keV impact energy. The generalized oscillator strength (GOS) of this transition has been determined and found to have a shape characteristic of a quadrupole transition with a maximum at ≈1 au of momentum transfer. Using the results from an ab initio GOS calculation and a single-excitation configuration interaction calculation, we show that this transition corresponds to the 1E ← 1A 1 (LUMO ← HOMO) transition with a very small computed dipole transition moment. In particular, this transition is related to an electronic transition from a non-bonding Cl 3p orbital (HOMO) to an antibonding pσ * CCl orbital (LUMO). The nature of the orbitals involved in the transition, together with its small calculated dipole transition moment, strongly suggests that this transition is dominated by quadrupole interaction. The calculated potential energy diagram along the CCl bond direction also shows that a vertical transition from the 1A 1 ground-state potential energy curve accesses the repulsive region of the 1E excited-state curve, suggesting that this quadrupole transition may lead to dissociation of the CCl bond.

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.

AM1 and X‐ray Studies of the Structures and Isomerization Reactions of Indigo Dyes

AbstractAM1‐SCF and AM1‐SDCI calculations have been carried out for indigo and three conformers of N,N′1‐diacetylindigo in their cis and trans configurations. The molecular structure of trans‐ N,N′1‐diacetylindigo was determined by X‐ray diffraction. The calculated ground‐state data obtained within the SCF approximation (relative energies, structural parameters) are in excellent agreement with the corresponding experimental values. Potential energy curves (PEC) for the isomerization reaction cis/trans in several electronic states were obtained from AM1‐SDCI calculations. For N,N′1‐diacetylindigo the ground state PEC has a maximum at a torsion angle about the central CC bond of 90°, whereas the S1‐ and T11‐state PEC's show minima at the corresponding geometry. For indigo itself significant barriers to the photoisomerization in the S1‐ and T11‐excited states are predicted because of increased NH…OC hydrogen bonding. The results provide an explanation for the phototropic behaviour of N,N′1‐diacetylindigo and the photostability of indigo. The calculated enthalpies of activation for the isomerization process cis → trans in the ground state compare well with available experimental data, thus rendering feasible the prediction of the thermal stability of cis isomers not yet synthesized.