Ground State Potential Energy Curves Research Articles

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.

The potential energy curves of the X 1Σg+ ground states of Mg2 and Ca2 using the interacting correlated fragments model

We report ground-state potential energy curves for Mg2 and Ca2 calculated in a large Slater-type basis using the interacting correlated fragments (ICF) model of Liu and McLean. Within the framework of the model, we study convergence of the potential curves with respect to the amount of intrafragment electron correlation introduced into each of the interacting atoms. The ICF model requires localized orbitals and the convergence rate can be affected dramatically by the localization choice; we illustrate and discuss this effect. Successful application of the ICF model requires careful treatment of the basis set superposition error and we discuss this. Our best calculations with four electrons correlated in Mg2 give De=458.8 cm−1 compared with an estimated lower limit for the four correlated electron calculation of 464 cm−1 and an experimental value of 429.6 cm−1. The bulk of the difference between calculation and experiment is attributed to intrafragment core–valence correlation effects which decrease the dissociation energy by nearly 30 cm−1. In parallel calculations on Ca2, our computed four correlated electron De is 1236 cm−1 compared to the experimental 1095.4 cm−1, showing that core–valence electron correlations are responsible for decreasing the dissociation energy by approximately 149 cm−1.

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.

Polynomial expressions for rydberg-klein-rees curves of diatomic covalent molecules

The ground-state potential-energy curves for 17 diatomic covalent molecules were calculated using a recent version of the functional method. We consider a point at infinity to improve the long-range potential behaviour. For all these molecules the results obtained are satisfactory.

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.

Theoretical investigations of small multiply charged cations. III. NeN2+

First-order configuration-interaction calculations based on 4–6 σ, 1–2 π complete active space self-consistent-field reference wave functions are reported for the potential-energy curves of the 21 lowest-lying electronic states of NeN2+ which dissociate into (2P)Ne++(3P)N+ or (2P)Ne++(1D)N+. Using the same complete active space self-consistent-field SCF reference function, second-order configuration-interaction wave functions have been calculated for the X2Π ground state of NeN2+. At this level the potential minimum lies 4.57 eV above the (3P)N++(2P)Ne+ dissociation limit and there is a barrier to dissociation of 0.94 eV. All other states of NeN2+ are either repulsive, or exhibit a flat potential curve at some closer interatomic distance. In addition, the X 3Σ− ground-state potential-energy curve of single charged NeN+ was computed at the complete active space SCF + second-order configuration-interaction level. The dissociation energy is predicted as De =0.47 eV at re =3.30 a0. Bonding in NeN2+ and NeN+ is discussed in terms of donor–acceptor interactions between Ne and N2+ or N+, respectively. [For paper II of this series see W. Koch and G. Frenking, J. Chem. Phys. 86, 5617 (1987).]

Isoelectronic analogs of phosphorus nitride: remarkably stable multiply charged cations

The structures and stabilities of PN and its 27 isoelectronic analogues, CS, SiO, BCl, AlF, BeAr, MgNe, Sn{sup +}, PO{sup +}, CCl{sup +}, SiF{sup +}, BAr{sup +}, AlNe{sup +}, SO{sup 2+}, NCl{sup 2+}, PF{sup 2+}, CAr{sup 2+}, SiNe{sup 2+}, OCl{sup 3+}, SF{sup 3+}, NAr{sup 3+}, PNe{sup 3+}, FCl{sup 4+}, OAr{sup 4+}, SNe{sup 4+}, FAr{sup 5+}, ClNe{sup 5+}, and ArNe{sup 6+}, have been examined by ab initio molecular orbital theory. The CASSCF/6-311G(MC)(d) level was used to determine the ground-state potential energy curves and spectroscopic constants for the 28 diatomic systems. Equilibrium structures were also obtained with the 6-311G(MC)(d) basis set at the MP3 and ST4CCD levels, and dissociation energies were determined at the MP4/6-311 + G(MC)(2df) and MP4/6-311 + G(MC)(3d2f) levels. For the neutral and monocation analogues of PN, the calculated equilibrium geometries (at MP3/6-311G(MC)(d)) and dissociation energies (at MP4/6-311 + G(MC)(3d2f)) are in very good agreement with available experimental values. All the dication analogues of PN, namely, SO{sup 2+}, NCl{sup 2+}, PF{sup 2+}, CAr{sup 2+}, and SiNe{sup 2+}, are predicted to be experimentally observable species. Of these, the SO{sup 2+}, NCl{sup 2+}, and CAr{sup 2+} dications are calculated to be kinetically stable species, with large barriers associated with the exothermicmore » charge-separation reactions, while the PF{sup 2+} and SiNe{sup 2+} dications are predicted not only to be kinetically stable but also to be thermodynamically stable species.« less

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.

Ab initio study including electron correlation of the ground state (X 1Σ +) of SiS

Although many experimental investigations of silicon sulfide, SiS, have appeared in the literature, only a very few ab initio studies of this molecule, which is of much interest to astrophysicists, have been reported. In this paper, we present results from a set of large-scale, multireference configuration interaction calculations on the ground-state potential energy curve of SiS. We present a comparison of various spectroscopic constants derived from our calculations with those from experiment. Additionally, we present a functional representation of the dipole moment of this molecule and compare it with experiment and another semiempirically derived functional form.

MC SCF study of potential curves of small radicals

A series of calculations of the ground state potential energy curves of some diatomic hydride radicals (CH, BH +, NH and AlH +) has been carried out in the framework of the MC SCF method. Although the configuration space and basis sets used are not very large, the calculated spectroscopic constants are in relatively good agreement with experimental data.

The interaction potential and diffusion coefficients of sodium in neon

We have calculated the ground state potential energy curve of the Na-Ne interaction using the method of Tang and Toennies. It is the sum of the SCF repulsion and the properly damped dispersion energies. The spectroscopically determined well location is used to select the leading dispersion coefficients between its upper and lower bounds. The resulting potential is compared with previous experimental and theoretical potentials. Diffusion coefficients are calculated from the present as well as previous potentials. Compared with experiment, results from the present potential are in best agreement.

Nonlocality in the density-functional description of bonding in Li2, N2, O2, and F2.

The fully self-consistent implementation of the nonlocal-density functional of Langreth and Mehl has been used in conjunction with the augmented Gaussian method to calculate the potential-energy curves and dissociation energies of N/sub 2/, Li/sub 2/, O/sub 2/, and F/sub 2/. The nonlocal functional gives ground-state potential-energy curves in very good agreement with experiment. We compare these nonlocal results with other local-density calculations, and examine the effect of nonlocal-potential self-consistency on the dissociation energy.

Pseudopotential calculations on the ground state of the alkaline-earth monohydride ions

The ground state potential energy curves of alkaline-earth monohydride ions have been investigated. A pseudopotential formalism including a corepolarization potential has been used. For the valence correlation energy a local spin density functional with corrections for self interaction has been employed. Dissociation energies, bond lengths and vibrational frequencies are reported, and so are the vertical and adiabatic ionization potentials of the alkali and alkaline-earth monohydrides, which were obtained using the same theoretical model. A discussion and a comparison with other values, both theoretical and experimental, are also included.

Ground state properties of alkali and alkaline–earth hydrides

The ground state potential energy curves of alkali (LiH to CsH) and alkaline–earth monohydrides (BeH to BaH) have been calculated. A pseudopotential formalism including a core-polarization potential has been used. For the valence correlation energy, two different methods, the local spin-density functional and the configuration interaction with single and double excitations, have been employed. Dissociation energies, bond lengths, vibrational frequencies, anharmonicity constants, and dipole moments are reported. The agreement with experimental values, where available, is very good. A discussion and a comparison with other theoretical values, at different levels of approximation, are also included.

Potential energy curves for the (ArH)+ and (NeH)+ systems from the interplay of theory and experiments

The ground state potential energy curves for protons interacting with Ar and Ne atoms are determined by the analysis of new, highly accurate measurements of the elastic differential cross sections at a laboratory collision energy of 14.8 eV. Accompanying theoretical results from SCF-CI calculations are used as starting points to generate analytic potentials that are able to fit all available experimental cross sections for both systems. The final results provide the full shape of the potential curves and give the best existing fit to the measured cross sections for elastic scattering at several energies from 2eV to 30eV.

On the direct determination of constrained pure state one-electron density matrices: II. A modified algorithm and its applications

An algorithm recently proposed by us for the direct determination of pure state one-electron density matrices (P) under externally imposed constraints has been remodelled. The modified algorithm is applied to the construction of ground state potential energy curve of lithium hydride molecule usingknown values of dipole moments of LiH at various internuclear distances as theexternal constraint. The equilibrium internuclear distances (R c) is seen to be unaffected by the constraint, but the force constant improves remarkably. The relevant features of the constrained density vis-a-vis those of the unconstrained one are analyzed revealing some of the improved features of the constrained density.

Numerical MC SCF and CI calculations of the ground-state potential energy curve of N 2

The numerical procedure of McCullough is used in calculations of Hartree-Fock and MC SCF wavefunctions for ground state of N 2. The latter are derived using the complete set of 18 spin and symmetry adapted configurations in the space of MOs that arise from 2p atomic orbitals. An increase in dissociation energy of 0.17 eV is observed when compared to MC SCF calculations in a large basis of Slater-type functions and the same set of configurations. Integrals involving the numerical MC SCF MOs are used in CI calculations in which substitutions involving the 1s and 2s electrons are included. The increase in dissociation energy due to numerical versus basis set valence CI is 0.08 eV. Spectroscopic constants and molecular quadrupole moments are reported.

The ground state potential energy. Curve of Be 2: Is the MBPT approach capable of predicting it?

The X 1Σ g + ground state potential energy curve of the beryllium dimer is studied by using different many-body perturbation theory methods. A careful examination of the dependence of the calculated data on the basis set choice and the completeness of the perturbation expansion through the given order has been carried out. It is shown that the many-body perturbation theory is capable of dealing with the weak interaction potential in the beryllium dimer provided a complete well-balanced scheme is used and the basis set is large and flexible enough. In spite of some near-degeneracy effects in Be 2: the complete fourth-order perturbation results calculated with a large (spdf) GTO basis set are very close to the corresponding variational data. The complete fourth-order treatment predicts the existence of a minimum at = 4.8 au with the dissociation energy of = 1.9 kcal/mole. Some small discrepancies between our perturbation results and very recent experimental data are within the limits of accuracy of best theoretical calculations which can be currently carried out for a system of the size of Be 2. Moreover, the existence of a long-range van der Waals minimum on the Be 2 potential energy curve is not confirmed by the present perturbation theory results.

Spin-coupled VB theory of molecular electronic structure. Ground and low-lying 1Σ+ states of CH+

The spin-coupled VB theory is applied to the ground and low-lying 1Σ+ states of CH+. Using 500 spin-coupled structures, the calculated values of the spectrosopic constants for the ground states De(eV)=4.14 (4.26), ωe(cm−1)=2845 (2858), Re(Å) =1.135 (1.131); experimental results are given in parentheses. The form of the ground state potential energy curve is very close to the MCSCF-CI curve of Green et al. [Phys. Rev. A 5, 1614 (1972)], and similarly the excited states are very similar to those obtaind by MCSCF-CI methods by Saxon et al. [J. Chem. Phys. 73, 1873 (1980)]. The only exception is in the 4 1Σ+ state below R=3.5a0 where there is an avoided intersection with a Rydberg state. At least for small systems of this kind, the spin-coupled VB approach is capable of the same level of accuracy as the best MCSCF-CI methods, but uses an order of magnitude fewer functions. Each state in the spin-coupled VB calculation is dominated by one or two structures. This provides the wave function with much visuality, but without the usual attendant loss in accuracy.