Scaled AMO calculations on the hydrogen molecule II. The 1s σ 2p σ 1∑ state

A scaled version of the AMO method is applied to the 1sσ2pσ ¹∑ state of the hydrogen molecule. A method to extend the domain of the mixing parameter λ to the whole complex plane is described and applied in the present calculation. All the parameters introduced have been varied completely. A considerable improvement in the computed energy values is found for large internuclear separations R. The comparison between our potential energy curve and the accurate curve calcualted by Kolos and Wolniewicz is studied and, for example, for R = 12 a.u. the energy difference is only 18% of that for R = 2.43 a.u. The equilibrium separation is found to be 2.140 a.u. in poor agreement with 2.429 a.u. obtained by the previously mentioned authors. In the separated atom limit, the state under consideration does not dissociate into H⁺ + H^?, although the ionic character of the wave function is dominating in the region 3 ≦ R ≦ 8 a.u. The connections with earlier calculations and methods, especially the scaled version of the MO –LCAO approximation, are also pointed out and discussed.     

The MTXαR method. The determination and use of “molecular” α values in molecular multiple scattering Xα calculations

A semiempirical approach is used to fix the α value for use in the extraatomic regions in multiple-scattering (MS Xα) calculations which retain the muffin-tin treatment of the potential. Such a “molecular” α value for an atom is determined by requiring the corresponding homonuclear diatomic molecule to have its minimum at the experimentally determined equilibrium separation; hence they are called α _R. Molecular α _R values are determined for the ground state Li₂ and F₂ molecules and are tested in a calculation of the ground state LiF potential curve. We find a binding energy at the calculated equilibrium separation to be within 1% of the experimental value. The LiF curve based entirely on the ordinary atomic α values is substantially inferior. The present MT Xα _R approach appears to be competitive with others which are intended to improve the muffin-tin version of MS Xα calculations.     

Configuration-Interaction study of lower excited states of O2: Valence and rydberg characters of the two lowest 3Σu − states

Configuration-interaction calculations, with an extended basis, are carried out on the ground and lower excited states of O₂ and O₂⁺ at and near the equilibrium internuclear distance (R = 2.3 a.u.) of the ground state of O₂. Particular attention has been paid to the two lowest ³Σ_u^? states, and the mixing of the valence and Rydberg characters in these states are studied. The lowest ³Σ_u^? state is a Rydberg-type state for R < 2.3 a.u., but becomes valence-type for R ? 2.3 a.u. The second ³Σ_u^? state, which is 1.6 eV above the lowest ³Σ_u^? at R = 2.3 a.u., changes its character from Rydberg to valence, valence to Rydberg, and then to valence again when R increases from 1.9 to 3.1 a.u. Satisfactory agreement between the calculated and experimental vertical excitation energies is obtained.     

Interatomic potential for the X1Σ+g state of Be2

An extended geminal model has been applied to determine the interatomic potential for the X¹Σ⁺_g state Be₂. By adopting a [11s, 9p, 6d, 4f, 2g] contracted Gaussian-type basis, the following potential minimum parameters are obtained: R_e = 4.67 a.u. (4.63 a.u.) and D_e = 3.70 mH (3.82 ± 0.05 mH), experimental values in parentheses. A calculation with a nuclei-centered [9s, 7p, 4d, 2f, 1g] GTO basis plus two sets of bond-type function, each set comprising diffuse (2s, 2p, 2d, 2f, 1g) GTOs, yielded −3.79 mH as the value of the potential at R = 4.63 a.u. On the basis of an error analysis the best theoretical estimate of the binding energy is determined to be 3.83 ± 0.08 mH. The calculated value for the fundamental vibrational frequency is v_0→1 = 224.7 cm⁻¹ (exp. = 224 ± 3 cm). © 1996 John Wiley & Sons, Inc.     

Accurate calculations of dissociation energies of weakly bonded He<Subscript>2</Subscript> and Be<Subscript>2</Subscript> molecules by MRCI method

The He₂ and Be₂ ground state potential curves have been calculated by extrapolating to an infinite basis BSSE corrected MRCI total energies obtained with large Gaussian basis sets, large reference configuration spaces, and pseudo-natural molecular orbitals. The calculated D _e = 11.0031 K and R _e = 5.607 a.u. of He₂ are in an excellent agreement with D _e = 11.006 ± 0.004 K and R _e = 5.608 ± 0.012 a.u. obtained recently by SAPT with SM energy correction. The obtained Be₂ non-relativistic D _e = 822 cm⁻¹ and relativistically corrected D _e = 818 cm⁻¹ are in a good agreement with experimental D _e = 790 ± 30 cm⁻¹ and the value of 829 ± 64 cm⁻¹ obtained recently by a quantum Monte Carlo method.     

Long-range interaction between 1s and 2s or 2p hydrogen atoms

Long-range interaction energy between two hydrogen atoms has been computed in the second order of the perturbation theory. All states of the system arising when one of the atoms is in the 1s and the other in the 2s or 2p state have been considered. The energy represented by a series expansion in inverse powers of the internuclear distance, R, has been computed up to the terms in R^?8. The results are believed to give reliable interaction energies for R > 15 a.u. Accurate interaction energy for two ground-state hydrogen atoms has also been obtained up to the terms in R^?10. Results for the B′ ¹∑ state are employed to discuss the experimental ground-state dissociation energy of H₂, D₂, and HD. For H₂ all values of the dissociation energy obtained from various experimental absorption limits, by using the computed potential energy curve to separate off the effect of rotation, are shown to be satisfactorily consistent. The resulting total energy of H₂ is, however, higher than the most accurate theoretical value.     

Theoretical determination of the X 2Σ+ and A 2Π potentials of CsO using relativistic effective core potentials

Theoretical potential energy curves are computed for the X ²Σ⁺ and A ²Π states of CsO using a relativistic effective core potential and a large valence Gaussian basis set. Seventeen electrons are correlated by a CI (SD ) calculation from each HF reference. We find the X ²Σ⁺ state lower by 497 and 726 cm^?1 at the HF and CI(SD) levels. Our calculated ω_e of 312 cm^?1 for the X ²Σ⁺ state agrees well with experimental values deduced from studies in matrices.     

Theoretical evidence for multiple 3d bondig in the V2 and Cr2 molecules

Calculated CAS SCF potential curves are reported for the ³Σ_g^? state of V₂ and the ¹Σ_g⁺ state of Cr₂. At the CAS SCF level the ³Σ_g^? state of V₂ is calculated to be bound (R_c = 1.77 Å ω_c = 593.6 cm^?1, D_e 0.33 eV) and to involve a triple 3d bond; while the Cr₂ potential curve is not bound but shows a shoulder near the experimental R_e and the wave function shows multiple 3d bonding in this region.     

Theoretical calculation of the low laying electronic states of the molecular ion RbH+

Using an ab initio method, the potential energy has been calculated for the 29 lowest molecular states of symmetries ²Σ⁺, ²Π, ²Δ for the molecular ion RbH⁺. The calculation is based on nonempirical pseudopotentials and parameterized ?‐dependent polarization potentials. Gaussian basis sets have been used for both atoms. The spectroscopic constants for 18 electronic sates have been calculated by fitting the calculated energy values to a polynomial in terms of the internuclear distance R. Through the canonical functions approach the eigenvalue E_v, the abscissas of the corresponding turning points (R_min and R_max) and the rotational constants B_v have been calculated up to 24 vibrational levels for the considered bound states. The comparison of the present results with those available in literature shows a very good agreement. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

ACS symposium

The SCF potential surface of the ground state for NO₂ was calculated by using program JAMOL 3. The McLean–Loew–Berkowitz CGTO 's were used as basis functions. One of the two N? O distance R is fixed to 2.25 a.u. and the other one r and the ONO angle θ are varied from 2.25 to 5.0 a.u. and from 0° to 180°, respectively. The potential surface has the minimum around r = 2.50 a.u. and θ = 120°, where the energy is found to be ?203.954 a.u.     

Theoretical calculation of the low laying electronic states of the molecular ion KH

Using an ab initio method the potential energy has been calculated for the 25 lowest molecular states of symmetries ²Σ⁺, ²Π, ²Δ for the molecular ion KH⁺. The calculation is based on nonempirical pseudopotentials and parameterized ℓ-dependent polarization potentials. Gaussian basis sets have been used for both atoms. The spectroscopic constants for 18 electronic sates have been calculated by fitting the calculated energy values to a polynomial in terms of the internuclear distance R. Through the canonical functions approach the eigenvalue E_v, the abscissas of the corresponding turning points (R_min and R_max) and the rotational constants B_v have been calculated up to 24 vibrational levels for the considered bound states. The comparison of the present results with those available in literature shows a very good agreement.     

Thermodynamic and kinetic characteristics of intermediates of electrode reactions: A comparative investigation of a number of alkylaryl and alkyl halide radicals by the laser photoemission methods

A comparative investigation of thermodynamic and kinetic properties of a number of alkylaryl intermediates (benzyl and benzhydryl radicals) and alkyl halide intermediates (chloromethyl, dichloromethyl, and trifluoromethyl radicals) is performed by methods of laser photoemission. Techniques, aimed at the determination of thermodynamic and kinetic properties of intermediates (standard potentials E ⁰ of redox pairs R/R^-, standard adsorption free energies -G _a(R) ⁰ , values of rate constants W ⁰ at an equilibrium potential, as well as lifetimes (times of death in the bulk) _R of radicals R and _X of products of their reduction R^-) from a comparison of Tafel plots for quasi-reversible reduction of intermediates with calculated ones and standard potentials E ⁰—from Tafel plots for irreversible electroreduction of intermediates, are presented. The transition from irreversible to quasi-reversible reduction in aprotic solvents at EE ⁰ is observed only in the case of benzyl, benzhydryl, and trifluoromethyl radicals, for which this particular collection of thermodynamic and kinetic properties is obtained, and is not observed for the chloromethyl and dichloromethyl radicals. In this case redox characteristics of intermediates (E ⁰, W ⁰) are estimated from absolute values of rates of their electroreduction. Possible reasons for the differences in the probability of a reversible electron transfer are discussed for the systems studied.Translated from Elektrokhimiya, Vol. 41, No. 2, 2005, pp. 157–174.Original Russian Text Copyright © 2005 by Krivenko, Kotkin, Kurmaz.This revised version was published online in April 2005 with corrections to the article note and article title and cover date.     

Configuration interaction calculations on the propane radical cation,C3H 8 +

Summary Proton isotropic hyperfine coupling constants have been calculated for three low-energy nuclear conformations on the ground state potential surface of the propane cation, using a multireference singles and doubles configuration interaction (MR-SDCI) wave function. The lowest point found on the potential surface hadC _2v symmetry and the electronic wave function at this point had²B₂ symmetry. At this point, the largest isotropic coupling constant is calculated to be 88.6 G, which is in fair agreement with the experimental value of 98 G obtained in an SF₆ matrix at 4 K. No support is found for a long-bond ground state of lower symmetry thanC _2v . AnotherC _2v minimum on the ground state potential energy surface was found at which the wave function had² B ₁ symmetry. At this point, two large coupling constants of 198 G and 35 G were calculated. AC _2v stationary point was also found on the ground state potential surface at which the wave function had² A ₁ symmetry. At this point, couplings of 86 G and 25 G were obtained. None of these agree closely with the other experimental result of couplings at both 100–110 G and 50–52.5 G which was obtained in freon matrices. It is suggested that the latter spectra might correspond to a dynamical average of two distorted² A' states inC _s symmetry.     

The orbital description of the potential energy curves and properties of the lower excited states of the BH molecule

The electronic wavefunctions for the ground (X¹ Σ⁺) and the low-lying excited states (a³Π, A¹Π, ³Σ⁺) of the BH molecule have been calculated as a function of internuclear distance using the ab initio generalized valence bond method (GVB) with optimization of spin coupling (SOGI). The potential curve of the A¹Π state in the zero rotational level is found to have a hump of 0.150 eV at R = 3.8₉a_o (experimentally a hump of unknown size is found at 3.9 ± 0.4 a₀); a smaller hump at larger R (0.02 eV at R = 4.9₂a₀) is also found for the calculated a³Π state. The presence of such humps is found to result from the recoupling of orbitals that must occur as R is decreased from ∞ to R_e and is comparable in origin to the activation barrier in a radical exchange reaction (e.g., H₂ + D ? HD + H). The calculated binding energies of the BH states are 3.272 eV (X¹ Σ⁺), 2.216 eV (a³ Π), and 0.502 eV (A¹ Π). The ³Σ⁺ state is unbound although it does exhibit a small unbound minimum. The dipole moment, quadrupole moment, and electric field gradient are calculated as a funtion of R. The shapes of the potential curves and the properties are interpreted in terms of simple qualitative considerations of the GVB orbitals.     

Interatomic potential for the X1Σ state of Be2, revisited

An extended geminal model has been applied to determine the interatomic potential for the X¹Σ state of Be₂. By adopting a (23s, 10p, 8d, 6f, 3g, 2h) uncontracted Gaussian‐type basis, the following spectroscopic parameters are obtained: R_e = 4.633 a.u. (4.63 a.u.), D_e = 945 ± 15 cm (790 ± 30 cm), G(1)–G(0) = 221.7 cm^?1 (223.8 ± 2 cm^?1), G(2)–G(1) = 175.0 cm^?1 (169 ± 3 cm^?1), G(3)–G(2) = 123.1 cm^?1 (122 ± 3 cm^?1), and G(4)–G(3) = 80.8 cm^?1 (79 ± 3 cm^?1), experimental values in parentheses. The calculated binding energy is substantially higher than the accepted experimental value. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

The 3[ndσ*(n+1)pσ] Emissions of Linear Silver(I) and Gold(I) Chains with Bridging Phosphine Ligands

The complexes [Au₃(dcmp)₂][X]₃ {dcmp=bis(dicyclohexylphosphinomethyl)cyclohexylphosphine; X=Cl^? ( 1 ), ClO₄^? ( 2 ), OTf^? ( 3 ), PF₆^? ( 4 ), SCN^?( 5 )}, [Ag₃(dcmp)₂][ClO₄]₃ ( 6 ), and [Ag₃(dcmp)₂Cl₂][ClO₄] ( 7 ) were prepared and their structures were determined by X‐ray crystallography. Complexes 2 – 4 display a high‐energy emission band with λ_max at 442–452 nm, whereas 1 and 5 display a low‐energy emission with λ_max at 558–634 nm in both solid state and in dichloromethane at 298 K. The former is assigned to the ³[5dσ*6pσ] excited state of [Au₃(dcmp)₂]³⁺, whereas the latter is attributed to an exciplex formed between the ³[5dσ*6pσ] excited state of [Au₃(dcmp)₂]³⁺ and the counterions. In solid state, complex [Ag₃(dcmp)₂][ClO₄]₃ ( 6 ) displays an intense emission band at 375 nm with a Stokes shift of ≈7200 cm^?1 from the ¹[4dσ*→5pσ] absorption band at 295 nm. The 375 nm emission band is assigned to the emission directly from the ³[4dσ^*5pσ] excited state of 6 . Density functional theory (DFT) calculations revealed that the absorption and emission energies are inversely proportional to the number of metal ions (n) in polynuclear Au^I and Ag^I linear chain complexes without close metal???anion contacts. The emission energies are extrapolated to be 715 and 446 nm for the infinite linear Au^I and Ag^I chains, respectively, at metal???metal distances of about 2.93–3.02 Å. A QM/MM calculation on the model [Au₃(dcmp)₂Cl₂]⁺ system, with Au???Cl contacts of 2.90–3.10 Å, gave optimized Au???Au distances of 2.99–3.11 Å in its lowest triplet excited state and the emission energies were calculated to be at approximately 600–690 nm, which are assigned to a three‐coordinate Au^I site with its spectroscopic properties affected by Au^I???Au^I interactions.     

Increasing the π–π Interactions in Trinuclear NiII3 Triplesalophen Complexes

The new triplesalophen ligand H₆kruse^Br was synthesized as a variation of the triplesalophen ligands H₆baron^R by replacing a phenyl by a methyl group at the terminal ketimine in order to allow closer contacts of trinuclear complexes due to less steric hindrance by the smaller methyl group. The ligand H₆kruse^Br was used to synthesize the trinuclear complex [(kruse^Br)Ni^II₃], which is insoluble in organic solvents despite the coordinating solvent pyridine. Recrystallization from pyridine results in the complex [(kruse^Br){Ni₂(Ni(py)₂)}], which was characterized by single‐crystal X‐ray diffraction. Two Ni^II ions are four‐coordinate by the salophen‐like subunits while the third Ni^II ion is six‐coordinate by two additional pyridine donors. The analysis of the molecular and crystal structure in comparison to that of Ni^II₃ complexes of (baron^R)^6– reveals that the methyl group in [(kruse^Br){Ni₂(Ni(py)₂)}] results in less ligand folding and in closer contact distance of two Ni^II₃ complexes by π–π interactions of 3.2 Å. This indicates that trinuclear complexes of H₆kruse^Br are more suitable than complexes of H₆baron^R as molecular building blocks for the anticipated synthesis of nonanuclear single‐molecule magnets.     

CEPA calculations on open-shell molecules. III. Potential curves for the six lowest excited states of He2 in the vicinity of their equilibrium distances

CEPA-PNO and PNO-CI calculations have been performed for the potential energy curves of the He ₂ ⁺ ground state and the six lowest excited states of He₂ in the range of 1.4 a₀ ≤R ≤ 3.5 a₀. The calculated equilibrium distances as well as the spectroscopic constants are in very good agreement with molecular constants as derived experimentally from the rotation-vibration spectrum of He₂ by Ginter, except for thec ³∑ _g ⁺ state. This latter discrepancy is probably due to an “obligatory” hump in thec ³∑ _g ⁺ state occurring at 3.5 a₀ which cannot be properly treated in our calculation. The relative energetic positions of the six lowest states and their ionization energies are reproduced by our calculations with an accuracy of 0–400 cm⁻¹. Extrapolation of our results to infinite basis sets leads to estimates of the dissociation energies of He₂ excited states which cannot be measured spectroscopically because of the humps in all these states.