Long range interaction energies between ground and first excited state hydrogen atoms using a one centre method

A one centre method is used to evaluate the long range interaction energies, through O(R ^-10), between ground and first excited state hydrogen atoms. General pseudo spectral results for both the direct and resonant parts of the expanded second and third order interaction energies are given through any order in R ^-1. Of particular interest is an O(R ^-9) third order energy which is totally resonant in character. The advantage of the one centre method for interactions involving degenerate energy states is discussed briefly.     

The interaction between first excited state hydrogen atoms and a different non-degenerate atom: an example of second-order resonance forces

The interaction of a first excited state hydrogen atom with a different non-degenerate atom is considered in the R ^-1 multiple approximation. The interaction energies for the Π states arising from this interaction have the form usually associated with second-order dispersion energies while those for the Σ states behave quite differently as a function of R. Because of a second-order ‘resonance within one molecule effect’ the second-order Σ-state energies do not possess single R ^-1 expansions that are formally valid for all values of R consistent with the multipole treatment. The expansions of these Σ-state energies, that are valid for ‘small’ R, contain terms varying as both even and odd powers of R ^-1; the lead R ^-7 ‘odd’ term competes strongly with the usual R ^-6 dispersion energy. The expansions that are valid for ‘large’ R contain terms varying as even powers of R ^-1 only and usually have little physical meaning. The He(¹S)-H(n=2) interaction is considered as a specific example of these results and the interaction energies for this system are evaluated through O(R ^-8) by using one-centre pseudostate methods. The general significance of the results is also discussed briefly.     

Padé approximation methods applied to the intermolecular force series

The H(1s)-H⁺, He-He, H(1s)-H(1s) and H(1s)-H(2s) interactions are considered as model systems for investigating the use of the Padé approximation method in summing the R ^-1 intermolecular force series. Various Padé approximants and partial sums of the R ^-1 expansions of the second-order Coulomb interaction energies are compared with the corresponding non-expanded results for each interaction. The computations are based on Unsöld's average energy approximation and on exact results for the H(1s)-H interaction. The results indicate that the Padé approximation method is a simple, useful way to remove some of the difficulties associated with the slow rate of convergence of the R ^-1 force series but that it does not alleviate the problems associated with the asymptotic divergent nature of the series. The results for the H(1s)-H⁺ interaction illustrate a possible difficulty in using Unsöld's method in the calculation of interaction energies.     

Charge overlap effects dependence on the nature of the interaction

The He-He, He-H(1s), H(1s)-H(1s) and H(1s)-H(2s) interactions are considered as model systems for studying how charge overlap effects in second-order dispersion energies vary as a function of the nature of the interacting species. The non-expanded second-order energy and the corresponding multipole R ^-1 expansions, through all powers of R ^-1, are obtained for each interaction using Unsöld's average energy approximation. The results are used to discuss the limitations of the usefulness of the R ^-1 expansions.     

PdCO分子结构与势能函数

用密度泛函理论的B3LYP方法,对钯原子采用LANL2DZ收缩价基函数,碳原子和氧原子采用AUG-cc-pVTZ基组,对PdC,PdO和PdCO体系的结构进行优化,计算表明：PdC分子基态为¹Σ⁺态,键长为R_e=0.17285nm,离解能为4.919eV.PdO分子基态的平衡核间距为0.18546nm,其电子态为³Π,离解能为2.455eV,并拟合得到Murrell-Sorbie势能函数;PdCO分子有两 关键词： PdCO 分子结构 势能函数     

Lithium dipole properties and van der Waals constants using a pseudo spectral one-centre method

A pseudo spectral one-centre method is used to evaluate the moments of the dipole oscillator strength distribution for the ground-state Li atom and the van der Waals constants for the ground-state Li-Li, Li-He and Li-H interactions. Various combinations of C.I. type Li atom ground and excited ² P ⁰-state wavefunctions are used to construct the required pseudo spectral dipole oscillator strengths and excitation energies. The analysis of all the pseudo-state data yields recommended values for the Li dipole properties and van der Waals constants that are probably more accurate than those obtained previously. The calculations illustrate some of the advantages of the pseudo spectral approach for the evaluation of atomic and molecular properties and interaction energies.     

A CNDO/2 study of σ- and π- relaxation energies and core electron binding energy shifts in some simple molecules

A relaxation potential model has been used to study relaxation energies and shifts in core electron binding energies for some substituted alkenes and carbonyl compounds in terms of σ- and π-contributions.The conclusions from this study may be summarized as follows:(A) For the series R₁R₂C^*CH₂ and R₁R₂C^*O: (i) The total shifts vary in a regular manner, similar to the shifts in saturated systems; (ii) The variation in σ-relaxation energies is greater than the variation in π-relaxation energies.(B) For the series R₁R₂CCH₂ and R₁R₂CO: (i) There is little variation in the σ-relaxation energies; (ii) The π-relaxation energies show moderately large variations and the higher values are associated with unsaturated substituents which can donate π-electrons to the core-ionized atom via the conjugated π-system; (iii) The π-relaxation energies in the fluorinated systems are similar to those in the unsubstituted molecules; and (iv) The large -ve π-shift in the fluorinated systems results from a ground state build up of electron density at the site of core ionization.     

Studies on the full vibrational energy spectra for some electronic states of diatomic molecular ions XY+

The first accurate studies on the vibrational spectroscopic constants and the corresponding full vibrational energy spectra of some electronic states of diatomic molecular ions XY⁺ were performed using algebraic method(AM). The AM is applied on the X¹Σ⁺ state of BeH⁺, the X²Σ⁺ state of CO⁺, the X²Π_g state of F ₂ ⁺ , the A²Π_u state of O ₂ ⁺ and the X²Σ _g ⁺ state of Li ₂ ⁺ . The results show that AM can generate accurate vibrational spectroscopic constants as well as accurate full vibrational energy spectra by using some accurate experimental vibrational energies, and that the AM vibrational energies are better than other theoretical data. __________ Translated from Chinese Journal of Atomic and Molecular Physics, 2005, 22 (4) (in Chinese)     

Properties of nuclear matter andN=Z closed-shell nuclei

A simple three-parameter density dependent effective interaction is used to study the properties of nuclear matter, neutron matter and some bulk properties such as ground state energies and rms charge radii of three double-closed shell nuclei⁴He,¹⁶O and⁴⁰Ca. The three parameters of the effective interaction are determined by requiring to fit the binding energy and density of infinite nuclear matter at saturation density as well as ground state energy of¹⁶O in the first order perturbation theory. This interaction gives correct saturation in nuclear matter with a value of 283 MeV for compressibility. The symmetry coefficienta _T atk _F=1·36 fm^–1 is 28·58 MeV. The energy per particle in neutron matter is calculated in the range of nuclear matter densities and it compares well with those ofNemeth andSprung. Groundstate energies and rms charge radii of⁴He,¹⁶O and⁴⁰Ca are calculated using oscillator eigen functions as single particle wave functions. Results for ground state energies are in good agreement with empirical values and rms charge radii are slightly better than those obtained byMoszkowski with the MDI.The authors are thankful to the Computer Centre, Utkal University, Bhubaneswar for providing computational facilities for this work.     

On the validity of the triple-dipole interaction as a representation of non-additive intermolecular forces

A complete partial wave analysis of the non-expanded non-additive coulomb interaction energy for three non-degenerate S-state atoms is given through third-order in the interatomic potential energy function. Pseudo state techniques are used to evaluate various partial wave components of the non-expanded second and third-order non-additive interaction energies for various isosceles triangular configurations of three interacting ground-state hydrogen atoms. These second and third-order non-expanded coulomb results are used, in conjunction with Heitler-London results for the first-order non-additive energies for the quartet spin state of the H(1s)-H(1s)-H(1s) interaction, to discuss the relative importance of various parts of the non-additive energy as a function of the geometrical configuration of the atoms, and the validity of both the non-expanded triple-dipole energy and the expanded Axilrod-Teller-Muto triple-dipole result as a representation of non-additive coulomb energies. For example, in the non-bonded interaction of three S-state atoms it appears that representing the non-additive energy by the non-additive coulomb energy is not reliable until the interatomic separations are somewhat larger than R*, the interatomic distance associated with the van der Waals minimum in the corresponding non-bonded dimer interaction. Further, the use of the triple-dipole interaction energy, with or without charge overlap corrections, to represent the non-additive coulomb energy is of doubtful validity until the interatomic separations are considerably greater than R*.     

An ab initio study of the Ne-CO complex

A new ab initio potential energy surface of the Ne-CO complex is developed using single and double excitation coupled-cluster theory with noniterative treatment of triple excitations [CCSD(T)].The potential has a minimum value of 49.396 cm 1 at R e = 6.40a 0 with approximately T-shaped geometry(θ e = 82.5).Bound state energies are calculated up to J = 12.The theoretically predicted transition frequencies and spectroscopic constants are in good agreement with the available experimental results.     

Microwave spectra of the ground vibrational state of formaldehyde substituted with O and O

Pure rotational transitions in the ground vibrational state have been measured for H₂¹²C¹⁸O, H₂¹²C¹⁷O, H₂¹³C¹⁸O, and H₂¹³C¹⁷O in the frequency region 8–75 GHz. These have included both Q- and R-branch transitions, and have permitted accurate evaluation of rotational constants and several quartic centrifugal distortion constants for each species. These in turn have permitted the prediction of several transitions of possible use in radioastronomy.     

Mass spectrometric and ab initio study of the interaction between 9-methylguanine and amino acid amide group

The temperature dependent field ionization mass spectrometry method combined with ab initio calculations was used to determine the interaction energies and the structures of 9-methylguanine-acrylamide dimers. Acrylamide mimics the side chain amide group of the natural amino acids asparagine and glutamine. The experimental enthalpy of the dimer formation derived from the van't Hoff plot is ?59.5 ± 3.8 kJ mol^?1. The value is higher than interaction energies between acrylamide and other nucleic acid bases which were determined to be ?57.0 for 1-methylcytosine, ?52.0 for 9-methyladenine, and ?40.6 kJ mol^?1 for 1-methyl-uracil. In total, eight hydrogen bonded dimers formed by the three lowest energy 9-methylguanine tautomers and acrylamide were found in the quantum chemical calculations performed at the DFT/B3LYP/6-31++G?? and MP2/6-31++G?? levels of theory. The relative stability and the interaction energies of the dimers were calculated accounting for the basis set superposition error and the zero-point vibrational energy correction. The lowest energy dimer found in the calculations is formed by acrylamide (Ac) with the keto tautomer of 9-methylguanine (Gk). It is stabilized by two intermolecular H bonds, C6=O(Gk) · · · H—N(Ac) and Nl—H(Gk) · · ·O(Ac), and it is more stable than the second lowest energy dimer by ≈ 25 kJ mol^?1. The calculated interaction energies of the lowest energy 9-methylguanine-acrylamide dimer are ?65.0 kJ mol^?1 and ?67.7 kJ mol^?1 at the MP2 and DFT levels of theory, respectively. The experimental enthalpy of the dimer formation is in good agreement with both the calculated interaction energies of the GkAc dimer and much higher than the interaction energies calculated for all other 9-methylguanine-acrylamide dimers. This proved that only one dimer was present in the experimental samples. To verify whether acrylamide is a good model of the amino acid-amide group, we performed direct calculations of the 9-methylguanine-glutamine dimers at the same levels of theory as used for the complexes involving acrylamide. The interaction energies found for the lowest energy 9-methylguanine-glutamine dimer are ?65.1 kJ mon^?1 (MP2/6-31++G??) and ?66.2 kJ mol^?1 (DFT/B3LYP/6-31++G??) and these values are very close (within 0.5 kJ mol^?1) to the interaction energies obtained for the 9-methylguanine-acrylamide dimers.     

AlO2和Al2O分子的结构与解析势能函数

运用密度泛函理论的B3LYP方法在6-311++G^**水平上,对AlO₂,Al₂O分子的结构进行了优化计算,得到AlO₂,Al₂O分子的稳定结构都为D_∞h构型.　AlO₂电子态为X²Π_u,平衡核间距R_Al-O关键词： 2')" href="#">AlO₂ 2O')" href="#">Al₂O Murrell-Sorbie函数 多体项展式理论     

Ab initio configuration interaction study on the electronic structure of the X2Σ+, B2Σ+ and 32Σ+ states of SiO+

The energy levels and electronic structure of the X²Σ⁺, B²Σ⁺ and 3²Σ⁺ states of SiO⁺ are studied using ab initio configuration interaction (CI) calculations at and around their equilibrium internuclear distances R _e. Spectroscopic constants and the vertical excitation energy from the SiO⁺ X²Σ⁺ state are predicted for the 3²Σ⁺ state. Based on the calculated CI wavefunctions, avoided crossings of the potential energy curve for the 3²Σ⁺ state and a near-degeneracy effect in the avoided crossing region are examined. The effects of the mixing of excited configuration state functions in the total electronic wavefunctions for the 1–3 ²Σ⁺ states are investigated by analysing correlation energies in terms of the contributions from classes of excited configurations. The importance of both the near-degeneracy effect and the correlation energy effect in describing correctly the electronic structure of the 3 ²Σ⁺ state in the neighbourhood of its R _e is discussed.     

Accurately solving the electronic Schrödinger equation of atoms and molecules using explicitly correlated (r 12-)MR-CI IV. The helium dimer (He 2)

The helium dimer interaction potential is computed using the recently proposed (explicitly correlated) r ₁₂-MR-ACPF (averaged coupled-pair functional) method and a [11s8p6d5f4g] basis set. With an MR-ACPF ansatz that contains 121 references we obtain interaction energies that are close to full CI. In a smaller reference space containing 9 functions, however, even by successively adding [3h] and [2i] functions to the basis set mentioned above, the basis set limit could not be reached. While convergence to the basis set limit is slow, it nevertheless is monotonic and therefore allows for extrapolation to the limit. We obtain basis set corrections at R = 4 a ₀ and 5.6 a ₀ which we further extend to all distances and which we apply to the potential energy curve mentioned above. From our calculations, we conclude that a very recent potential which has been calculated using the SAPT (symmetry adapted perturbation theory) method, and which previously was assumed to be the most accurate available, is insufficiently repulsive at short distances. We correct our extrapolated potential for retardation and finally calculate the expectation value of the interatomic distance (?R?) and dissociation energy (D ₀) by solving the Schrödinger equation of the vibrating ⁴He₂. Our results (?R? = 41 ± 13 Å and D ₀ = 2.2 ± 1.0 mK) are in acceptable agreement with very recent calculations in the literature, but they disagree with a recent experiment.     

Fourier Transform Spectrum and Term Values for the CO-Stretching Mode of CD3OH Methanol

The Fourier transform infrared (FTIR) spectrum of the CO-stretching fundamental band of CD₃OH has been recorded at a resolution of 0.002 cm^-1. Assignments are reported for 35 subbands in the n = 0 ground torsional state, covering K = 0 to 9 for all torsional symmetries plus K = 10 A, and 12 assorted A and E subbands in the n = 1 first excited torsional state ranging from K = 0 up to K = 5. The subband wavenumbers have been fitted to J(J + 1) power-series energy expansions to obtain subband origins and a compact representation of the spectral observations. With the use of known ground-state energies, CO-stretch energy term values have been determined and tabulated. Least-squares fitting of the subband origins to a fourth-order Hamiltonian model for the CO-stretch mode is discussed.     

MBPT studies of van der Waals molecules

The many-body perturbation theory is employed for the calculation of the interaction potential for the F^- … He system in the framework of the supermolecule method. A particular attention is paid to the choice of the basis set functions for the two subsystems and the related basis set superposition effects. It has been found that the main features of the interaction potential are recovered in the SCF approximation. The SCF potential has its minimum at the distance R = 6·4 a ₀ with the interaction energy of 53 cm^-1. The complete fourth-order MBPT method gives the potential minimum position and depth equal to 6·5 a ₀ and 64 cm^-1, respectively. The basis set superposition effects estimated by using the counterpoise technique are negligibly small for the SCF interaction potential, while at the correlated level their magnitude is comparable to the value of the total correlation contribution to the interaction energy. The basis set superposition effect in calculations of the electron correlation contribution to weak intermolecular interactions is found to be the major factor limiting the reliability of the corresponding theoretical data.     

Discussion of the He-He interaction energy in the average energy approximation

Using the Unsöld average energy method a double perturbation theory expression for the interaction energy through second order is obtained which includes intra-atomic correction terms arising from the use of trial wavefunctions to represent the non-interacting molecules. These formal expressions are applied to the ground state He-He interaction and results for the interaction energy are obtained that compare favourably with recent semiempirical and ab initio calculations. The Unsöld calculations are used to investigate approximations that have been introduced into the average energy calculation by other workers, and as a model for discussing the relative importance of second-order charge overlap and exchange effects and the convergence of the multipole treatment of the interaction energy for this typical non-bonded interaction. The results illustrate the importance of knowing as many terms as possible in the R ^-1 expansion of the energy. Finally a portion of this work required the recalculation of the He-He repulsive energy obtained by using the Eckart wavefunction to represent the helium atom. The resultant energy is approximately 25 per cent lower than that previously obtained using this wavefunction for most values of R.     

Saturation effects on phosphorescence anisotropy measurements at high laser pulse energies

Triplet spectroscopic methods such as time-resolved phosphorescence anisotropy permit successful measurement of slow rotational diffusion of membrane proteins. However, these methods are potentially subject to saturation phenomena. We present theoretical and experimental studies of how high excitation energy densities can complicate measurements of phosphorescence intensity and anisotropy. Increases in excitation laser pulse energy initially increase phosphorescence intensity. Further increases then lead to phosphorescence saturation. As a consequence, the initial phosphorescence anisotropy decreases and approaches zero at very high excitation energies. The relative standard deviation of anisotropies measured in any system reaches a minimum at some particular excitation energy density. These results allow us to define optimum experimental conditions for time-resolved phosphorescence anisotropy measurements. For example, for excitation of erythrosin chromophores at typical wavelengths by the center of a Gaussian laser beam, optimum pulse energies in microjoules are approximately 5.0R ², whereR is the beam 1/e² radius in mm.