The non-empirical calculation of second-order molecular properties by means of effective states. II. Effective TDCHF spectra for NO+ CO,CO2, and C2H2

Time-dependent coupled Hartree-Fock calculations have been performed in the large bases molecules NO⁺, CO. CO₂ and C₂H₂. Some first- and second-order properties are presented, in particular the isotropic dispersion interaction coefficients C₆⁰⁰⁰, C₈⁰⁰⁰ and C₁₀⁰⁰⁰ for all possible van der Waals dimers consisting of these monometers. These coefficients, and also the corresponding long-range anisotropic interaction coefficients, can be calculated easily for any of these dimers using the effective TDCHF multipole spectra presented in this paper. Formulas to this end are given.     

Nonempirical Atom-Atom Potentials for Main Components of Intermolecular Interaction Energy

Atom-atom potentials representing separate contributions to the nonempirical interaction energy have been derived in the SCF decomposition scheme corrected for basis set superposition error by the counterpoise method. The nontransferable long-range electrostatic multipole and classical induction terms have been evaluated directly from cumulative atomic multipole expansions, whereas the short-range exchange, charge-transfer, and electrostatic penetration contributions have been represented by simplified potentials of the form (β + δR^?1) exp(?δR) fitted to the corresponding ab initio results for 336 dimer configurations formed by HF, H₂O, NH₃, CH₄, CO, and CO₂. The dominant anisotropic character of electrostatic multipole atom-atom potentials and much more isotropic nature of the potentials representing short-range terms is illustrated in the Appendix for head-on interactions in CO ‥ OC and HF ‥ FH dimers.     

Field and field-gradient polarizabilities of BeH,BH and CH+

The multipole moments and independent components of the α, β, A, C, and B polarizability tensors have been calculated for BeH, BH, and CH⁺ at both SCF and MC SCF levels. To our knowledge, this is the first time that electron correlation has been taken into account in evaluating these properties for these species.     

Triple differential generalized oscillator strength of direct and resonance He(e, 2e)He+ reaction at high incident energies

The triple differential cross section and triple differential generalized oscillator strength of the direct and resonance He(e, 2e)He⁺ reaction in the first Born approximation for incident energiesE ₀≥4keV are calculated. For the direct (e, 2e) process our results obtained in definite structure models of the atom are found to be in good agreement with the available experimental data and theoretical estimates. The resonance profiles calculated in these models exhibit a complicated structure formation of overlapping¹ P and¹ D autoionization states (AIS) excited in the (e, 2e) reaction. The specific kine-matical conditions, when the overlap and interference of the¹ P and¹ D resonances are small and the¹ P and¹ D AIS yields can be measured separately, are discussed. It is also shown that in a certain range of ejection angles and at large momentum transfers (Q>2au) the yield of the¹ D AIS dominates over the¹ P resonance yield.     

CAS SCF/CI calculations of potential energy surfaces of He3+ and He2+

Complete active space MC SCF (CAS SCF) calculations followed by second-order configuration interaction (SOCI) calculations are carried out on the potential energy surfaces (bending surface, linear surfaces) of the ²Σ_g⁺ ground state of He₃⁺. The potential minimum for the ²Σ_g⁺ state occurs at a linear geometry with HeHe bond length of 1.248 Å. The binding energy of He₃⁺ with respect to He + He⁺ + He was calculated to be 2.47 eV at the SOCI level. The energy required to dissociate He₃⁺ (²Σ_g⁺) into He₂⁺ (²Σ_u⁺) and He(¹S) is calculated to be 0.14 eV. The same level of SOCI calculations of He₂⁺ yield a D_e value of 2.36 eV.     

Absolute dipole oscillator strengths for photoabsorption,photoionization and ionic photofragmentation processes in HBr

Absolute dipole oscillator strengths (cross section) have been obtained for valence shell photoabsorption (7–100eV) and a variety of partial photoionization (11–40 eV) processes in gaseous HBr. Partial dipole oscillator strengths are reported for the formation of the X²Π, A²Σ⁺ and B²Σ electronic state of HBr⁺ as well as the respective photoelectron branching ratios. The photoelectron binding energy spectra show clear evidence of many-body effects in photoionization to the B²Σ state of HBr⁺ with the ionization oscillator strength divided over many bands as predicted by many-body Green's function calculations. Partial dipole oscillator strengths are also reported for molecular ion formation as well as for all dissociative ionization processes. The measurements have been made by the dipole (e,e) (e,2e) and (e,e + ion) methods, which respectively provide quantitative measurements of photoabsorption, photoelectron spectroscopy and photoionization mass spectrometry at continuously tuneable energies. The measurements of dipole oscillator strengths for production of electronic states of HBr⁺ are combined with those for molecular and dissociative photoionization. These, considered together with the ionization and appearance potentials, provide a quantitative dipole breakdown picture for the ionic photofragmentation pathways of HBr in the energy region up to 40 eV.     

Resonances in helium atoms associated with theN=4 andN=5 He+ thresholds

Some doubly excited autoionising states of helium atoms converging on theN=4 andN=5 He⁺ thresholds are calculated by use of a method of complex-coordinates. States withL≧2 and with parities of (?1) ^L and (?1) ^L+1 are calculated by using products of Slater-orbital type wave functions with expansion lengths up to 319 terms. Resonance parameters (both resonance energy and autoinoisation width) are calculated for states with angular momentum up toL=7 forN=4 resonances, andL=8 forN=5 resonances.     

Invariance properties of the multipole expansion

The calculations of long-range interaction energy are often based on multipole expansion. The truncated multipole expansion and interaction energy calculated with it are noninvariant with respect to an arbitrary choice of local coordinate systems. In this paper we show that truncated multipole expansion of form Σ C_kR^?k is “numerically” independent on a choice of local coordinate systems, if convergence conditions are satisfied.     

Ab initio potential energy curves and transition dipole moments for the interaction of a ground state He with Na(3s–3p)

Potential energy curves of the states X ²Σ⁺, B (1)²Σ⁺ and A (1)²Π of the NaHe molecule have been calculated accurately in a large range of internuclear distances R from SA-CASSCF-MRCI calculations, using molecular orbitals expanded in cc-pV5Z basis sets. Transition dipole moments have also been calculated for the X–B, X–A and A–B transitions, in the same range of R. Their long-range behaviour have been considered.     

Superexcited states of CH4

The energy spectrum of a superexcited state (the different between the total photoabsorption and photoionization cross section) is calculated using ultraviolet photoelectron data for CH₄ and oscillator strength data for the iso-electronic atom, Ne. From this estimate we have concluded that the superexcited state of CH₄ is interpreted in terms of Jahn-Teller distortion of high Rydberg states referring to the ²T₂ state of CH⁺₄. The inconsistency between the data of the UV optical spectrum and results of other measurements or analyses is pointed out and discussed.     

Theoretical study of single-electron capture in He2+ —H− collision

We present a detailed theoretical treatment of single-electron transfer between He²⁺ and H^?. The total cross section is calculated using stationary molecular states which are appropriate in the energy range covered by the experiments (between 0.5 and 2250 eV in the centre of mass frame). We use an expansion on a two-electron basis built with one-electron diatomic molecule (OEDM) orbitals and including the common translation factor of Errea et al. All coupling terms are calculated explicitly. Because of the small binding energy of H^? compared to that of the ground state of He⁺, capture occurs into highly excited states of He⁺. Results obtained with a straight-line quasiclassical calculation are in good agreement with the experimental data. At low energy, He⁺ (n=5) +H(1s) is the dominant capture channel; at higher energy, the He⁺ (n=4) + H(1s) channel becomes important. The rise in the cross section below 6 eV can be attributed to the Coulomb attraction in the incoming channel. To account for this effect, a fully quantal calculation has been performed. The agreement with the low-energy measurements is then excellent.     

The inversion of spectroscopic data to the diatomic effective Hamiltonian containing the generalized potential energy function. Ground state of PbO

A method of inversion of spectroscopic data of a diatomic molecule to the effective Hamiltonian containing adiabatic and non-adiabatic corrections is reported. The method is based on the use of a previously suggested generalized potential energy function with correct long-range part. The potential energy function for the X¹Σ⁺ state of PbO is calculated by inversion of the infrared and microwave spectra.     

Optical oscillator strengths of 3p63d 2D → 3p53d22po, 2Do, 2Fo transitions in Co8+, Cu1O+ and Zn11+ ions

We have calculated the excitation thresholds and optical oscillator strengths (OOS) for 3p⁶3d ²D → 3p⁵3d²²po, ²Do and ²F^o transitions Co⁺⁸, Cu¹⁰⁺ and Zn¹¹⁺ ions of the potassium isoelectronic sequence using Hartree-Fock (HF) and configuration interaction (Cl) wavefunctions for both initial and final states. Our Cl values of the length and velocity form of OOS are in good agreement with each other. The trends in the oscillator strengths for the potassium isoelectronic sequence are plotted.     

Electronic transitions in C60 and its ions

The electronic spectrum of C₆₀ is calculated using quantum mechanical methods. The first allowed transition in C₆₀ is calculated at an energy of 3.5 eV and with an oscillator strength of 0.09. Several transitions are found at higher energies with comparatively strong oscillator strengths, the strongest one being at 5.78 eV (λ=214 nm). The calculated energy level diagram of C₆₀ is also used to predict wavelengths for transitions in C ₆₀ ⁺ and C ₆₀ ^? . A comparison is made with some recently observed diffuse interstellar bands at 1180 nm and 1320 nm, which have been speculated to originate from C ₆₀ ⁺ .     

Oscillator strengths in first row neutral,singly and doubly ionized atoms: Comparison of recent theoretical and experimental values

Using correlated wave functions, oscillator strengths for transitions of the type 1s²2s²2pⁿ → 1s²2s2pⁿ⁺¹ in neutral, singly and doubly ionized B, C, N, O and F atoms are calculated. Such oscillator strengths are extremely sensitive to the details of electronelectron interactions. Comparison with results for other many-body calculations and beam-foil, phase-shift, emission and Hanle spectroscopies shows an overall agreement in the case of ionized atoms but an occasional discrepancy in the case of the neutrals. It appears that, assuming experiment is correct, in these cases one still needs a better understanding of electron correlation and its effect on oscillator strengths.     

Ab initio study of small He cluster ions He n + ,n=2, 3, 4, 5, and low-lying Rydberg states of He4

SCF and CEPA calculations are applied to study the structure of small He cluster ions, He _n ⁺ ,n=2, 3, 4, 5 and some low-lying Rydberg states of He₄. The effect of electron correlation upon the equilibrium structures and binding energies is discussed. He ₃ ⁺ has a linear symmetric equilibrium geometry with a bond length of 2.35a ₀ and a binding energyD _e =0.165 eV with respect to He ₂ ⁺ +He (experimentally:D ₀=0.17 eV which corresponds toD _e ≈0.20 eV). He ₄ ⁺ is a very floppy molecular ion with several energetically very similar geometrical configurations. Our CEPA calculations yield a T-shaped form with a He ₃ ⁺ centre (R _e = 2.35a ₀) and one inductively bound He atom (4.39a ₀ from the central He atom of He ₃ ⁺ ) as equilibrium structure. Its binding energy with respect to He ₃ ⁺ +He is 0.031 eV. A linear symmetric configuration consisting of a He ₂ ⁺ centre with a bond length of 2.10a ₀ and two inductively bound He atoms (4.20a ₀ from the centre of He ₂ ⁺ ) is only 0.02–0.03 eV higher in energy. We expect that in larger He cluster ions structures with He ₂ ⁺ and He ₃ ⁺ centres andn?2 orn?3 inductively bound He atoms have nearly the same energies. In He₄ a low-lying metastable Rydberg state (³ Π symmetry for linear He ₄ ^* ,³ B ₁ for the T-shaped form) exists which is slightly stronger bound with respect to He ₃ ^* +He than the corresponding ion.     

Transfer of state multipoles in excited A 1Σ+u7Li2 following rotationally inelastic collisions with He: Experiment and theory

Circularly polarized dye laser radiation is used to prepare rotational levels j = 1 to j = 20 of the A ¹Σ⁺_u excited state of ⁷Li₂ with well defined values of the state multipoles K = 0, 1 and 2. Inelastic collisions with helium atoms populate other j levels and we have measured the circular polarisation ratio of emission, C, from these levels. C is plotted versus final j′ for each value of Δj from +2 to +18 and a family of curves is obtained which may be used as a critical test of current theories. The results are interpreted in terms of cross sections σ^K for transfer of the state multipoles under isotropic collision conditions. The observation of substantial polarisation following inelastic collision indicates that the σ^K are dominated by certain restricted scattering channels. Relative magnitudes of the multipole cross sections are calculated using the “l-dominant”, “restricted Δm_j channels” nd the Born approximation. These cross sections are then used to calculate C.     

Study of Electronic,Optical Absorption and Emission in Pure and Metal‐Decorated Graphene Nanoribbons (C29H14‐X; X=Ni,Fe, Ti,Co+, Al+, Cu+): First Principles Calculations

Density functional theory (DFT) and time‐dependent density functional theory (TDDFT) calculations were performed with the basis sets 6‐31G for DFT and 6‐31G(d), 6‐31+G(d,p) for TDDFT on pure graphene nanoribbon (GNR) C₃₀H₁₄ and metal‐decorated C₂₉H₁₄‐X (MGNRs; X=Ni, Fe, Ti, Co⁺, Al⁺, and Cu⁺). The metal/carbon ratio (X:C 3.45 %) and the doping site were fixed. Electronic properties, that is, the dipole moment, binding energy, and HOMO–LUMO gaps, were calculated. The absorption and emission properties in the visible range (λ=400–720 nm) were determined. Optical gaps, absorption and emission wavelengths, oscillator strengths, and dominant transitions were calculated. Pure graphene was found to be the most stable form. However, of the MGNRs, C₂₉H₁₄?Co⁺ and C₂₉H₁₄?Al⁺ were found to be the most and least stable, respectively. All GNRs were found to have semiconducting nature. The optical absorption of pure graphene undergoes a shift on metal doping. Emission from the pure graphene followed Kasha′s rule, unlike the metal‐doped GNRs.     

Calculation of the franck-condon factors for the transitions of CS2 ions and comparison with related photodissociation spectra

On the basis of the approximation of harmonic oscillation between SC and S for the symmetric stretching vibration of the CS₂⁺ ions, the Franck-Condon factors for the transitions of CS⁺₂ ions have been calculated using the potential curves and wavefunctions of the harmonic oscillator. The calculation results have been used for comparison with the photodissociation spectra via the transition, and for estimating the validity of the rotation constants and the bond length of state given in the previous studies. The photodissociation mechanism via the transitions of CS⁺₂ ions has also been discussed.     

Invariance properties of the multipole expansion with respect to the choice of the coordinate system

The physical interpretation of intermolecular interactions is usually based on the well-known multipole expansion of the inverse of the interparticle distance. The interaction energy is then interpreted as a sum of terms arising from the interaction of various multipole moments of both systems. It is supposed that the interaction energy calculated via the truncated multipole expansion generally depends on the choice of local coordinate systems through the coordinate dependence of the multipole moments. In this paper we prove that each term of the multipole expansion given in the form ∑_{k = 1} C_k/R^k is invariant with respect to identical translations and arbitrary rotations of the local coordinate systems. The invariant form of the convergence criterion of the multipole expansion is given and discussed.