Configuration Interaction Wavefunctions Research Articles

Important configurations in configuration interaction and coupled-cluster wave functions

Using a new general-order determinant-based program, we construct compact configuration interaction and coupled-cluster wave functions by selecting the most important configurations, by weight, from a full configuration interaction or full coupled-cluster wave function. Our results show that for the symmetric dissociation of water, chemical accuracy can be achieved across the surface with ∼2% of the full coupled-cluster expansion compared to ∼10% of the full configuration interaction expansion.

Electron Collision Rates for Ultraviolet and X‐Ray Lines of S x

Electron collisional excitation strengths and rates for ultraviolet and X-ray lines arising from transitions between the fine-structure levels of the 2s22p3 4So, 2Do, and 2Po terms and from these levels to the levels of the 2s2p4, 2p5, 2s22p23s, 2s22p23p, and 2s22p23d configurations have been calculated using Breit-Pauli R-matrix method. Configuration-interaction wave functions have been used for an accurate representation of target levels. These wave functions give excitation energies and oscillator strengths which are in close agreement with experiment and other accurate calculations. The Rydberg series of resonances converging to the n = 2 and n = 3 excited levels are explicitly included in the scattering calculation. Resonance structures make significant contribution to collision strengths. The effective collision strengths are obtained by integrating total collision strengths over a Maxwellian distribution of electron energies, and these are presented over a wide temperature range suitable for modeling of astrophysical plasmas. Significant differences with earlier results of effective collision strengths are noted.

Fine structure effective collision strengths for the electron impact excitation of Al III

Context. $\ion{S}{v}$ emission lines have been observed in solar flares, solar upper atmospheres, quiet sun regions and broad band absorption line quasars, with particular lines being used as diagnostics for electron temperature and density. Accurate atomic data are needed to analyse the observational data and to date the best available calculations for this ion have not included contributions from resonances. Aims. To calculate fine structure effective collision strengths for the electron impact excitation of $\ion{S}{v}$ using a method which incorporates resonances. Methods. A 14-state R -matrix calculation has been performed. The target states are represented by configuration interaction wavefunctions and consist of the 14 lowest LS states, having configurations (2p 6 )3s 2 , 3s3p, 3p 2 , 3s3d, 3s4s, 3p3d. These target states give rise to 26 fine structure levels and 325 possible transitions. The fine structure collision strengths were obtained by transforming to a jj -coupling scheme using the JAJOM program of Saraph and have been determined at a sufficiently fine energy mesh to delineate properly the resonance structure. The effective collision strengths were calculated by averaging the electron collision strengths over a Maxwellian distribution of velocities. Results. Tabulations of the non-zero effective collision strengths for transitions between both the LS states and the fine structure levels are given for electron temperatures ( T e ) in the range $\log_{10} T_{\rm e} ({\rm K}) = 4.0{-}6.0$. Comparisons are made with previous R -matrix and distorted-wave calculations.

Many-body effects in the4fx-ray photoelectron spectroscopy of theU5+andU4+free ions

A strictly ab initio many-electron theory was used to calculate the $4f$ x-ray photoelectron spectroscopy (XPS) of the free ${\mathrm{U}}^{5+}$ and ${\mathrm{U}}^{4+}$ ions. The calculations, based on relativistic Dirac-Fock self-consistent field (DF-SCF) and Dirac configuration interaction (DCI) wave functions (WF's), indicate that the atomic spectra have a considerable multiplet structure. However, the multiplet splitting, which is mainly manifest as a broadening of the $4{\mathrm{f}}_{5∕2}$ and $4{\mathrm{f}}_{7∕2}$ lines, is not as strong as for the first-row transition metals. As expected, the ${\mathrm{U}}^{4+}$ primary peaks are broader and have more associated satellite structure than does ${\mathrm{U}}^{5+}$. A comparison of a synthetic spectrum for ${\mathrm{U}}^{4+}$ with the observed XPS of $\mathrm{U}{\mathrm{O}}_{2}$ indicates that interatomic, solid-state, effects may decrease the multiplet and spin-orbital splitting, relative to the free ion. Notably, the $7\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ satellite characteristic of $\mathrm{U}{\mathrm{O}}_{2}$ is absent from the calculated XPS of ${\mathrm{U}}^{4+}$.

Electron spin resonance g tensors for complexes of Ne and Ar with AlO: Theoretical studies related to the large matrix effect observed for AlO

For Ne(n)-AlO (n=2, 4, 6, 8, 10) and Ar(n)-AlO clusters (n=2, 4, 6, 8), the perpendicular (relative to AlO) component of the g tensor was calculated by second-order perturbation theory, using multireference configuration-interaction wave functions. The rare-gas (Rg) atoms were placed axially and/or off axially (one or two rings of four Rg atoms each), and the distance of the Rg atoms from the Al and O atoms, or from the AlO axis, was varied from 4 to 12 bohrs. Rg atoms placed axially mostly increase g(perpendicular), whereas off-axially placed ones lower it below the gas-phase value of AlO. The largest deviations from g(perpendicular) of isolated AlO occur at Ne-Al,O distances of 5-6 bohrs, and Ar-Al,O distances of 6-9 bohrs, with maximal lowerings of about 1600 ppm for Ne and about 2200 ppm (estimated) for Ar in the case of two axial and eight off-axial Rg atoms. Electron spin resonance studies by Knight and Weltner found large matrix effects for AlO, with downshifts of g(perpendicular) observed to be about 450 and 1150 ppm in Ne and Ar matrices, respectively.

Effective collision strengths for electron impact excitation of C II

We extend a previous calculation of effective collision strengths for electron impact excitation of the boron-like ion C . The earlier work was restricted to the excitation within the 2s 2 2p ground configuration and the sixteen 2s 2 2p-2s2p 2 fine-structure transitions whilst the present paper considers all fine-structure transitions among the levels arising from the lowest 16 LS states. The collisional cross sections are computed in the multichannel close-coupling R-matrix approximation, in which sophisticated configuration-interaction wave functions are used to represent the target states. The 16 states included have the following basis configurations: the 2s 2 2p ground state, four 2s2p 2 states, three 2p 3 states, one 2s2p3s state as well as the 2s 2 3l(l = s, p, d) and 2s 2 4l(l = s, p, d, f) states. The 16 LS target states correspond to 30 fine-structure levels and lead to a total of 435 fine-structure transitions. In this paper we tabulate effective collision strengths, obtained by averaging the electron collision strengths over a Maxwellian distribution of velocities, for electron temperatures in the range given by log10 Te(K) = 3.0−5.5, suitable for most astrophysical applications and laboratory plasma diagnostics. Significant differences from a previous calculation are noted and comparisons are made with some recent experimental data.

Collisional excitation of neon-like Ni XIX using the Breit-PauliR-matrix method

Collision strength for the transition within the first five fine-structure levels in Ni XIX are calculated using the Breit-PauliR-matrix method. Configuration interaction wave functions are used to represent the target states included in theR-matrix expansion. The relativistic effects are incorporated in the Breit-Pauli approximation by including the one-body mass correction, Darwin and spin-orbit interaction terms in scattering equations.

Calculated Rate Coefficients for the Electron Impact Excitation of Singly Ionized Nitrogen

A 23-state R-matrix calculation has been performed to generate finestructure collision strengths for the electron impact excitation of N II. The target states are represented by configuration interaction wavefunctions and consist of the set of configurations having the form 2s22p2, 2s2p3, 2s22p3l (l = s,p,d). The fine structure collision strengths are generated by transforming to a jj-coupling scheme using the JAJOM program of Saraph, and a sufficiently fine energy mesh has been used to properly delineate the resonance structure. The collision strengths are then averaged over, using a Maxwellian distribution of velocities in order to generate the effective collision strengths. In this paper we use our data to calculate the excitation rate coefficients for six LS transitions so that comparison can be made with experimental and theoretical data presented in Frost et al. The transitions involved are those from the ground state to the 2s22p3s 1Po, 2s2p31Do, 2s22p3p 3Se, 2s2p33So, 2s22p3d 3Do and 2s22p3d 3Po levels, and involve 30 fine-structure levels. The theoretical calculation detailed by Frost et al (also a 23 state R-matrix calculation) produces effective collision strengths for transitions between LS levels, and the authors note `good agreement' with an earlier 13-state R-matrix calculation by Stafford et al. The current calculation improves upon the work of Stafford et al and provides much more data, allowing for comparisons to be made with transitions not included by Stafford et al. In general we find that the current calculation is in better agreement with the calculation described in Frost et al than with that of Stafford et al, and that our calculation provides the same `broad trend' of agreement with the Frost et al experimental rates.

Excitation Energies, Oscillator Strengths and Lifetimes in Ca IX

We have calculated the excitation energies for the lowest 46 LS and 86 fine-structure levels as well as oscillator strengths and radiative decay rates for transitions among the (1s22s22p6)3s2(1S), 3s3p(1,3Po), 3s3d(1,3D), 3s4s(1,3S), 3s4p(1,3Po), 3s4d(1,3D), 3s4f(1,3Fo), 3p2(1S, 3P, 1D), 3p3d(1,3Po, 1,3Do, 1,3Fo), 3p4s(1,3Po), 3p4p(1,3S, 1,3P, 1,3D), 3p4d(1,3Po, 1,3Do, 1,3Fo), 3p4f(1,3D, 1,3F, 1,3G) and 3d2(1S, 3P, 1D, 3F, 1G) states in Ca IX. These states are represented by extensive configuration-interaction (CI) wavefunctions obtained with the CIV3 computer code of Hibbert. From our transition probabilities we have also calculated the radiative lifetimes of singlet and triplet states of Ca IX. Our results are compared with other available theoretical calculations and experimental data. To assess the importance of relativistic effects on our calculated values, we have also carried out calculations in the intermediate-coupling scheme. These effects are incorporated through the Breit-Pauli approximation via spin-orbit, spin-other-orbit, spin-spin, Darwin and mass correction terms. In order to keep our calculated energy splittings as close as possible to the experimental values, we have made small adjustments to the diagonal elements of the Hamiltonian matrices. The energy splittings of 87 fine-structure levels, the oscillator strengths and transition probabilities for some strong dipole-allowed and intercombination transitions and the lifetimes of some fine-structure levels are presented and compared with available experimental and other theoretical values. Our calculated lifetimes of the relatively long-lived 3p3d(3FJ) levels show remarkable improvement over the theoretical values of Fawcett, compared to the experimental results of Trabert et al. Also, our lifetime for the 3p2(1D2) level calculated in intermediate-coupling scheme, while differing significantly from our LS value, shows good agreement with the experimental value and thus confirms the need to include relativistic effects in calculations. In this calculation we also predict new data for several levels where no other theoretical and experimental results are available.

Correlation energy extrapolation by intrinsic scaling. II. The water and the nitrogen molecule

The extrapolation method for determining benchmark quality full configuration-interaction energies described in preceding paper [L. Bytautas and K. Ruedenberg, J. Chem. Phys. 121, 10905 (2004)] is applied to the molecules H(2)O and N(2). As in the neon atom case, discussed in preceding paper [L. Bytautas and K. Ruedenberg, J. Chem. Phys. 121, 10905 (2004)] remarkably accurate scaling relations are found to exist between the correlation energy contributions from various excitation levels of the configuration-interaction approach, considered as functions of the size of the correlating orbital space. The method for extrapolating a sequence of smaller configuration-interaction calculations to the full configuration-interaction energy and for constructing compact accurate configuration-interaction wave functions is also found to be effective for these molecules. The results are compared with accurate ab initio methods, such as many-body perturbation theory, coupled-cluster theory, as well as with variational calculations wherever possible.

Large scale CIV3 calculations of fine-structure energy levels, oscillator strengths, and lifetimes in Fe XIV and Ni XVI

We have performed large scale CIV3 calculations of excitation energies from ground states for 109 fine-structure levels as well as of oscillator strengths and radiative decay rates for all electric-dipole-allowed and intercombination transitions among the (1s 22s 22p 6)3s 23p( 2P 0), 3s3p 2( 2S, 2P, 2D, 4P), 3s 23d( 2D), 3p 3( 4S 0, 2P 0, 2D 0), 3s3p( 3P 0)3d( 2P 0, 2D 0, 2F 0, 4P 0, 4D 0, 4F 0), 3s3p( 1P 0)3d( 2P 0, 2D 0, 2F 0), 3p 2( 1S)3d( 2D), 3p 2( 1D)3d( 2S, 2P, 2D), 3p 2( 3P)3d( 2P, 2D, 4P), 3s3d 2( 2S, 2P, 2D, 4P), 3p3d 2( 1S)( 2P 0), 3p3d 2( 1D)( 2P 0, 2D 0, 2F 0), 3p3d 2( 1G)( 2F 0), 3p3d 2( 3P)( 2P 0, 2D 0, 4S 0, 4P 0, 4D 0), 3p3d 2( 3F)( 2D 0, 2F 0, 4D 0, 4F 0), 3s 24s( 2S), 3s 24p( 2P 0), 3s 24d( 2D), 3s 24f( 2F 0), 3s3p( 3P 0)4s( 2P 0, 4P 0), and 3s3p( 1P 0)4s( 2P 0) states of Fe XIV and Ni XVI. These states are represented by very extensive configuration-interaction (CI) wavefunctions obtained using the CIV3 computer code of Hibbert. The relativistic effects in intermediate coupling are incorporated by means of the Breit–Pauli Hamiltonian which consists of the nonrelativistic term plus the one-body mass correction, Darwin term, and spin–orbit, spin-other-orbit, and spin–spin operators. The errors which often occur with sophisticated ab initio atomic structure calculations are reduced. Our calculated excitation energies, including their ordering, are in excellent agreement with the available experimental results for both of the ions studied. From our transition probabilities, we have also calculated radiative lifetimes of the lowest 37 fine-structure levels in Fe XIV and Ni XVI and compared them with available theoretical and experimental results. The mixing among several fine-structure levels is found to be so strong that the correct identification of these levels becomes very difficult. We predict new data for several levels where no other theoretical and/or experimental results are available. We hope that our extensive calculations will be useful to experimentalists in identifying the fine-structure levels in their future work.

(e, 3e) collisions on Mg in the impulsive regime studied by the second Born approximation

Five-fold differential cross sections for electron-impact double ionization of the 3s electrons of magnesium have been calculated in the second Born approximation in the impulsive regime. Comparing these results with calculations carried out in the first Born approximation demonstrates the dominant contribution of the second Born term. The second Born calculation shows that the contribution of the two-step 2 (TS2) process becomes large under the condition where sequential binary collisions on the Bethe ridge can occur. The effect of electron correlation in the initial target state is also examined by using a configuration interaction wavefunction.

The [formula omitted] and [formula omitted] states of N 2+: hyperfine and nuclear quadrupole coupling constants, electric quadrupole moments, and electron-spin g-factors. A theoretical study

The variation with bond distance of hyperfine coupling constants (hfcc) [ A iso, A dip], nuclear quadrupole coupling constants (nqcc) [ χ], molecular electric quadrupole moments [ Θ], and electron-spin g-factors is reported for X 2 Σ g +(1σ u 21π u 42σ g) and B 2 Σ u +(1σ u1π u 42σ g 2) of N 2 +. The hfcc’s, nqcc’s, and Θ’s are studied with ab initio and density functional theory methods. Calculated A iso/ A dip of 91.3/29.7 MHz for the X state have to be compared with experimental values of 102.4/23.3 MHz. For the B state, theoretical values A iso/ A dip=793/6.8 MHz support an experimental A iso=708 MHz (1 σ u is largely s) but disagree with A dip=26 MHz (large p). The nqcc χ( B) is one order of magnitude larger than χ( X), 4.80 versus −0.58 MHz, in line with literature results. Omission of nqcc contributions in the analysis of optical spectra is most probably responsible for the anomalously high “experimental” A dip( B). The quadrupole moment Θ is positive for both X and B states of N 2 +, whereas it is negative for neutral N 2( X). The vibrational absorption intensity for the v=1←0 quadrupole transition of N 2 +( X) is about six times stronger than for N 2( X). The g ⊥-shift (Δ g ⊥= g ⊥− g e ) is evaluated with multireference configuration interaction wavefunctions, via second-order sum-over-states expansions. The Δ g ∥’s are small (≈−100 ppm), while Δ g ⊥( v=0) is −2710 ppm for X 2 Σ g + and −6165 ppm for B 2 Σ u + . Interaction parameters | α el|=31.12 cm −1 and β el=1.01 a.u. calculated for the A 2 Π u∼B 2 Σ u + perturbation are in line with 31.30 cm −1 and 1.07 a.u. averaged over five experimental studies. Our Δ g ⊥( v)’s are compared with Curl’s shifts obtained from experimental spin-rotation ( γ) and rotational constants. Good agreement is found for X but not for the B state, for which it is suggested that experimental γ( B, v)’s recently reported—where γ decreases sharply with vibrational level v—should be revised.

Dipole allowed and intercombination transitions in K$^{\mathsf7+}$ and Ti$^{\mathsf{10+}}$ ions

We have calculated 87 fine-structure energy levels of K 7+ and Ti 10+ belonging to the lowest 14 configurations within the n = 3 and n = 4 complexes using Program CIV3 of Hibbert. Relativistic effects are included through the Breit-Pauli approximation. New improved results of oscillator strengths, transition probabilities and line strengths for all allowed and intercombination transitions among these fine-structure levels are calculated using large-scale configuration interaction wavefunctions. Lifetimes of some relatively longer-lived levels are also computed. Our results are compared with a wide variety of other calculations and available experimental data. It is noted that most of our results compare more favourably with the measurements than the other available theoretical results.

A systematic theoretical investigation of the lowest valence- and Rydberg-excited singlet states of trans-butadiene. The character of the 1 1 B u (V) state revisited

In the present work systematic procedures for the balanced description of the lowest singlet excited valence and Rydberg states of butadiene, especially for the correct description of the 11B u state, are presented. In the first step of the calculation averaged natural orbitals (ANOs) were computed from the density matrices of the ground state, the 21A g and the 11B u states. For the 11B u state the configuration interaction (CI) wave function used for the computation of the respective density matrix contained all possible single and double excitations from the 1b g (π) orbital into all virtual orbitals and double excitations describing σ–π electron correlation. For the ground and 21A g states a standard multireference (MR) CI with singles and doubles (CISD)/complete-active-space (CAS)(4,4) wave function was used. In the second step, these ANOs were used in extended MR-CISD, MR-CISD with Davidson correction and MR averaged quadratic coupled cluster calculations. This scheme was also extended to state-averaging including the four lowest Rydberg states 11B g (3s), 11A u (3p σ ), 21A u (3p σ ) and 21B u (3p π). Our best value for the vertical excitation energy to the 11B u state is 6.18 eV, close to previous equation-of-motion coupled-cluster with singles and doubles including noniterative triples [EOM - CCSD( )] and complete-active-space perturbation theory to second order (CASPT2) results, but significantly lower than most of the previous MR-CI and MR-CI based results. The computed vertical excitation energy to the 21A g state of 6.55 eV is significantly below previous EOM-CCSD(T) and EOM - CCSD( ) results and demonstrates the deficiencies of these methods in the case of MR situations. On the other hand, this excitation energy is larger than previous CASPT2 results for the 21A g state. The character of the 11B u state is predominantly of valence character, but is more diffuse than the ground state. <x 2>values for the 11B u state range between 25.4 and 26.3a 0 2 in the three-state calculations.

Ab initio configuration interaction study of the low-lying 1Sigma+ electronic states of LiCl.

Ab initio configuration interaction calculations have been performed for the X 1Sigma+ and B 1Sigma+ electronic states of LiCl. Potential energy curves, dipole moment functions, and dipole transition moments have been computed for internuclear distances between R = 2.5a0 and 50a0. Single- and double-excitation configuration interaction wave functions were constructed using molecular orbitals obtained from a two-state averaged multiconfiguration self-consistent-field calculation. This procedure yielded an accurate energy splitting between the covalent and ionic separated-atom limits. The calculated avoided crossing of the X and B state curves occurs at R = 16.2a0, in close agreement with previous calculations using a semiempirical covalent-ionic resonance model. X 1Sigma+ state spectroscopic constants are in excellent agreement with experimental values.

Inner-shell photodetachment of excited 4S° and 6S° metastable bound states of Be−

The total cross sections for photodetachment of the metastable 1s22p3 4S° and 1s2s2p3 6S° excited bound states of the negative ion of beryllium are presented for a range of initial photon energies across and beyond the 1s detachment threshold. A multichannel close-coupling R-matrix approximation is used to compute the cross sections, with sophisticated configuration-interaction wavefunctions being used to represent the initial and final states. At present there are no other theoretical or experimental data available with which to compare the cross sections for these two photodetachment processes.

Momentum space properties for the atoms helium to neon from energy‐optimized explicitly correlated wave functions

AbstractAtomic momentum space properties have been calculated starting from explicitly correlated wave functions. The one‐body momentum distribution and some of their radial moments and related properties for the atoms helium to neon are reported. The wave functions include a generalized Jastrow factor and in some cases a multideterminant expansion to take care of the nondynamic correlation effects such as the 2s‐2p near degeneracy. Both the variational trial wave functions and the momentum space properties have been calculated using the variational Monte Carlo method. The optimization of the free parameters of the trial wave functions is done by using a recently developed energy‐optimization technique. Most of the previous variational Monte Carlo applications to quantum chemistry rely on variance‐optimized wave functions. A comparison of momentum space properties calculated with energy‐optimized wave functions with those obtained by means of variance‐optimized wave functions shows a better performance of the former. Despite the simple parameterization of the wave functions used here, they present a good agreement with the results obtained from extensive configuration interaction wave functions. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004

Electron Impact Excitation Collision Strengths and Rates for P ii

The Breit-Pauli R-matrix method has been used to calculate electron collisional excitation strengths for transitions between the 41 lowest fine-structure levels of the 3s23p2, 3s3p3, 3s23p3d, 3s23p4s, and 3s23p4p configurations in P II. Accurate representation of target levels have been obtained on the basis of configuration-interaction wave functions. The relativistic effects in the scattering equations are included through mass correction, Darwin, and spin-orbit operators of the Breit-Pauli Hamiltonian. The collision strengths in the threshold energy regions are dominated by complicated resonance structures. The effective collision strengths are determined by integrating collision strengths and assuming a Maxwellian distribution of electron energies. The effective collision strengths are listed over a wide temperature range (103-106 K) applicable to astrophysical plasmas.

Exciton migration dynamics in a dendritic molecule: quantum master equation approach using ab initio molecular orbital configuration interaction method.

We investigate the exciton migration dynamics in a dendritic molecular model composed of pi-conjugation linear-leg units (acetylenes and diacetylene) and a benzene ring (branching point) using the quantum master equation approach with the ab initio molecular orbital (MO) configuration interaction (CI) method. The efficient migration of exciton from short-length linear legs (acetylenes) to long-length linear leg (diacetylene) via a benzene ring is observed. As predicted in previous studies, the exciton (electron and hole) distributions are relatively well localized in each generation segmented by the meta-branching point (meta-substituted benzene ring) though the electron and hole distributions are delocalized and are somewhat spatially different from each other within each generation. It is found that the excitons localized in the generation composed of short linear legs occupy in higher-lying exciton states, while those in the generation composed of long linear legs do in lower-lying ones. These features suggest the decoupling of pi-conjugation at the meta-branching point. On the other hand, the relaxation effect between exciton states is found to be caused by the exciton-phonon coupling, in which the existence of common configurations (electron-hole pairs) in CI wave functions between adjacent exciton states (having primary distributions on short and long linear-leg regions, respectively) is important for the relaxation between their exciton states. This feature indicates the importance of partial penetration of pi-conjugation through the meta-substituted benzene ring in excited states for such exciton migration.