Unnatural parity states of helium with screened Coulomb potentials

Effect of screened Coulomb (Yukawa) potentials on the doubly excited meta‐stable bound states and the resonance states with unnatural parities of the helium atom have been investigated in the framework of stabilization method using CI‐type basis functions. A total of 54 resonances (6 each of ¹D^o and ³D^o states, 12 each of ¹F^e and ³F^e states, 9 each of ¹G^o and ³G^o states) below the He⁺(3P) thresholds have been estimated by calculating the density of resonance states using a stabilization method. The resonances belong to the different 3lnl′ (n ≥ 3) series. We have also calculated the doubly excited ^1,3F^e and ^1,3G^o meta‐stable bound states of He atom below the He⁺ (2P) thresholds. The resonance energies and widths along with the meta‐stable bound states energies are reported for various screening parameters. In free atom case, some of the F‐wave resonance states and most of the cases, F‐ and G‐wave resonance widths are reported for the first time. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Calculations of D‐wave bound states and resonance states of the screened helium atom using correlated exponential wave functions

We have investigated the effects of screened Coulomb (Yukawa) potentials on the bound ^1,3D states and the doubly excited ^1,3 D^e resonance states of helium atom using highly correlated exponential basis functions. The Density of resonance states are calculated using stabilization method. Highly correlated exponential basis functions are used to consider the correlation effect between the charged particles. A total of 18 resonances (nine each for ¹ D^e and ³ D^e states) below the n = 2 He ⁺ threshold has been calculated. For each spin states, this includes four members in the 2pnp series, three members in the 2snd series, and two members in 2pnf series. The resonance energies and widths for various screening parameters ranging from infinity to a small value for these ^1,3 D^e resonance states are reported along with the bound‐excited 1s3d ^1,3 D state energies. Overall behavior of the spectral profile of 1s3d ¹D state of helium atom due to electron‐electron and electron‐nucleus screening are also presented. Accurate resonance energies and widths are also reported for He in vacuum. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Efficient method to perform CAP/CI calculations for temporary anions

Electronically metastable states can efficiently be investigted using ??² techniques, such as the complex absorbing potential (CAP) or the stabilization method; but, the study of autodetaching systems is nonetheless far more expensive than the investigation of comparable bound states. The costly step of the ??² methods for resonances involves the repeated diagonalization of a parameterized Hamilton operator, and in this communication we investigate representations of the needed operators in very small basis set consisting of a few eigenstates of the physical Hamiltonian. It is shown that CAP calculations can indeed be performed using a very small eigenstate basis set, whereas basis sets of comparable size are unsuitable for stabilization calculations. Our results allow us to study the frequently employed energy selection procedure in the context of Siegert energies. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 218–226, 2001     

Using the charge-stabilization technique in the double ionization potential equation-of-motion calculations with dianion references

The charge-stabilization method is applied to double ionization potential equation-of-motion (EOM-DIP) calculations to stabilize unstable dianion reference functions. The auto-ionizing character of the dianionic reference states spoils the numeric performance of EOM-DIP limiting applications of this method. We demonstrate that reliable excitation energies can be computed by EOM-DIP using a stabilized resonance wave function instead of the lowest energy solution corresponding to the neutral + free electron(s) state of the system. The details of charge-stabilization procedure are discussed and illustrated by examples. The choice of optimal stabilizing Coulomb potential, which is strong enough to stabilize the dianion reference, yet, minimally perturbs the target states of the neutral, is the crux of the approach. Two algorithms of choosing optimal parameters of the stabilization potential are presented. One is based on the orbital energies, and another--on the basis set dependence of the total Hartree-Fock energy of the reference. Our benchmark calculations of the singlet-triplet energy gaps in several diradicals show a remarkable improvement of the EOM-DIP accuracy in problematic cases. Overall, the excitation energies in diradicals computed using the stabilized EOM-DIP are within 0.2 eV from the reference EOM spin-flip values.     

Energy and lifetime of temporary anion states of uracil by stabilization method

To investigate the temporary anion states of uracil, density functional theory with asymptotically corrected potentials is adopted. The stabilized Koopmans' theorem and stabilized Koopmans-based approximation are used in conjunction with an analytic continuation procedure to calculate its resonance energies and lifetimes. Results indicate the presence of several low-lying π* and σ* temporary anion states of uracil. The characteristics of these resonance orbitals are also analyzed. By comparing them with the experimental values and theoretical calculations, it is believed that the stabilization approach can provide more information on the resonance states.     

A simple method for estimating the superaromatic stabilization energy of a super-ring molecule

A simple graph-theoretical method is proposed for readily estimating the degree of extra stabilization due to macrocyclic conjugation (superaromaticity). This method is based theoretically on the concept of circuit resonance energy previously defined for cyclic pi systems. We confirmed that kekulene and related super-ring molecules are essentially nonsuperaromatic, with very small superaromatic stabilization energies.     

Eigenvalue lower bounds with Bazley’s special choice of an infinite-dimensional subspace

Bazley’s special choice of a finite-dimensional space to construct an intermediate operator between a base operator and the full Hamiltonian is a standard technique to calculate lower bounds to the energies of a system. We modify Bazley’s method to accommodate an infinite-dimensional space that is complete in one particle of the system. An application to the helium atom shows improvement in the lower bound to the ground-state energy, indicating promise in our method. However, significant problems are revealed which include (1) poorer bounds for the excited states, (2) lack of symmetry in the intermediate operator, and (3) lack of direction for improvement.     

Characterization of the temporary anion states on perfluoroalkanes via stabilized Koopmans' theorem in long-range corrected density functional theory

The stabilized Koopmans' theorem (SKT) in long-range corrected density functional theory is used to characterize the temporary anion states of perfluoro-n-alkanes (n-PFAs) from C(2) to C(5), and perfluorocycloalkanes (c-PFAs) from C(3) to C(4). In this approach, stabilization is accomplished by varying the exponents of appropriate diffuse functions. The energies of temporary anion states are then identified by investigating the relationship between the resultant eigenvalues and scale parameter. The characteristics of resonance orbitals are also examined. For the lowest unfilled orbitals of perfluoroalkanes, results indicate that they are mainly from the π-bonding interactions between all neighboring C atoms. In addition, their energies decrease as the sizes of the perfluoroalkanes increase. Moreover, the energies of the c-C(3)F(6)/c-C(4)F(8) are lower than those of the corresponding n-C(3)F(8)/n-C(4)F(10). When compared with experimental data, our SKT calculations can yield conformable results. Thus, this SKT approach can provide more information on the resonance states of perfluoroalkanes.     

Extrapolating bound state data of anions into the metastable domain

Computing energies of electronically metastable resonance states is still a great challenge. Both scattering techniques and quantum chemistry based L2 methods are very time consuming. Here we investigate two more economical extrapolation methods. Extrapolating bound states energies into the metastable region using increased nuclear charges has been suggested almost 20 years ago. We critically evaluate this attractive technique employing our complex absorbing potential/Green's function method that allows us to follow a bound state into the continuum. Using the (2)Pi(g) resonance of N2- and the (2)Pi(u) resonance of CO2- as examples, we found that the extrapolation works suprisingly well. The second extrapolation method involves increasing of bond lengths until the sought resonance becomes stable. The keystone is to extrapolate the attachment energy and not the total energy of the system. This method has the great advantage that the whole potential energy curve is obtained with quite good accuracy by the extrapolation. Limitations of the two techniques are discussed.     

Theoretical prediction of the electronic excited states and resonance Raman intensities in formamide from coupled cluster calculations

Electronic excitations and the resonance Raman spectrum of formamide were obtained from ab initio electron correlation calculations using the equation of motion coupled cluster (EOM-CCSD) method. Interpretation of the UV spectrum on the basis of calculated vertical excitation energies and oscillator strengths accounts for all experimental bands previously assigned. Our assignment, however, suggests an additional Rydberg band at about 7.4 eV which may be hidden under the main absorption. We also show that the Rydberg states appear pairwise, corresponding to n and π hole states, respectively. Using analytic derivative techniques, derivatives of the excited state energies with respect to normal coordinates of the ground state were calculated. Approximate resonance Raman intensities have been determined.     

Finite lifetime effects on the polarizability within time-dependent density-functional theory

We present an implementation for considering finite lifetime of the electronic excited states into linear-response theory within time-dependent density-functional theory. The lifetime of the excited states is introduced by a common phenomenological damping factor. The real and imaginary frequency-dependent polarizabilities can thus be calculated over a broad range of frequencies. This allows for the study of linear-response properties both in the resonance and nonresonance cases. The method is complementary to the standard approach of calculating the excitation energies from the poles of the polarizability. The real and imaginary polarizabilities can then be calculated in any specific energy range of interest, in contrast to the excitation energies which are usually solved only for the lowest electronic states. We have verified the method by investigating the photoabsorption properties of small alkali clusters. For these systems, we have calculated the real and imaginary polarizabilities in the energy range of 1-4 eV and compared these with excitation energy calculations. The results showed good agreement with both previous theoretical and experimental results.     

A simplified relativistic time-dependent density-functional theory formalism for the calculations of excitation energies including spin-orbit coupling effect

In the present work we have proposed an approximate time-dependent density-functional theory (TDDFT) formalism to deal with the influence of spin-orbit coupling effect on the excitation energies for closed-shell systems. In this formalism scalar relativistic TDDFT calculations are first performed to determine the lowest single-group excited states and the spin-orbit coupling operator is applied to these single-group excited states to obtain the excitation energies with spin-orbit coupling effects included. The computational effort of the present method is much smaller than that of the two-component TDDFT formalism and this method can be applied to medium-size systems containing heavy elements. The compositions of the double-group excited states in terms of single-group singlet and triplet excited states are obtained automatically from the calculations. The calculated excitation energies based on the present formalism show that this formalism affords reasonable excitation energies for transitions not involving 5p and 6p orbitals. For transitions involving 5p orbitals, one can still obtain acceptable results for excitations with a small truncation error, while the formalism will fail for transitions involving 6p orbitals, especially 6p1/2 spinors.     

On the role of scattering resonances in the F+HD reaction dynamics

We study scattering resonances in the F+HD-->HF+D reaction using a new method for direct evaluation of the lifetime Q-matrix [Aquilanti et al., J. Chem. Phys. 2005, 123, 054314]. We show that most of the resonances are due to van der Waals states in the entrance and exit reaction channels. The metastable states observed in the product reaction channel are assigned by calculating the energy levels and wave functions of the HF...D van der Waals complex. The behavior of resonance energies, widths, and decay branching ratios as functions of total angular momentum is analyzed. The effect of isotopic substitution on resonance energies and lifetimes is elucidated by comparison with previous results for the F+H2 reaction. It is demonstrated that HF(v'=3) products near threshold are formed by decay of the narrow resonances supported by van der Waals wells in the exit channel. State-to-state differential cross sections in the HF(v'=3) channel exhibit characteristic forward-backward peaks due to the formation of a long-lived metastable complex. The role of the exit-channel resonances in the interpretation of molecular beam experiments is discussed.     

A study of complex scaling transformation using the Wigner representation of wavefunctions

The complex scaling operator exp(-θ ?x?p/?), being a foundation of the complex scaling method for resonances, is studied in the Wigner phase-space representation. It is shown that the complex scaling operator behaves similarly to the squeezing operator, rotating and amplifying Wigner quasi-probability distributions of the respective wavefunctions. It is disclosed that the distorting effect of the complex scaling transformation is correlated with increased numerical errors of computed resonance energies and widths. The behavior of the numerical error is demonstrated for a computation of CO(2+) vibronic resonances.     

Calculations of the energies of resonances for atoms and ions with two and three electrons by the stabilization method

An approach to calculating the energies and widths of resonances for atoms and ions with two and three electrons was developed on the basis of the stabilization method. The energies of 28 resonances of ⁿ S symmetry with the spin multiplicities n = 1, 2, 3, and 4 were calculated for H^?, He, Li⁺, He^?, and Li. The energies of several resonances were obtained for the first time. Four resonance widths for H^?, He, and He^? were determined. The calculation results are compared with experimental data and calculations performed by other authors. Very close agreement was obtained for resonance energies (uncertainties of from 0.005 to 0.5 eV) and widths (uncertainties of ～10–20%).     

Generalized valence bond orbital interactions (GVB-OIs) and stabilization (resonance) energies: Part III--Nitrogenous heterocyclic compounds

In order to determine the stabilization (resonance) energies of nitrogenous heterocyclic compounds, the generalized valence bond orbital interactions (GVB-OIs) have been considered within the cyclic periphery of 2p_z-GVB orbitals. The overall process of GVB-OIs goes through a number of successive three-electron interactions (known as Pauli's orbital interactions (POIs)), each of which involves interaction between the two 2p_z-GVB bonding orbitals and the one 2p_z-GVB nonbonding orbital, and occurs following pauli's principle. After taking into account the total number of POIs involved and their associated minimization energies, the stabilization energies (SE)/resonance energies (RE) of mononitrogenous five- and six-membered heterocyclic compounds have been calculated by the formulae derived for them. The SE/RE values of polynitrogenous heterocyclic compounds have been calculated individually.     

Interpretation of resonance states of the molecular negative perfluoropropylene ion

An algorithm for interpreting resonance states of molecular negative ions has been suggested. This algorithm, using quantum-chemical calculations, allows one to select vacant MO that can be excited in a series of resonances, the energy gap between which coincides with the difference between the corresponding ionization energies. The resonance states of the molecular negative perfluoropropylene ion at energies of electrons from 0.5 to 12.0 eV are formed according to the mechanism of electron-excited Feschbach resonance. Spectral parameters of these resonances have been established.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1701–1704, September, 1995.     

Resonance effect in the allyl cation and anion: a revisit

The interest over the magnitude of the conjugation effect in the allyl cation (1) and anion (2) has been revived recently by Barbour and Karty (J. Org. Chem. 2004, 69, 648-654), who derived the resonance energies of 20-22 and 17-18 kcal/mol for 1 and 2, respectively, using an empirical extrapolation approximation. This paper revisits the case by explicitly calculating the Pauling-Wheland resonance energy, which measures the stabilization from the most stable resonance structure to the delocalized energy-minimum state of a conjugated system, using our newly developed block-localized wave function (BLW) method. This BLW method has the geometrical optimization capability. The computations result in adiabatic resonance energies of 37 kcal/mol for 1 and 38 kcal/mol for 2. The significant disagreement between these values and Barbour and Karty's results originates from the neglect of structural and electronic variations in their derivation which are energy costing.