Nearly 100 low-, moderately high-, and high-lying singly and doubly excited states of He, Li, and Be have been calculated using a nonvariational, work-function-based exchange potential within the nonrelativistic Hohenberg-Kohn-Sham density-functional theory ͑DFT͒. The nonlinear gradient included in the Lee-Yang-Parr correlation functional is used to incorporate the correlation potential. The generalized pseudospectral method is used for nonuniform and optimal spatial grid discretization and solution of the Kohn-Sham equation to obtain accurate eigenvalues, expectation values, and radial densities for both ground and excited states. The results are compared with the available theoretical and experimental data. The discrepancy in the calculated singly excited state energies is within about 0.01% for He ͑for other atoms, it is less than 0.2%͒, while that for the doubly excited states of He is well within 3.6%. The deviations in the calculated single-and doubleexcitation energies for 31 selected states are in the error ranges 0.009-0.632 % and 0.085-1.600 %, respectively. The overall agreement of the present results is quite gratifying, especially in the light of DFT's difficulties in dealing with excited states. The exchange-only results are practically of Hartree-Fock quality, and the correlation-included results are usually slightly overestimated. The present method offers a simple, computationally efficient and general scheme for accurate calculation of multiply excited Rydberg states within DFT.

The generalized pseudospectral method is employed to calculate the bound states of Hulthén and Yukawa potentials in quantum mechanics, with special emphases on higher excited states and stronger couplings. Accurate energy eigenvalues, expectation values and radial probability densities are obtained through a nonuniform and optimal spatial discretization of the radial Schrödinger equation. Results accurate up to thirteen to fourteen significant figures are reported for all the 55 eigenstates of both these potentials with n ≤10 for arbitrary values of the screening parameters covering a wide range of interaction. Furthermore, excited states as high as up to n = 17 have been computed with good accuracy for both these potentials. Excellent agreement with the available literature data has been observed in all cases. The n > 6 states of Yukawa potential has been considerably improved over all other existing results currently available, while the same for Hulthén potential are reported here for the first time. Excepting the 1s and 2s states of Yukawa potential, the present method surpasses in accuracy all other existing results in the stronger coupling region for all other states of both these systems. This offers a simple and efficient scheme for the accurate calculation of these and other screened Coulomb potentials. * Electronic address: akroy@unb.ca

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More than 200 low-lying and moderately high-lying doubly excited states ( 1

Density functional calculations are performed for twelve 2l2l ′ nl ′′ (n≥2) triply excited hollow resonance series of Li, viz., 2s 2 ns 2 S e , 2s 2 np 2 P o , 2s 2 nd 2 D e , 2p 2 ns 2 D e , 4 P e , 2s2pns 4 P o , 2s2pnp 4 D e , 2p 2 np 2 F o , 4 D o , 2p 2 nd 2 G e , 4 F e and 2s2pnd 4 F o , covering a total of about 270 low-, moderately highand high-lying states, with n as high as up to 25. The work-function-based exchange potential and the nonlinear gradient plus Laplacian included Lee-Yang-Parr correlation energy functional is used.The relevant Kohn-Sham-type equation is solved numerically using the generalized pseudospectral method offering nonuniform, optimal spatial discretization to obtain the orbitals and densities. The present single determinantal approach yields fairly accurate results for the nonrelativistic energies, excitation energies as well as the radial densities and other expectation values. Except for the one state, the discrepancy in the calculated state energies remains well within 0.98%, whereas the excitation energies deviate by 0.02-0.58% compared to the available experimental and other theoretical results. Additionally companion calculations are also presented for the 37 3l3l ′ nl ′′ (n≥3) doubly hollow states (seven are n=3 intrashell type) of Li with both K and L shells empty (up to n=6) in the photon energy range 175.63-180.51 eV, with varying symmetries and multiplicities.Our calculation shows good agreement with the recent literature data for the only two such doubly hollow states reported so far, viz., 3s 2 3p 2 P o and 3s3p 2 4 P e . The resonance series are found to be inextricably entangled to each other, leading to complicated behavior in their positions. Many new states are reported here for the first time. This provides a simple, efficient and general scheme for the accurate calculation of these and other multiply excited Rydberg series of many-electron atomic systems within density functional theory.

Accurate low and high-lying bound states of Tietz-Hua oscillator potential are presented. The radial Schrödinger equation is solved efficiently by means of the generalized pseudospectral method that enables optimal spatial discretization. Both ℓ = 0 and rotational states are considered. Rovibrational levels of six diatomic molecules viz., H 2 , HF, N 2 , NO, O 2 , O + 2 are obtained with good accuracy. Most of the states are reported here for the first time. A detailed analysis of variation of eigenvalues with n, ℓ quantum numbers is made. Results are compared with literature data, wherever possible. These are also briefly contrasted with the Morse potential results. *

Shannon entropy (S), Rényi entropy (R), Tsallis entropy (T), Fisher information (I), and Onicescu energy (E) have been explored extensively in both free H atom (FHA) and confined H atom (CHA). For a given quantum state, accurate results are presented by employing respective exact analytical wave functions in r space. The p‐space wave functions are generated from respective Fourier transforms—for FHA these can be expressed analytically in terms of Gegenbauer polynomials, whereas in CHA these are computed numerically. Exact mathematical expressions of Rrnormalα,Rpnormalβ, Trnormalα,Tpnormalβ,Er,Ep are derived for circular states of a FHA. Pilot calculations are done taking order of entropic moments (α, β) as (35,3) in r and p spaces. A detailed, systematic analysis is performed for both FHA and CHA with respect to state indices n, l, and with confinement radius (rc) for the latter. In a CHA, at small rc, kinetic energy increases, whereas Sboldr,Rboldrnormalα decrease with growth of n, signifying greater localization in high‐lying states. At moderate rc, there exists an interplay between two mutually opposing factors: (i) radial confinement (localization) and (ii) accumulation of radial nodes with growth of n (delocalization). Most of these results are reported here for the first time, revealing many new interesting features. Comparison with literature results, wherever possible, offers excellent agreement.

Bound states of the power-law and logarithmic potentials are calculated using a generalized pseudospectral method. The solution of the single-particle Schrödinger equation in a nonuniform and optimal spatial discretization offers accurate eigenvalues, densities and expectation values.The calculations are carried out for states with arbitrary n and ℓ quantum numbers. Comparisons are made with the available literature data and excellent agreement is observed. In all the cases, the present method yields considerably improved results over the other existing calculations. Some new states are reported. * Electronic address: akroy@unb.ca