Statistical Average Of Orbital Potentials Research Articles

Physical Meaning of Virtual Kohn-Sham Orbitals and Orbital Energies: An Ideal Basis for the Description of Molecular Excitations.

In recent years, several benchmark studies on the performance of large sets of functionals in time-dependent density functional theory (TDDFT) calculations of excitation energies have been performed. The tested functionals do not approximate exact Kohn-Sham orbitals and orbital energies closely. We highlight the advantages of (close to) exact Kohn-Sham orbitals and orbital energies for a simple description, very often as just a single orbital-to-orbital transition, of molecular excitations. Benchmark calculations are performed for the statistical average of orbital potentials (SAOP) functional for the potential [J. Chem. Phys. 2000, 112, 1344; 2001, 114, 652], which approximates the true Kohn-Sham potential much better than LDA, GGA, mGGA, and hybrid potentials do. An accurate Kohn-Sham potential does not only perform satisfactorily for calculated vertical excitation energies of both valence and Rydberg transitions but also exhibits appealing properties of the KS orbitals including occupied orbital energies close to ionization energies, virtual-occupied orbital energy gaps very close to excitation energies, realistic shapes of virtual orbitals, leading to straightforward interpretation of most excitations as single orbital transitions. We stress that such advantages are completely lost in time-dependent Hartree-Fock and partly in hybrid approaches. Many excitations and excitation energies calculated with local density, generalized gradient, and hybrid functionals are spurious. There is, with an accurate KS, or even the LDA or GGA potentials, nothing problematic about the "band gap" in molecules: the HOMO-LUMO gap is close to the first excitation energy (the optical gap).

Performance assessment of density functional theory-based models using orbital momentum distributions

The performance of a number of established and widely used density functional theory (DFT) methods (B3LYP, Bhandh, BP86, PW91, Vosko, Wilk, and Nusair (VWN), LB94, PBe0, statistical average of orbital potentials (SAOP) and X3LYP) and the Hartree–Fock (HF) method has been assessed using the 7σ orbital momentum distributions (MDs) of nitrous oxide (N2O). The DFT methods are combined with a number of Gaussian basis sets as well as even-tempered Slater basis sets. Orbital MDs of N2O are compared with experimental measurement of the same orbital from electron momentum spectroscopy. This study reveals information regarding the performance of (a) the DFT methods and their long-range behaviour, (b) Gaussian and Slater basis set contributions to this orbital, (c) combinations (i.e. the models) of the DFT methods and basis sets and (d) the entire region of chemical significance of the orbital. In general, for any given method, it is found that Slater basis sets achieve better overall agreement with experiment than Gaussian basis sets. Dunning's aug-cc-pVTZ basis set achieves the best performance for the MDs for this orbital among the Gaussian basis sets. The B3LYP and BP86 models exhibit similar overall performance to more recent models such as X3LYP and SAOP. This study also demonstrates that the particular combination of density functional method and basis set employed have a significant effect on the quality of the calculated orbitals.

Experimental and theoretical studies of 2‐amino‐3‐methylimidazo[4,5‐f]quinoline derivatives: Cooked‐food mutagens

AbstractThe UV absorption spectra of two potent mutagens, 2‐amino‐3‐methylimidazo[4,5‐f]quinoline (IQ) and NO2‐IQ, dissolved in ethanol, were observed at room temperature. General appearance of the two spectra is somewhat different. The absorption spectra show five bands in the region above 200 nm. The peak positions of the five bands are similar in the two spectra. The observed bands in the two molecules were assigned using transition energies calculated with time‐dependent density functional theory with triple‐zeta polarized basis set with the statistical average of orbital potentials exchange‐and‐correlation functional. The emission spectra of the two molecules dissolved in ethanol were obtained at 77 K. Only fluorescence emission was observed in IQ. No phosphorescence emission of the molecule was observed. Both fluorescence and phosphorescence emissions were observed in NO2‐IQ. These observations were interpreted with the aid of the calculated transition energy spectra. Some lowest vertical ionization energies of the two molecules were also calculated. The first ionization energy of NO2‐IQ is greater than that of IQ by 1.2 eV. Core electron binding energies (CEBEs) of the two molecules were calculated as well. Using CEBE shifts of atoms in the molecules, it was possible to observe the changes of chemical environment when substituent changes. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010

The van der Waals coefficients between carbon nanostructures and small molecules: A time-dependent density functional theory study

We employ all-electron ab initio time-dependent density functional theory based method to calculate the long-range dipole-dipole dispersion coefficient, namely, the van der Waals (vdW) coefficient (C(6)) between fullerenes and finite-length carbon nanotubes as well as between these structures and different small molecules. Our aim is to accurately estimate the strength of the long-range vdW interaction in terms of the C(6) coefficients between these systems and also compare these values as a function of shape and size. The dispersion coefficients are obtained via Casimir-Polder relation. The calculations are carried out with the asymptotically correct exchange-correlation potential-the statistical average of orbital potential. It is observed from our calculations that the C(6) coefficients of the carbon nanotubes increase nonlinearly with length, which implies a much stronger vdW interaction between the longer carbon nanostructures compared with the shorter ones. Additionally, it is found that the values of C(6) and polarizability are about 40%-50% lower for the carbon cages when compared with the results corresponding to the quasi-one-dimensional nanotubes with equivalent number of atoms. From our calculations of the vdW coefficients between the small molecules and the carbon nanostructures, it is observed that for H(2), the C(6) value is much larger compared with that of He. It is found that the rare gas atoms have very low values of vdW coefficient with the carbon nanostructures. In contrast, it is found that other gas molecules, including the ones that are environmentally important, possess much higher C(6) values. Carbon tetrachloride as well as chlorine molecule show very high C(6) values with themselves as well as with the carbon nanostructures. This is due to the presence of the weakly bound seven electrons in the valence state for the halogen atoms, which makes these compounds much more polarizable compared with the others.

Tetrakis(thiadiazole)porphyrazines. 6. Spectroelectrochemical and Density Functional Theory Studies of the Anions [TTDPzM]n− (n = 1−4; M = ZnII, MgII(H2O), CuII, 2HI)

Following previous cyclic voltammetric studies of tetrakis(thiadiazole)porphyrazines [TTDPzM] where M = Zn(II), Mg(II)(H(2)O), Cu(II), or 2H(I) in nonaqueous media, a thin-layer spectroelectrochemical investigation was carried out in pyridine to characterize each stepwise one-electron reduction of the electrogenerated [TTDPzM](n-) complexes where n = 1-4. A similar UV-visible spectrum was observed for each form of the anion, independent of the central metal ion and detailed theoretical calculations by density functional theory (DFT) and time-dependent DFT (TDDFT) methods were applied to interpret the spectral features of [TTDPzZn](n-) (n = 1-4) which was selected as representative for describing the ground and excited-state electronic structures of the entire [TTDPzM](n-) series. The use of two exchange-correlation functionals, the pure, asymptotically correct statistical average of orbital potentials (SAOP) and the hybrid B3LYP functionals, proved to be essential for attaining a correct assignment of the key spectral features. The nature and intensity of the main spectral features are highlighted and interpreted on the basis of the ground-state electronic structure of the complexes.

Time‐dependent density functional theory calculation of van der Waals coefficient of potassium clusters

AbstractWe employ all‐electron ab initio time‐dependent density functional theory (DFT)‐based method to calculate the long range dipole–dipole dispersion coefficient (van der Waals coefficient)C6of potassium atom clusters (Kn) containing even number of atoms,nranging from 2 to 20. The dispersion coefficients are obtained via Casimir–Polder relation. The calculations are carried out with the asymptotically correct statistical average of orbital potential and compared with the results obtained using Vosko–Wilk–Nusair representation of exchange‐correlation potential within local density approximation. We report the dispersion coefficients between clusters of sodium and potassium atoms as well. The present results have been compared with the available jellium‐based model and other DFT results in the literature. We also study the relationship between volume of the cluster and theC6for K clusters. It is observed that theC6scales as square of the volume. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

An evaluation of exchange-correlation functionals for the calculations of the ionization energies for atoms and molecules

In this paper, ionization energies of gas-phase atoms and molecules are calculated by energy-difference method and by approximate transition-state models with density functional theory (DFT). To determine the best functionals for ionization energies, we first study the H to Ar atoms. An approximation is used in which the electron density is first obtained from Kohn–Sham computations with an exchange-correlation potential V xc known as statistical average of orbital potentials (SAOP), after which the energy is computed from that density with 59 different exchange-correlation energy functionals E xc. For the 18 atoms, the best E xc functional providing an average absolute deviation (AAD) of only 0.110 eV is one known as the Krieger–Chen–Iafrate–Savin functional modified by Krieger, Chen, Iafrate, and Kurth, if one uses the spin-polarized spherical atom description. On the other hand, if one imposes the condition of integer-electrons, the best functional is the Becke 1997 functional modified by Wilson, Bradley, and Tozer, with an AAD of 0.107 eV, while several other functionals perform almost as well. For molecules, we can achieve an accuracy of AAD = 0.21 eV for valence VIPs of nonperhalo molecules with Δ E( V xc = SAOP;PBE0) using integer-electron description. For perhalo molecules our best approach is Δ E( V xc from either E xc or SAOP;mPW1PW) with full symmetry to obtain an AAD = 0.24 eV.

Circular dichroism of some high-symmetry chiral molecules: B3LYP and SAOP calculations

Computational modeling of optical activity, circular dichroism (CD) and optical rotatory dispersion, is rapidly becoming a useful supplement to experimental studies of absolute configuration. Here, we investigate the predictions of two alternative formulations of the rotational strength based on time-dependent density functional theory (TD-DFT), for a series of high symmetry chiral systems. We employ the TD-DFT method as realized in Gaussian 03 suite with the hybrid functional B3LYP and as incorporated in the Amsterdam density functional (ADF) suite with PBE and SAOP functionals. The high-symmetry systems described here are somewhat larger than those used to evaluate the influence of basis sets and density functional choice, and for such large systems the very extensive basis sets recommended by most investigators may not be suitable for routine use. We observe that useful results for these systems can be obtained in modest bases, and in particular that diffuse functions may not be required for informative use of the ADF implementation. The statistical average of orbital potentials (SAOP) model developed by Baerends is essential to the success of the ADF implementation. In some cases chirality is defined by features of the molecular structure remote from the chromophore. This is a severe test of the TD-DFT theory, since high-lying excitations define the most prominent features of the CD spectra, and complicates the use of computations to guide the assignment of absolute configuration. Experimental investigation of the high symmetry systems described here is desirable.

Calculation of ionization potential and chemical hardness: A comparative study of different methods

AbstractThe suitability of ab initio and density functional theory (DFT) methods for an accurate determination of ionization potential and chemical hardness is the subject of systematic analysis for a panel of molecules. Comparison of experimental ionization potential values with theoretical results indicates that using orbital energies obtained from the so‐called statistical average of orbital potential (SAOP) model exchange correlation potential in Koopman's theorem is an efficient method to evaluate the correct ionization potentials. Experimental ionization potential and electron affinity values have been used to calculate the absolute chemical hardness. Comparative results show that the chemical hardness values calculated by using Hartree–Fock orbital energies in Koopman's theorem are sufficiently good rather than Möller–Plesset second order perturbation method and DFT‐generalized gradient approximation (GGA) exchange correlation functional orbital energies. A new method given by Tozer et al. (J Phys Chem A 2005, 109, 8923) to calculate the chemical hardness works well with the orbital energies of DFT‐GGA functionals together with the ionization potential values calculated from SAOP orbital energies. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

Density functional study of double ionization energies

In this paper, double ionization energies (DIEs) of gas-phase atoms and molecules are calculated by energy difference method with density functional theory. To determine the best functional for double ionization energies, we first study 24 main group atoms in the second, third, and fourth periods. An approximation is used in which the electron density is first obtained from a density functional computation with the exchange-correlation potential V xc known as statistical average of orbital potentials, after which the energy is computed from that density with 59 different exchange-correlation energy functionals E xc. For the 24 atoms, the two best E xc functional providing DIEs with average absolute deviation (AAD) of only 0.25 eV are the Perdew-Burke-Ernzerhof functional modified by Hammer et al. [Phys. Rev. B 59, 6413 (1999)] and one known as the Krieger-Chen-Iafrate-Savin functional modified by Krieger et al. (unpublished). Surprisingly, none of the 20 available hybrid functionals is among the top 15 functionals for the DIEs of the 24 atoms. A similar procedure is then applied to molecules, with opposite results: Only hybrid functionals are among the top 15 functionals for a selection of 29 molecules. The best E xc functional for the 29 molecules is found to be the Becke 1997 functional modified by Wilson et al. [J. Chem. Phys. 115, 9233 (2001)]. With that functional, the AAD from experiment for DIEs of 29 molecules is just under 0.5 eV. If the two suspected values for C2H2 and Fe(CO)5 are excluded, the AAD improves to 0.3(2) eV. Many other hybrid functionals perform almost as well.

Density functional theory calculation of 2p spectra of SiH4, PH3, H2S, HCl, and Ar

AbstractThe method developed recently for prediction of 1s electron spectra is now extended to the 2p spectra of SiH4, PH3, H2S, HCl, and Ar. The method for X‐ray absorption spectra involves the use of ΔE for the excitation and ionization energies, and application of time‐dependent density functional theory using the exchange‐correlation potential known as statistical average of orbital potentials for the intensities. Additional assumptions and approximations are also made. The best exchange‐correlation functional Exc for the earlier calculation of ΔE in 1s spectra of C to Ne (namely Perdew–Wang 1986 exchange, combined with Perdew–Wang 1991 correlation) is no longer used in this work on 2p spectra of Si to Ar. Instead, recently tested Exc good for 2p core‐electron binding energies (known as OPTX) for exchange and LYP for correlation, plus scalar zeroth‐order regular approximation is adopted here for the ΔE calculations. Our calculated X‐ray absorption spectra are generally in good agreement with experiment. Although the predictions for the higher excitations suffer from basis set difficulties, our procedure should be helpful in the interpretation of absorption spectra of 2p electrons of Si to Ar. In addition, we report calculated results for other kinds of electron spectra for SiH4, PH3, H2S, HCl, and Ar, including valence electron ionizations and excitations as well as X‐ray emission. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008

Time-dependent density functional theory calculation of van der Waals coefficient of sodium clusters

In this paper we employ all-electron ab initio time-dependent density functional theory based method to calculate the long range dipole-dipole dispersion coefficient (van der Waals coefficient) C(6) of sodium atom clusters containing even number of atoms ranging from 2 to 20 atoms. The dispersion coefficients are obtained via Casimir-Polder relation [Phys. Rev. 3, 360 (1948)]. The calculations are carried out with two different exchange-correlation potentials: (i) the asymptotically correct statistical average of orbital potential (SAOP) and (ii) Vosko-Wilk-Nusair representation [Can. J. Phys. 58, 1200 (1980)] of exchange-correlation potential within local density approximation. A comparison with the other theoretical results has been performed. We also present the results for the static polarizabilities of sodium clusters and also compare them with other theoretical and experimental results. These comparisons reveal that the SAOP results for C(6) and static polarizability are quite accurate and very close to the experimental results. We examine the relationship between volume of the cluster and van der Waals coefficient, and find that to a very high degree of correlation C(6) scales as the square of the volume. We also present the results for van der Waals coefficient corresponding to cluster-Ar atom and cluster-N(2) molecule interactions.

Theoretical Study on the Electronic Spectrum and the Origin of Remarkably Large Third-Order Nonlinear Optical Properties of Organoimide Derivatives of Hexamolybdates

Electronic spectrum of organoimide derivatives of hexamolybdates have first been calculated within the time-dependent density-functional theory in conjunction with Van Leeuwen-Baerends (LB94) exchange correlation potential, statistical average of orbital potentials (SAOP), and gradient-regulated connection potential (GRAC), respectively. The GRAC yields much better agreement with experiments for the excitation energies comparing with both LB94 and SAOP. The analysis of transition nature indicates that there is a significant difference between the diagonal and the orthogonal substituted derivatives. The static and dynamic third-order polarizabilities are calculated using time-dependent density-functional theory combined with the sum-over-states method. The results show that these derivatives possess remarkable large molecular third-order polarizabilities, especially for system 8 with -17882.6 x 10(-36) esu. This value is about 250 times that for the C(60) molecule. Adding the organoimide segment to the [Mo(6)O(19)](2-) can substantially increase the nu value. This variation can be traced to the different electronic transition characteristics between the derivatives of [Mo(6)O(19)](2-) and [Mo(6)O(19)](2-). For our studied systems, increasing the conjugation length and diagonal substituted are efficient ways to enhance the third-order polarizability. Thus, the organoimide derivatives of hexamolybdates may comprise a new promising class of nonlinear optical materials from the standpoint of large values, small dispersion behavior, and high transparency.

Time-dependent density functional study of the electronic potential energy curves and excitation spectrum of the oxygen molecule

Orbital energies, ionization potentials, molecular constants, potential energy curves, and the excitation spectrum of O(2) are calculated using time-dependent density functional theory (TDDFT) with Tamm-Dancoff approximation (TDA). The calculated negative highest occupied molecular orbital energy (-epsilon(HOMO)) is compared with the energy difference ionization potential for five exchange correlation functionals consisting of the local density approximation (LDAxc), gradient corrected Becke exchange plus Perdew correlation (B(88X)+P(86C)), gradient regulated asymptotic correction (GRAC), statistical average of orbital potentials (SAOP), and van Leeuwen and Baerends asymptotically correct potential (LB94). The potential energy curves calculated using TDDFT with the TDA at internuclear distances from 1.0 to 1.8 A are divided into three groups according to the electron configurations. The 1pi(u) (4)1pi(g) (2) electron configuration gives rise to the X (3)Sigma(g) (-), a (1)Delta(g), and b (1)Sigma(g) (+) states; the 1pi(u) (3)1pi(g) (3) electron configuration gives rise to the c (1)Sigma(u) (-), C (3)Delta(u), and A (3)Sigma(u) (+) states; and the B (3)Sigma(u) (-), A (1)Delta(u), and f (1)Sigma(u) (+) states are determined by the mixing of two or more electron configurations. The excitation spectrum of the oxygen molecule, calculated with the aforementioned exchange correlation functionals, shows that the results are quite sensitive to the choice of functional. The LDAxc and the B(88X)+P(86C) functionals produce similar spectroscopic patterns with a single strongly absorbing band positioned at 19.82 and 19.72 eV, respectively, while the asymptotically corrected exchange correlation functionals of the SAOP and the LB94 varieties yield similar excitation spectra where the computed strongly absorbing band is located at 16.09 and 16.42 eV, respectively. However, all of the exchange correlation functionals yield only one strongly absorbing band (oscillator strength greater than 0.1) in the energy interval of 0-20 eV, which is assigned to a X (3)Sigma(g) (-) to (3)Sigma(u) (-) transition. Furthermore, the oxygen molecule has a rich spectrum in the energy range of 14-20 eV and no spin allowed absorption bands are predicted to be observed in the range of 0-6 eV.

Photoionization cross section and angular distribution calculations of carbon tetrafluoride

Correlation in the photoionization dynamics of carbon tetrafluoride is studied in the framework of the time-dependent density-functional theory (TDDFT) approach by employing a multicentric basis set expansion of the scattering wave function linear combination of atomic orbitals (LCAO) TDDFT. Results obtained with the statistical average of orbital potentials and LB94 exchange-correlation (xc) potentials are compared with photoabsorption, photoionization, and electron-scattering experiments as well as with past theoretical calculations. Inadequacies in both the V(xc) parametrizations employed have been suggested from the analysis of the intensity plots for the D2A1 ionization. The formation of resonant scattering states in selected continuum channels has been studied through the analysis of the dipole-prepared scattering wave function; our findings are then compared with results of electron-scattering calculations. Overall, the LCAO-TDDFT results highlight the effectiveness of the approach for the calculation of the unbound spectrum of fairly large molecules.

Photoabsorption and photoionization dynamics study of silicon tetrafluoride in the framework of time-dependent density-functional theory

Photoionization cross sections and angular distributions of silicon tetrafluoride have been calculated in the framework of the time-dependent density-functional theory approach. Both valence and inner shell ionizations have been considered in an extended photon energy range. Calculations have been carried out by using two different exchange-correlation (xc) potentials characterized by the correct asymptotic behavior. Theoretical results obtained with both the van Leeuwen--Baerends and statistical average of orbital potentials (SAOP) xc potentials are compared with photoabsorption, photoionization, and electron-scattering experiments as well as with previous theoretical calculations. It is suggested that even if both xc potentials provide a reasonably good description of the photoionization dynamics, correlation effects are phenomenologically better accounted for by the SAOP xc potential. Overall, the good accuracy attained with the linear combination of atomic orbitals-time dependent density-functional theory method in reproducing the experimental findings for ${\mathrm{SiF}}_{4}$ makes it a promising and powerful method for the characterization of the photoionization dynamics from medium and large-size molecules.

Understanding glycine conformation through molecular orbitals

The four most stable C(s) conformers of glycine have been investigated using a variety of quantum-mechanical methods based on Hartree-Fock theory, density-functional theory (B3LYP and statistical average of orbital potential), and electron propagation (OVGF) treatments. Information obtained from these models were analyzed in coordinate and momentum spaces using dual space analysis to provide insight based on orbitals into the bonding mechanisms of glycine conformers, which are generated by rotation of C-O(H) (II), C-C (III), and C-N (IV) bonds from the global minimum structure (I). Wave functions generated from the B3LYP/TZVP model revealed that each rotation produced a unique set of fingerprint orbitals that correspond to a specific group of outer valence orbitals, generally of a' symmetry. Orbitals 14a', 13a', 12a', and 11a' are identified as the fingerprint orbitals for the C-O(H) (II) rotation, whereas fingerprint orbitals for the C-C (III) bond rotation are located as 16a' [highest occupied molecular orbital (HOMO)], 15a' [next highest molecular occupied molecular orbital (NHOMO)], 14a', and 12a' orbitals. Fingerprint orbitals for IV generated by the combined rotations around the C-C, C-O(H), and C-N bonds are found as 16a', 15a', 14a', 13a', and 11a', as well as in orbitals 2a" and 1a". Orbital 14a' is identified as the fingerprint orbital for all three conformational processes, as it is the only orbital in the outer valence region which is significantly affected by the conformational processes regardless rotation of which bond. Binding energies, molecular geometries, and other molecular properties such as dipole moments calculated based on the specified treatments agree well with available experimental measurements and with previous theoretical calculation.

Density functional calculation of K-shell spectra of small molecules

Both Δ E KS and time-dependent density functional theory (TD-DFT) methods, with approximations for the singlet–triplet splitting and for the relativistic corrections, were tested for the calculation of K-shell spectra of Ne, HF, H 2O, NH 3, CH 4, and CO. Results from several exchange-correlation functionals as well as diffuse basis sets were compared with available experimental data. Excellent core excitation and core-electron ionization energies for Ne, HF, H 2O, NH 3, CH 4, and CO can be obtained from Δ E with Perdew–Wang 1986 exchange and Perdew–Wang 1991 correlation functionals; and reasonable intensities for singlet excitations, from TD-DFT with exchange-correlation potential known as statistical average of orbital potentials. The dependence of the quality of Δ E on basis set is as expected: excitations to higher Rydberg levels requiring more diffuse functions. However, the oscillator strength seems to be more sensitive to the quality of the basis set. Suggestions are made for extending the procedure to larger systems.

DFT calculation of core-electron binding energies

A total of 59 core-electron binding energies (CEBEs) were studied with the Amsterdam Density Functional Program (ADF) program and compared with the observed values. The results indicate that a polarized triple-zeta basis set of Slater-type orbitals is adequate for routine assessment of the performance of each method of computation. With such a basis set, seven density functionals were tested. In addition, the performance of 21 energy density functionals were computed from the density calculated with the statistical average of orbital potentials (SAOP). Among all the choices tested, the best density functional for core-electron binding energies of C to F turns out to be the combination of Perdew-Wang (1986) functional for exchange and the Perdew-Wang (1991) functional for correlation, confirming earlier studies based on contracted Gaussian-type orbitals. For this best functional, five Slater-type orbital basis sets were examined, ranging from polarized double-zeta quality to the largest set available in the ADF package. For the best functional with the best basis set, the average absolute deviation (AAD) of the calculated value from experiment is only 0.16 eV.

Influence of the exchange-correlation potential in density-functional calculations on polarizabilities and absorption spectra of alkali-metal clusters

All-electron calculations in large basis sets of excitation energies, oscillator strengths, and polarizabilities of small alkali-metal clusters of Li, Na, and K, with up to eight atoms, are performed using time-dependent density-functional theory. It is shown that the use of the recently developed statistical average of orbital potentials (SAOP) exchange-correlation (xc) potential [P.R.T. Schipper et al., J. Chem. Phys. 112, 1344 (2000)] leads to polarizabilities of these alkali-metal clusters which are 10\char21{}15 % larger than polarizabilities calculated with the xc potential of the local-density approximation (LDA). The lower LDA polarizabilities (in comparison to the SAOP) are shown to originate from differences in the low-lying excitation energies, which are determined by the xc potential in the molecular inner and valence region. In spite of such differences, both SAOP and LDA results are shown to provide reliable assignments of the experimental absorption spectra, with typical errors in peak positions of only 0.1\char21{} 0.2 eV, or even less.