Ab initio model potential embedded-cluster study of the ground and lowest excited states of Cr[sup 3+] defects in the elpasolites Cs[sub 2]NaYCl[sub 6] and Cs[sub 2]NaYBr[sub 6] (original) (raw)
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Journal of Molecular Structure, 2007
Detailed microscopic study of the crystal field strength 10Dq, constants of electron-vibrational interaction and Huang-Rhys factors for Cs 2 NaYX 6 :Cr 3+ (X = F, Cl, Br) crystals is presented. The method used in the calculations is the first-principles fully relativistic discrete-variational Dirac-Slater (DV-DS) method based on solving Dirac equations with the local density approximation. The basic features of the method are: (1) the first-principles method without any phenomenological parameters; (2) wide area of applications: to any atom or ion in any symmetry from O h to C 1 for any energy interval from IR to X-ray; (3) possibility to take into account all effects of chemical bond formation. The key idea of the method is that the molecular orbitals (MO) consisting of the wave functions of an impurity ion and ligands are used throughout the calculations rather than atomic wave functions.
Physical Review A, 1999
van Leeuwen and Baerends proposed a Becke-like nonlocal correction to the local-density-approximation ͑LDA͒ exchange-correlation potential so that its asymptotic structure becomes exact i.e., Ϫ1/r ͓Phys. Rev. A 49, 2421 ͑1994͔͒. They showed that it significantly improves the value of the highest occupied orbital eigenvalue of atoms and molecules. However, the correction is exchangelike in nature. With this in mind, in this paper we investigate how this correction affects the total energies and highest eigenvalues within the exchangeonly approximation. We show that the potential also corrects the LDA errors substantially within this approximation, and leads to total energies and high eigenvalues which compare well with their Hartree-Fock counterparts. Improvement in the asymptotic behavior of the potential should also result in better values of the response properties of these systems. We show that with this correction one obtains better estimates, both within the exchange-only approximation and with correlation included, of the linear and nonlinear polarizabilities of inert gas atoms. This is quite significant, since the LDA is known to overestimate the nonlinear polarizabilities of these atoms by roughly 100%. On the other hand, for alkaline-earth atoms the values of polarizabilities obtained with this correction are not satisfactory. Nonetheless, hyperpolarizabilities show a marked improvement over the LDA results. ͓S1050-2947͑99͒06711-6͔
Rwanda Journal, 2012
Theoretical study of properties of Cs 2 Cl + , CsCl 2 − , Cs 3 Cl 2 + and Cs 2 Cl 3 − ions has been performed using the density functional theory (DFT/B3LYP) and the second order Møller-Plesset perturbation theory (MP2). Two triple-zeta basis sets, the midsized B1 and the extended one B2, have been used. Equilibrium structure, vibrational spectra, energies and enthalpies of dissociation reactions of the ions have been found. The effect of the basis set size and the computation method on the results has been analyzed. The MP2 method with the extended basis B2 set was accepted as the more accurate among the others. For the triatomic ions Cs 2 Cl + and CsCl 2 − , the equilibrium structure has been found to be linear. For the pentaatomic ions, three isomeric forms were considered. The most abundant isomer in saturated vapor was found to be the angular V-shaped of C 2v symmetry for Cs 3 Cl 2 + and the linear of D ∞h symmetry for Cs 2 Cl 3 −. Thermodynamic functions of the ions were computed and applied to the treatment of experimental mass spectrometric data. Enthalpies of formation ∆ f Hº(0 K) were determined (in kJ/mol): 51 ± 4 (Cs 2 Cl +), −622 ± 3 (CsCl 2 −), −301 ± 8 (Cs 3 Cl 2 +), −975 ± 6 (Cs 2 Cl 3 −).
The Journal of Chemical Physics, 2011
Communication: Orbital instabilities and triplet states from time-dependent density functional theory and longrange corrected functionals J. Chem. Phys. 135, 151103 (2011) Basis set convergence of explicitly correlated double-hybrid density functional theory calculations J. Chem. Phys. 135, 144119 (2011) Density functional theory calculations of dynamic first hyperpolarizabilities for organic molecules in organic solvent: Comparison to experiment J. Chem. Phys. 135, 134104 (2011) Communication: Rationale for a new class of double-hybrid approximations in density-functional theory J. Chem. Phys. 135, 101102 (2011) The performance and relationship among range-separated schemes for density functional theory J. Chem. Phys. 135, 074109 (2011) Additional information on J. Chem. Phys. The framework of ab initio density-functional theory (DFT) has been introduced as a way to provide a seamless connection between the Kohn-Sham (KS) formulation of DFT and wave-function based ab initio approaches [R. J. Bartlett, I. Grabowski, S. Hirata, and S. Ivanov, J. Chem. Phys. 122, 034104 (2005)]. Recently, an analysis of the impact of dynamical correlation effects on the density of the neon atom was presented [K. Jankowski, K. Nowakowski, I. Grabowski, and J. Wasilewski, J. Chem. Phys. 130, 164102 ], contrasting the behaviour for a variety of standard density functionals with that of ab initio approaches based on second-order Møller-Plesset (MP2) and coupled cluster theories at the singles-doubles (CCSD) and singles-doubles perturbative triples [CCSD(T)] levels. In the present work, we consider ab initio density functionals based on second-order manybody perturbation theory and coupled cluster perturbation theory in a similar manner, for a range of small atomic and molecular systems. For comparison, we also consider results obtained from MP2, CCSD, and CCSD(T) calculations. In addition to this density based analysis, we determine the KS correlation potentials corresponding to these densities and compare them with those obtained for a range of ab initio density functionals via the optimized effective potential method. The correlation energies, densities, and potentials calculated using ab initio DFT display a similar systematic behaviour to those derived from electronic densities calculated using ab initio wave function theories. In contrast, typical explicit density functionals for the correlation energy, such as VWN5 and LYP, do not show behaviour consistent with this picture of dynamical correlation, although they may provide some degree of correction for already erroneous explicitly density-dependent exchange-only functionals. The results presented here using orbital dependent ab initio density functionals show that they provide a treatment of exchange and correlation contributions within the KS framework that is more consistent with traditional ab initio wave function based methods.
Journal of Chemical Theory and Computation, 2014
The 3d-series transition metals (also called the fourth-period transition metals), Sc to Zn, are very important in industry and biology, but they provide unique challenges to computing the electronic structure of their compounds. In order to successfully describe the compounds by theory, one must be able to describe their components, in particular the constituent atoms and cations. In order to understand the ingredients required for successful computations with density functional theory, it is useful to examine the performance of various exchange−correlation functionals; we do this here for 4s N 3d N ′ transition-metal atoms and their cations. We analyze the results using three ways to compute the energy of the open-shell states: the direct variational method, the weighted-averaged broken symmetry (WABS) method, and a new broken-symmetry method called the reinterpreted broken symmetry (RBS) method. We find the RBS method to be comparable in accuracy with the WABS method. By examining the overall accuracy in treating 18 multiplicity-changing excitations and 10 ionization potentials with the RBS method, 10 functionals are found to have a mean-unsigned error of <5 kcal/mol, with ωB97X-D topping the list. For local density functionals, which are more practical for extended systems, the M06-L functional is the most accurate. And by combining the results with our previous studies of p-block and 4d-series elements as well as databases for alkyl bond dissociation, main-group atomization energies, and π−π noncovalent interactions, we find five functionals, namely, PW6B95, MPW1B95, M08-SO, SOGGA11-X, and MPWB1K, to be highly recommended. We also studied the performance of PW86 and C09 exchange functionals, which have drawn wide interest in recent studies due to their claimed ability to reproduce Hartree−Fock exchange at long distance. By combining them with four correlation functionals, we find the performance of the resulting functionals disappointing both for 3d transition-metal chemistry and in broader tests, and thus we do not recommend PW86 and C09 as components of generalized gradient approximations for general application. a GS − electronic state of neutral ground state; ES − electronic state of neutral excited state; ΔE − excitation energy of neutral atom, kcal/mol; GS + − electronic state of cation ground state; ES + − electronic state of cation excited state; ΔE + − excitation energy of cation, kcal/mol; IP − ionization potential, kcal/mol Journal of Chemical Theory and Computation Article dx.doi.org/10.1021/ct400712k | J. Chem. Theory Comput. 2014, 10, 102−121 Journal of Chemical Theory and Computation Article dx.doi.org/10.1021/ct400712k | J. Chem. Theory Comput. 2014, 10, 102−121 a MUE is in kcal/mol. The functionals are arranged in order of increasing MUE for the RBS method. When the MUE for RBS is the same (rounded to the nearest tenth of a kcal/mol), the order is the sum of the MUs for the variational, WABS, and RBS methods.
Comparative studies of the spectroscopy of Cu Cl 2: DFT versus standard ab initio approaches
Journal of Chemical Physics, 2005
The X 2 ⌸ g -2 ⌺ g + , X 2 ⌸ g -2 ⌬ g , X 2 ⌸ g -2 ⌺ u + , X 2 ⌸ g -2 ⌸ u transitions on CuCl 2 have been studied using several exchange-correlation functionals from the various types of density functional theory ͑DFT͒ approaches like local density approximation ͑LDA͒, generalized gradient approximation ͑GGA͒, hybrid and meta-GGA. The results are compared with the experience and with those coming from the most sophisticated nondynamic and dynamic electronic correlation treatments using the same relativistic effective core potentials and especially developed basis sets to study the electronic structure of the five lowest states and the corresponding vertical and adiabatic transition energies. The calculated transition energies for three of the hybrid functionals ͑B3LYP, B97-2, and PBE0͒ are in very good agreement with the benchmark ab initio results and experimental figures. All of the other functionals largely overestimate the X 2 ⌸ g -2 ⌺ g + and X 2 ⌸ g -2 ⌬ g transition energies, many of them even placing the 2 ⌬ g ligand field state above the charge transfer 2 ⌸ u and 2 ⌺ u + states. The relative weight of the Hartree-Fock exchange in the definition of the functional used appears to play a key role in the accurate description of the ⌳S⌺ density defined by the orientation of the 3d hole ͑, , or ␦͒ on Cu in the field of both chlorine atoms, but no simple connection of this weight with the quality of the spectra has been found. Mulliken charges and spin densities are carefully analyzed; a possible link between the extent of spin density on the metal for the X 2 ⌸ g state and the performance of the various functionals was observed, suggesting that those that lead to the largest values ͑close to 0.65͒ are the ones that best reproduce these four transitions. Most functionals lead to a remarkably low ionicity for the three ligand field states even for the best performing functionals, compared to the complete active space ͑SCF͒ ͑21, 14͒ ab initio values. These findings show that not only large variational ab initio calculations can produce reliable spectroscopic results for extremely complex systems where delicate electronic correlation effects have to be carefully dealt with. However, those functionals that were recently shown to perform best for a series of molecular properties ͓J. Chem. Phys. 121 3405 ͑2004͔͒ are not the ones that produce the best transition energies for this complex case.
Cl···Cl Interactions in Molecular Crystals: Insights from the Theoretical Charge Density Analysis
The Journal of Physical Chemistry A, 2013
The structure, IR harmonic frequencies and intensities of normal vibrations of 20 molecular crystals with the X−Cl···Cl−X contacts of different types, where X = C, Cl, and F and the Cl···Cl distance varying from ∼3.0 to ∼4.0 Å, are computed using the solid-state DFT method. The obtained crystalline wave functions have been further used to define and describe quantitatively the Cl···Cl interactions via the electron-density features at the Cl···Cl bond critical points. We found that the electron-density at the bond critical point is almost independent of the particular type of the contact or hybridization of the ipso carbon atom. The energy of Cl···Cl interactions, E int , is evaluated from the linking E int and local electronic kinetic energy density at the Cl···Cl bond critical points. E int varies from 2 to 12 kJ/mol. The applicability of the geometrical criterion for the detection of the Cl···Cl interactions in crystals with two or more intermolecular Cl···Cl contacts for the unique chlorine atom is not straightforward. The detection of these interactions in such crystals may be done by the quantum-topological analysis of the periodic electron density.