Application of the Colle–Salvetti model to the uniform electron gas

An application of the Colle–Salvetti wave function (Colle and Salvetti in Theor Chim Acta 37: 329, 1975) to the uniform electron gas model is made. Some different levels of approximation are used. Contrarily to the previous conclusions of other work (Tao et al. in Phys Rev A 63: 032513, 2001), the present result shows that the Colle–Salvetti wave function is able to reproduce, to a semiquantitative level, the properties of the uniform electron gas. The most important request for this result is an apropiate choice for the value of the only parameter entering in the Colle–Salvetti wave function. The present results are a good complement to those obtained by Moscardó et al. (Theor Chem Accounts 115: 334, 2006) for atoms. On the basis of the results obtained in this paper, a very simple functional for the correlation energy is put forward. Its application to the uniform electron gas, lead to a very reasonable set of results. It can be concluded that the Colle–Salvetti wave function remains being a good option to built, in an approximate way, the correlation component of a N-electron system. Contribution to the Serafin Fraga Memorial Issue.     

The Colle–Salvetti Wavefunction Revisited: a Comparison Between Three Approaches for Obtaining the Correlation Energy

The correlation factor of Colle and Salvetti is studied by comparing the behavior of three different correlation functionals. The normalization, sum rule, Coulomb hole, correlation energy integrand, and the Wigner exclusion hole have all been analyzed by applying the three approaches. The results indicate that the correlation factor proposed by Colle–Salvetti is a very good choice for modeling electron correlation in atoms. The flaws appearing in the development of the Colle–Salvetti equations seem mainly due to an inadequate use of the first mean value theorem of integral calculus. The Gaussian summation used for the two-body density matrix seems to be a good approximation to obtain the correlation factor equations.     

Theoretical Study of Intradimer Mechanism for Diamond Growth over Diamond (100)

The study of the energetics of the accepted intradimer diamond growth mechanism over (100) diamond surface is presented. The calculations were made in a density functional approach with the DGauss code using a DZVP2 basis set and a BLYP interchange and correlation potential. A simple 9-carbon cluster modeling the (100) diamond surface was used; its validity is discussed in relation with other calculations that used larger model clusters. The mechanism, presented in six steps, is based in the Harris and Garrison's work that considers the methyl radical as the main growth precursor agent and the breaking of the dimer surface bond with the corresponding methylene radical formation as a prior step to the formation of a CH₂-bridge structure, which is a feasible step; in contrast to these molecular dynamics results, Huang and Frenklach, using semiempirical methods, consider the breaking of the dimer surface bond and the formation of a CH₂-bridge structure as one step and this step as the energetically determinant of the mechanism. They also found an activation energy barrier for the interaction between a radical surface center with a H and CH₃. The present work tries to discern between these two ideas by calculating the activation barriers and the reaction energies for each step of the Harris and Garrison's mechanism in a density functional approach and comparing them to the results of Huang and Frenklach. The energy calculations point toward the scission of the dimer bond (step 4) as the determinant step; this step is endothermic, with an energy barrier of 50.43 kcal-mol^–1. On the other hand, the formation of the CH₂-bridge structure (step 5) is a feasible step with an energy barrier of 13.57 kcal-mol^–1. The adsorption of CH₃ (step 2) and H (step 6) species over radical surface sites did not involve any energy barriers, as it would be hoped. These steps were strongly exothermic and are close to the thermodynamic values for C—C and C—H bond energies. The removal of methylic hydrogen (step 3) did not show any problem because the activation barrier is only 3.68 kcal-mol^–1 less than the removal of a surface hydrogen (step 1), which has an energy barrier of 19.59 kcal-mol^–1. All steps, except number 4, were exothermic.     

Ab initio and density functional studies on the structure and vibrational spectra of 2-hydroxy-1,4-naphthoquinone-1-oxime derivatives

Structure and vibrational frequencies of lawsoneoxime and its C₃-substituted (R=CH₃, NH₂, Cl, NO₂) derivatives in keto and nitrosophenol forms have been obtained employing the Hartree–Fock and density functional methods. Charge distributions in different conformers have been studied using the molecular electrostatic potential topography as a tool. For all these derivatives except for nitrolawsoneoxime the amphi conformer in the keto form is predicted to be of lowest energy, which can partly be attributed to hydrogen bonding through the oximino nitrogen. In the nitro derivative, however, the preference to form a six membered ring owing to O–H–O hydrogen-bonded interactions makes the anti conformer (keto) the stablest. Further one of the nitrosophenol conformers of nitrolawsoneoxime turns out to be very close in energy (0.21 kJ mol^–1 higher) to this anti conformer. The consequences of hydrogen bonding on charge distribution and vibrational spectra are discussed.     

Basis-independent potential energy curves for the neutral diatomics of Li,Na and K evaluated by means of Hartree-Fock and different density functional potentials

Summary The solution of the Schrödinger equation for diatomic molecules when the finite element method is used gives the possibility to evaluate highly accurate basis-independent potential energy curves. In this work such types of numerically accurate potential energy curves on the HF level have been evaluated for Li₂, Na₂ and K₂ and could be used as benchmarks in the optimization of basis sets. A comparison between recent LCAO HF calculations in which extended basis sets are used and the accurate values determined in this work show that there is a difference in total energy of 4×10^–5 and 10^–3 a.u. for Li, Li₂, and Na, Na₂, respectively. Evaluated dissociation energies are, however, due to the cancellation of numerical errors in much better agreement. Further, it is found that different exchange correlation potentials for the heavier molecules such as those given by von Barth-Hedin and Vosko, Wilk and Nusair reproduce experimental properties such as dissociation energies, vibrational frequencies almost as well as those achieved with advanced CI methods. TheX potential gives accurate bond lengths for Na₂ and K₂, whereas the dissociation energies are too small.     

A theoretical investigation of the electronic and geometrical structure of silicon fluorides SiF n and their anions SiF n −,n=1−6

The electronic and geometrical structure of the ground and low-lying excited states of the SiF _n and SiF_n ^– series (n = 1-6) are calculated using the density functional method. Energies of fragmentation through different decay channels were evaluated for both series and found to be in good accord with the experimental data and results of nonempirical calculations. The adiabatic electron affinity (EA) of the neutral series is estimated for the first time. The SiF₄ ^– anion is shown to be stable toward dissociation though its neutral precursor possesses adiabatic EA close to zero. The SiF₅ ^– and SiF₆ ^– anions are stable toward dissociation in the gas phase; however, the neutral radical SiF₅ is near the stability threshold and SiF₆ is unstable as regards dissociation to SiF₄+F₂. An interesting peculiarity of the silicon fluoride anions is their similar energy of F-detachment, i.e. the affinities of all the neutral SiF_n, (n = 0-5) for the fluoride anion are similar.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 44–53, January, 1993.     

Potential-dependent chemisorption of carbon monoxide on platinum electrodes: new insight from quantum-chemical calculations combined with vibrational spectroscopy

Density functional theory (DFT) using the finite cluster approach is utilized to compute binding energies, bond geometries, and vibrational properties of carbon monoxide adsorbed on Pt(111) as a function of the external interfacial field, focusing attention on the metal–CO bond itself. Comparison with electrode potential-dependent frequencies for the metal–CO (ν_M–CO) as well as the much-studied intramolecular C---O (ν_CO) vibration, as measured by in-situ Raman and infrared spectroscopy, facilitate their interpretation in terms of metal-chemisorbate bonding for this archetypal electrochemical system. Decomposing the calculated metal–CO binding energy and vibrational frequencies into individual orbital and steric repulsion components enables the role of such quantum-chemical interactions to the field- (and hence potential-) dependent bonding to be assessed. No simple relationship between the field(F)-dependent binding energies and the ν_M–CO frequencies is evident. While the DFT ν_M–CO–F slopes are negative at positive and small–moderate negative fields, reflecting the prevailing influence of back-donation, a ν_M–CO–F maximum is obtained at larger negative fields for atop CO, and a plateau for hollow-site CO. This Stark-tuning behavior reflects largely offsetting field-dependent contributions from π and σ surface bonding, and can also be rationalized on the basis of changes in the electrostatic component of ν_M–CO from increasing M–CO charge polarization. A rough correlation between the field-dependent ν_M–CO frequencies and the corresponding bond distances, r_M–CO, is observed for hollow and atop CO in that r_M–CO shortens towards less positive fields, but becomes near-constant at moderate–large negative fields. A more quantitative correlation between the field-dependent C---O frequencies and bond lengths is also evident. In harmony with earlier findings (and unlike the ν_M–CO–F behavior), the ν_CO–F dependence is due chiefly to changes in the back-donation bonding component. The overall vibrational frequency-field behavior predicted by DFT is also in semi-quantitative concordance with experimental potential-dependent spectra.     

Conformational Analyses of Glycinal and Alaninal: A Computational Study

We present computational results from detailed gas-phase conformational analyses of the -substituted aldehydes, glycinal and alaninal. A synplanar conformer of glycinal and a synperiplanar conformer of alaninal in which the C=O and C–N bonds are in an eclipsing orientation are found to be lowest in energy; the two amino hydrogen atoms in these conformers are both directed over the C–C bond, i.e., in a compact arrangement. For the Group VA analogs, H₂P–CH₂–CHO and H₂P–CH(CH₃)–CHO, skew conformers in which the C–H and C–Me groups, respectively, are in an eclipsing orientation with the C=O bond are found to be lower in energy than the syn(peri)planar conformers. The results of various self-consistent reaction-field calculations suggest that the lowest-energy conformer of glycinal in 1, 2-dichloroethane is still synperiplanar, although the orientation of the amino hydrogen atoms may be different from that in the gas phase. Similar reaction-field calculations for alaninal raise the possibility that in this solvent a skew conformer, in which the C–H bond is nearly eclipsing the C=O bond, is energetically competitive with synperiplanar conformers.     

Test study on the excitation spectra of the N<Subscript>2</Subscript>–He van der Waals molecule

We have performed ab initio fourth-order Møller–Plesset perturbation theory calculations in the framework of the supermolecule approach on the vertical excitation spectra of the weakly bound van der Waals N₂–He dimer. They indicate a ``T-shaped' stablest ground N<sub>2</sub>(X<sup>1</sup><sub>g</sub><sup>+</sup>)–He(<sup>1</sup>S) electronic state with a well depth, D<sub>e</sub>, of 21.63 cm<sup>–1</sup> at a minimum distance, R<sub>e</sub>, of 3.44 Å and zero-point vibration correction, D<sub>o</sub>, of 7.07 cm<sup>–1</sup>. They also indicate a ``T-shaped' stablest excited conformer with R_e=3.25 Å, D_e=36.85 cm^–1 and D_o=17.06 cm^–1 for the N₂(B³_g)–He(¹S) triplet electronic level. In order to investigate the use of less-demanding correlation methods, test density functional theory calculations using the mPW1PW exchange–correlation functional are also presented for comparison.     

On the theoretical determination of the electron affinity of ozone

Summary Multiconfigurational electron correlation methods have been analyzed in order to theoretically compute the electron affinity (EA) of ozone. The near-degeneracy correlation effects, which are so important in O₃ and O ₃ ^– , have been described using complete active space (CAS) SCF wave functions. Remaining dynamic correlation effects are computed using second-order perturbation theory (the CASPT2 method). The best calculated adiabatic value (including zero-point energy corrections), 2.19 eV, is about 0.09 eV larger than the experimental value. Comparative studies using size-consistent coupled pair functional approaches (CPF and ACPF) have also been performed. The harmonic frequencies in O ₃ ^– have been determined to be: ₁=992, ₂=572, and ₃=879 cm^–1, which gives a zero-point energy of 0.151 eV.     

Density-functional investigation of the excited state properties and the Jahn-Teller effect in [CrX6]3− (X=Cl−, Br−)

Summary The luminescence of [CrX₆]^3– X=Br^–, Cl^– has been studied through density functional theory (DFT) using both deMon and ADF codes. Multiplet energies⁴A₂,²E,⁴T₂, and⁴T₁ have been expressed as energies of non-redundant single determinants and calculated as in Ref. [1]. The influence of the metal ligand distance on the multiplet energies has been investigated. Of particular interest to this work is the Jahn-Teller effect distortion. We found that the system moves to a more stable geometry when the axial bond length is compressed and the equatorial one elongated in agreement with the experimental value.     

Adiabatic integration formula for the correlation energy functional of the Hartree–Fock density

An adiabatic integration formula for the quantum chemistry correlation energy functional of the Hartree–Fock density, E _c ^QC[n], is presented. The functional E _c ^QC[n] is meant to be added to the completed Hartree–Fock energy to produce the exact ground-state energy of the system under consideration. The initial slope of the integrand in this connection formula is identified as a second-order energy and an explicit expression for the initial slope of the integrand is presented. Our expression should be useful for arriving at new improved approximations to E _c ^QC[n]. Previous numerical results by Huang and Umrigar (1997) Phys Rev A 56:290, for two-electron densities are proved, and a generalization to more than two electrons is presented. Results obtained by means of the present density functional theory correlation energy functionals, when used to approximate the initial slope in our adiabatic integration formula for E _c ^QC[n], are compared against exact numbers. Received: 10 September 1998 / Accepted: 3 February 1999 / Published online: 21 June 1999     

The non-N-representability of the Colle–Salvetti second-order reduced density matrix

The Colle–Salvetti second-order reduced density matrix (2-matrix) is an approximation to the 2-matrix obtained from a wave function that is a product of a reference wave function containing little or no correlation times a product of correlation factors that are functions of the coordinates of pairs of electrons. A formal proof is given for the non-N-representability for the Colle–Salvetti 2-matrix using the nonnegativity condition of the 2-matrix. The nonnegativity condition of the particle-hole overlap matrix (G matrix) is also not satisfied. The proof is valid for Colle–Salvetti 2-matrices obtained from both the Hartree–Fock and small multiconfigurational-self-consistent-field wave functions. Even though the Colle–Salvetti 2-matrix is not N-representable, it does satisfy the Pauli principle component of the G-matrix condition because it reduces to an N-representable first-order reduced density matrix. © 1993 John Wiley & Sons, Inc.     

Comparison of the effective core potential and model potential methods in studies of electron correlation energy in molecules: Dihalides and halogen hydrides

Summary The effective core potential and model potential methods were used in post-SCF calculations on HC1, HBr, Cl₂, and Br₂ in order to gain insight into the effect of insufficient representation of inner nodes in the valence orbitals of the approximate methods. The results show that while the correlation energy may be slightly overestimated (by 1–7%), both the electric moment functions and the quantities depending on energy differences are consistently similar for the methods studied and close to the results from all-electron calculations.Dedicated to Prof. Klaus Ruedenberg     

Density functional theory study on surface-enhanced Raman scattering of 4,4′-azopyridine on silver

Surface-enhanced Raman scattering (SERS) of 4,4′-azopyridine (AZPY) on silver foil substrate was measured under 1064 nm excitation lines. Density-functional theory (DFT) methods were used to calculate the structure and vibrational spectra of models such as Ag–AZPY, Ag₄–AZPY and Ag₆–AZPY complexes with B3LYP/6-31++G(d,p)(C,H,N)/Lanl2dz(Ag) basis set. The Raman bands of AZPY were identified on the ground of analog computation of potential energy distribution. The calculated spectra of Ag₄–AZPY and Ag₆–AZPY models were much approximated to the experimental results than that of Ag–AZPY model. The DFT results showed that the angles between two pyridyl rings keep 0° from AZPY to Ag–AZPY, Ag₄–AZPY and Ag₆–AZPY model. The energy gaps between the HOMO and LUMO changed from 363 to 1140 nm for AZPY-Ag complexes according to the DFT results. An conclusion was conceived that chemical enhancement mechanism may play an important role in the SERS of AZPY on silver substrate.     

Double H-bridged and single H-bridged diboryl radicals

The structures of B₂H₅·, B₂H₅CO·, and B₂H₅N₂· radicals are investigated using the 6–31G^* basis set. Both double H-bridged and single H-bridged isomers are found to be local minima on the potential energy surface. The effects of electron correlation are taken into account using single point MP4/6–31G^* calculations and, for the diboryl radicals, complete MP3/6–31G^* optimizations. In all cases the single H-bridged isomers are found to be more stable than the corresponding double H-bridged isomers.The transition state for the double H-bridged to single H-bridged B₂H₅· isomerization reaction is calculated to be 2.54 kcal mol^–1 above the double H-bridged radical at the MP4SDTQ/6-31G^*//UHF/ 6–31 G^* level when corrected for zero point energy. Barrier tunneling increased the reaction rate by a factor of 2.5–3.0, strongly suggesting the system is fluxional at this temperature.The addition of CO and N₂ to the diboryl radicals leads to relocation of the unpaired electron and rehybridization of the C and N atoms adjacent to the boron atoms. The isomers of B₂H₅CO· and B₂H₅N₂· are different and should be distinguishable experimentally. While the CO moiety is bound to the diboryl radicals isomers by over 19 kcal mol^–1, no binding energy is evident for N₂.     

The importance of Colle–Salvetti for computational density functional theory

The purpose of this presentation is to show the importance of the Colle–Salvetti (Theor Chim Acta 37:329, 1975) paper in the development of modern computational density functional theory. To do this we cover the following topics (1) the Bright Wilson understanding (2) the Kohn–Sham equations (3) local density exchange (4) the exchange-hole (5) generalised gradient approximation for exchange (Becke and Cohen) (6) left–right correlation and dynamic correlation (7) the development of the Lee–Yang–Parr dynamic correlation functional from the Colle–Salvetti paper (8) the early success of GGA DFT. Finally we observe that the the BLYP and OLYP exchange-correlation functionals are not semi-empirical; this may explain their great success.     

The electronic states of 1,2,5-oxadiazole studied by VUV absorption spectroscopy and CI, CCSD(T) and DFT methods

The 1,2,5-oxadiazole VUV absorption spectrum in the range 5–11.5 eV, shows broad bands centred near 6.2, 7.1, 8.3, 8.8, 10.6 and 11.3 eV. Rydberg states associated with three ionisation energies (IE) were identified in the complex fine structure above 8.7 eV. Electronic vertical excitation energies for singlet and triplet valence, and Rydberg states were computed using ab initio multi-reference multi-root CI methods. There is generally a good correlation between the envelope of the theoretical intensities and the experimental spectrum. The nature of the more intense calculated Rydberg states, and positions of the main valence and Rydberg bands are discussed. The lowest triplet, singlet and Rydberg 3s excited states have equilibrium structures that are non-planar with C_S symmetry, in a chair-like orientation where the O and H atoms lie out of the NCCN plane. This finding is consistent with the doubling of the low energy UV spectral lines [B.J. Forrest, A.W. Richardson, Can. J. Chem., 50 (1972) 2088].The nearly degenerate IE of the UV-photoelectron spectrum (UV–PES, Palmer et al. 1977) makes analysis of the VUV spectrum difficult, leading to the necessity for reinvestigation. Vertical studies (IE_V) using CI, Tamm–Dancoff (TDA) and Green’s Function (GF) methods all gave similar results, with near degeneracy of the first 3IE_V confirming the earlier study. Studies of the adiabatic IE (IE_A) using CCSD(T) and B3LYP methods, showed the energy sequence ²A₂ < ²B₁ < ²B₂, but these states are all saddle points, in contrast to the 4th state (²A₁) which is a minimum. In contrast, MP2 study of the ²B₂ state showed a minimum, with only two saddle points.Complete minima were found after minor twisting of the structures. The lowest energy cationic state is ²A^″ (C_S), which closely resembles the ²B₂ state. The O–N–C–C skeleton is twisted by 8°. The corresponding ²A^′ state (C_S) is effectively identical to the ²B₁ state. Attempts to find minima for other symmetry states were unsuccessful.     

Spin-flip approach within time-dependent density functional tight-binding method: Theory and applications

A spin-flip time-dependent density functional tight-binding (SF-TDDFTB) method is developed that describes target states as spin-flipping excitation from a high-spin reference state obtained by the spin-restricted open shell treatment. Furthermore, the SF-TDDFTB formulation is extended to long-range correction (LC), denoted as SF-TDLCDFTB. The LC technique corrects the overdelocalization of electron density in systems such as charge-transfer systems, which is typically found in conventional DFTB calculations as well as density functional theory calculations using pure functionals. The numerical assessment of the SF-TDDFTB method shows smooth potential curves for the bond dissociation of hydrogen fluoride and the double-bond rotation of ethylene and the double-cone shape of H₃ as the simplest degenerate systems. In addition, numerical assessments of SF-TDDFTB and SF-TDLCDFTB for 39 S₀/S₁ minimum energy conical intersection (MECI) structures are performed. The SF-TDDFTB and SF-TDLCDFTB methods drastically reduce the computational cost with accuracy for MECI structures compared with SF-TDDFT.