Exact Kohn-Sham versus Hartree-Fock in momentum space: Examples of two-fermion systems

The question of how density functional theory (DFT) compares with Hartree-Fock (HF) for the computation of momentum-space properties is addressed in relation to systems for which (near) exact Kohn-Sham (KS) and HF one-electron matrices are known. This makes it possible to objectively compare HF and exact KS and hence to assess the potential of DFT for momentum-space studies. The systems considered are the Moshinsky [Am. J. Phys. 36, 52 (1968)] atom, Hooke's atom, and light two-electron ions, for which expressions for correlated density matrices or momentum densities have been derived in closed form. The results obtained show that it is necessary to make a distinction between true and approximate DFTs.     

A study of nitrogen oxides by using density functional theory and their comparison with ab initio and experimental data

Ab initio and density functional theory (DFT) methods have been applied to generated geometries of chemical systems built only from nitrogen and oxygen. The results of hybrid, local, and nonlocal DFT methods were compared with ab initio HF and MP2 methods. The suitability of DFT methods for modeling nitrogen-oxygen chemical systems is discussed. © 1996 John Wiley & Sons, Inc.     

A solid-state nitrogen-15 NMR and ab initio study of nitrobenzenes

Insight into the unexpectedly small range of isotropic nitrogen chemical shifts in nitrobenzene derivatives is gained through measurements of the chemical shift (CS) tensor by solid-state NMR experiments and ab initio molecular orbital (MO) and density functional theory (DFT) calculations. The principal components, delta(ii), of the (15)N CS tensors have been measured for nitrobenzene, 4-nitroaniline, 4-nitrotoluene, 4-nitroanisole, 4-nitroacetophenone, nitromesitylene, and 2,4,6-tri-tert-butylnitrobenzene. No obvious correlations of the delta(ii) values with traditional reactivity parameters were observed. The CS tensor components change significantly for the para-substituted nitrobenzenes, but these variations nearly cancel to yield isotropic shifts that fall in a range of only 3 ppm. Ab initio calculations of the delta(ii) values at the HF level are in poor agreement with the experimental values, whereas MP2 calculations and DFT calculations employing the B3LYP functional are in better agreement with experiment. The calculated (B3LYP/6-311G) delta(ii) values follow a trend in which delta(11) and delta(33) increase while delta(22) decreases with the accepted electron withdrawing ability of the para substituent. These changes tend to cancel yielding a variation in delta(iso) of only 4 ppm. These calculations indicate that the CS tensor has the same orientation as the carbon CS tensor in the isoelectronic benzoate anion: delta(11) bisects the O-N-O angle, delta(33) is perpendicular to the NO(2) plane, and delta(22) is in the NO(2) plane and perpendicular to delta(11).     

Optical absorption and emission properties of fluoranthene, benzo[k]fluoranthene, and their derivatives. A DFT study

Fluoranthene and benzo[k]fluoranthene-based oligoarenes are good candidates for organic light-emitting diodes (OLEDs). In this work, the electronic structure and optical properties of fluoranthene, benzo[k]fluoranthene, and their derivatives have been studied using quantum chemical methods. The ground-state structures were optimized using the density functional theory (DFT) methods. The lowest singlet excited state was optimized using time-dependent density functional theory (TD-B3LYP) and configuration interaction singles (CIS) methods. On the basis of ground- and excited-state geometries, the absorption and emission spectra have been calculated using the TD-DFT method with a variety of exchange-correlation functionals. All the calculations were carried out in chloroform medium. The results show that the absorption and emission spectra calculated using the B3LYP functional is in good agreement with the available experimental results. Unlikely, the meta hybrid functionals such as M06HF and M062X underestimate the absorption and emission spectra of all the studied molecules. The calculated absorption and emission wavelength are more or less basis set independent. It has been observed that the substitution of an aromatic ring significantly alters the absorption and emission spectra.     

Comparative study of DFT methods applied to small titanium/oxygen compounds

The performance of a number of different local and nonlocal density functional theory (DFT) methods has been investigated for some small titanium—oxygen systems. Equilibrium geometries, ionization potentials, dipole moments, atomization energies, and harmonic vibrational frequencies have been calculated for the TiO, TiO₂, and Ti₂ molecules, and the results are compared with experimental data and ab initio calculations. It is shown that most DFT methods perform much better than the ab initio Hartree—Fock (HF), second-order perturbation theory (MP2), and configuration interaction including single and double excitations (CISD) treatments. For good agreement with experimental data, gradient corrections to the exchange part of the DFT functional are needed, as well as some type of correction for the errors in the calculated energy splittings between different atomic states of titanium. Hybrid methods including a mixture of HF exchange with DFT exchange correlation do not perform as well as “pure” DFT methods for the studied systems. © 1996 John Wiley & Sons, Inc.     

Theoretical studies of molecular structure and vibrational spectra of melaminium citrate

The molecular geometry and vibrational frequencies of melaminium citrate in the ground state have been calculated using the Hartree-Fock (HF) and density functional method (B3LYP) with 6-31G(d) basis set. The optimized geometric bond lengths and bond angles obtained by using HF and density functional theory (DFT, B3LYP) show the best agreement with the experimental data. Comparison of the observed fundamental vibrational frequencies of melaminium citrate and calculated results by density functional B3LYP and Hartree-Fock methods indicate that B3LYP is superior to the scaled Hartree-Fock approach for molecular vibrational problems.     

Geometric and chelation influences on the electronic structure and optical properties of tetra(carboxylic acid)phenyleneethynylene dyes

A quantum-chemical study on the consequences of geometric modification and chelation on the electronic structure and optical properties of a tetra(carboxylic acid)phenyleneethynylene dye, of interest for chemical sensing applications, is presented. Rotation within the central biphenylene and complexation with divalent metal ions--in particular Cu2+--lead to notable changes in the absorption and emission profiles. Calculations at both the density functional theory (DFT) and Hartree-Fock (HF) levels are used to evaluate geometric potential energy surfaces for rotation within the central biphenylene unit; HF coupled with configuration interaction singles (HF-CIS) is used to investigate the first excited state of the dye. Time-dependent DFT (TDDFT) calculations are employed to assess changes in optical absorption and fluorescence as a function of geometry and chelation.     

Computational structural determination and energy landscape analysis of the hepatic carcinogen 2-(acetylamino)fluorene

 2-(Acetylamino)fluorene (AAF), a potent mutagen and a prototypical example of the mutagenic aromatic amines, forms covalent adducts to DNA after metabolic activation in the liver. A benchmark study of AAF is presented using a number of the most widely used molecular mechanics and semiempirical computational methods and models. The results are compared to higher-level quantum calculations and to experimentally obtained crystal structures. Hydrogen bonding between AAF molecules in the crystal phase complicates the direct comparison of gas-phase theoretical calculations with experiment, so Hartree–Fock (HF) and Becke–Perdew (BP) density functional theory (DFT) calculations are used as benchmarks for the semiempirical and molecular mechanics results. Systematic conformer searches and dihedral energy landscapes were carried out for AAF using the SYBYL and MMFF94 molecular mechanics force fields; the AM1, PM3 and MNDO semiempirical quantum mechanics methods; HF using the 3-21G*and 6-31G* basis sets; and DFT using the nonlocal BP functional and double numerical polarization basis sets. MMFF94, AM1, HF and DFT calculations all predict the same planar structures, whereas SYBYL, MNDO and PM3 all predict various nonplanar geometries. The AM1 energy landscape is in substantial agreement with HF and DFT predictions; MMFF94 is qualitatively similar to HF and DFT; and the MNDO, PM3 and SYBYL results are qualitatively different from the HF and DFT results and from each other. These results are attributed to deficiencies in MNDO, PM3 and SYBYL. The MNDO, PM3 and SYBYL models may be unreliable for compounds in which an amide group is immediately adjacent to an aromatic ring. Received: 26 May 2002 / Accepted: 12 December 2002 / Published online: 14 February 2003     

MP2, DFT and ab initio calculations on thioxanthone

Density functional theory (DFT), HF and MP2 calculations have been carried out to investigate thioxanthone molecule using the standard 6-31+G(d,p) basis set. The results of MP2 calculations show a butterfly structure for thioxanthone. The calculated results show that the predicted geometry can well reproduce the structural parameters. The predicted vibrational frequencies were assigned and compared with experimental IR spectra. A good harmony between theory and experiment is found. The theoretical electronic absorption spectra have been calculated using CIS method. ¹³C and ¹H NMR of the title compound have been calculated by means of B3LYP density functional method with 6-31+G(d,p) basis set. The comparison of the experimental and the theoretical results indicate that density functional B3LYP method is able to provide satisfactory results for predicting NMR properties.     

Experimental and computational studies on (<Emphasis Type="Italic">Z</Emphasis>)-1-((4-phenylamino)phenylamino)-methylene)naphthalen-2(1<Emphasis Type="Italic">H</Emphasis>)-one

The Schiff base compound (Z)-1-((4-phenylamino)phenylamino)methylene)naphthalen-2(1H)-one has been synthesized and characterized by IR, UV–Vis, and X-ray single-crystal determination. Molecular geometry from X-ray experiment of the title compound in the ground state have been compared using the Hartree–Fock (HF) and density functional method (B3LYP) with 6−31G(d,p) basis set. Calculated results show that density functional theory DFT and HF can well reproduce the structure of the title compound. Using the time-dependent density functional theory (TD-DFT) and Hartree–Fock (TD-HF) methods, electronic absorption spectra of the title compound have been predicted and a good agreement with the TD-DFT method and experimental ones is determined. The energetic behavior of the title compound in solvent media has been examined using B3LYP method with the 6−31G(d,p) basis set by applying the polarizable continuum model (PCM). The total energy of the title compound decreases with increasing polarity of the solvent. In addition, DFT calculations of the title compound, molecular electrostatic potential (MEP), natural bond orbital analysis (NBO), and non-linear optical (NLO) properties were performed at B3LYP/6−31G(d,p) level of theory.     

Quantum-chemical analysis of the CuCl2 molecule

This paper reports on quantum-chemical analysis of the linear structure of CuCl₂ by Hartree-Fock (HF) and density functional theory (DFT) methods and also by time-dependent HF (TD HF) and DFT (TD DFT) techniques. Using pure DFT exchange correlation functional (B3LYP) yields the best agreement with the experimental electronic spectra of CuCl₂. In this case, the odd electron is delocalized over the molecule, spin density on copper being 0.27. The ground state of the CuCl₂ molecule is ²Π_g with linear geometry.     

Impact of electron acceptor on three-photon absorption cross-section of the fluorene derivatives

Small three-photon absorption (3PA) cross-section values of present nonlinear organic molecules limit their practical applications. Although electron donors and electron acceptors have a great effect on 3PA cross-section, little is known about how the strength and situation of electron acceptors influence the 3PA cross-section value of a compound. The present work reports 3PA effects of two fluorene derivatives with symmetric D-π-π(A)-π-D archetype, which are named as 2,7-bis(4-methoxyphenylacetylene)-9-fluorenone (FATT) and 2,7-bis(4-methoxyphenylacetylene)-9-thoine-fluorene (TSATL). Large 3PA cross-section and ideal 3PA-induced optical limiting effects have been found in the two fluorene derivatives. The two molecules both have a different electron acceptor on the fluorene core, by which the 3PA cross-section value for FATT is enhanced by nearly 3-fold compared with that for TSATL. The mechanism of this significant enhancement in 3PA cross-section has been investigated by density functional theory (DFT) and configuration interaction singles (CIS) method with use of 6-311+G basis set in combination with conductor polarizable continuum model (CPCM). The theoretical results show that increase of electronegative character of the electron acceptor on the core is responsible for the increase of 3PA cross-section values of the two molecules.     

Proton affinity of diastereoisomers of modified prolines using the kinetic method and density functional theory calculations: role of the cis/trans substituent on the endo/exo ring conformation

The proton affinity (PA) of cis/trans-3-prolinoleucines and cis/trans-3-prolinoglutamic acids have been studied by the kinetic method and density functional theory (DFT) calculations. Several conformations of the neutral and the protonated modified prolines, in particular the endo and exo ring conformations, were analyzed with respect to their contribution to the PA values. When the substituent is an alkyl, both the diastereoisomers have the same PA value. However, the PA values for the diastereoisomers are different when the substituted chain contains functional groups (e.g. a carboxyl group). This variation in PA values could be attributed to the existence of intramolecular hydrogen bonds.     

Evaluating Shielding‐Based Ring‐Current Models by Using the Gauge‐Including Magnetically Induced Current Method

Magnetically induced current densities and integrated ring‐current strength susceptibilities have been calculated at the density functional theory (DFT) level for a test set consisting of 17 ring‐shaped molecules using the gauge‐including magnetically induced current (GIMIC) method. Reliable values for the ring‐current strengths have been obtained by performing numerical integration of the current‐density susceptibility passing a cut plane perpendicularly to the molecular ring. The current densities and ring current strengths were calculated at the DFT level using the B3LYP functional and def2‐TZVP basis sets. Current densities and ring‐current strengths have also been calculated at the Hartree‐Fock self‐consistent field (HF‐SCF) level using Dunning’s aug‐cc‐pVTZ basis sets, which allow a direct comparison with ring‐current strengths that have previously been estimated using ring‐current models based on magnetic shielding calculations. Current density calculations at both levels of theory show that the magnetic shielding based ring‐current models are not a very accurate means to estimate the magnetically induced ring current strengths, whereas they provide qualitatively the correct aromaticity trends for the studied molecules.     

De novo prediction of the ground state structure of transition metal complexes using semiempirical and ab initio quantum mechanics. Coordination isomerism

The ground state coordination isomers for 30 different trigonal bipyramidal transition metal complexes have been predicted using different levels of quantum mechanics: semiempirical (PM3(tm)), ab initio (MP2//HF), pure (BPW91) and hybrid (B3PW91) density functional theory (DFT) methods. For species where these methods failed to reproduce crystallographic data, hybrid quantum mechanics/molecular mechanics (QM/MM) methods were used to study more exact experimental models. Literature deficiencies regarding ground state multiplicity of these species were supplemented by spin predictions using previously tested PM3(tm) methods. Geometry optimization calculations were performed for each possible coordination isomer. The predicted ground state minima provided by the different methods are compared to each other and with crystallographic data. Pure DFT functionals outperformed hybrid functionals and MP2//HF. The very rapid PM3(tm) parameterization method provided accurate predictions in comparison to other levels of theory. An integrated MM/PM3(tm)/DFT de novo scheme accurately reproduced crystallographic data for species where the individual methods failed.     

Structural Characteristics of Graphane‐Type C and BN Nanostructures by Periodic Local MP2 Approach

The structural characteristics of fully‐hydrogenated carbon and boron nitride mono‐ and multilayer slabs, together with nanotubes derived from the slabs, are investigated mainly by means of periodic local second‐order Møller–Plesset perturbation (LMP2) calculations and the results are compared with Hartree–Fock (HF), density functional theory (DFT), and dispersion function‐augmented DFT (DFT‐D) obtained ones. The investigated systems are structurally analogous to (111) and (110) slabs of diamond, where the hydrogenated (111) slab of diamond corresponds to the experimentally known graphane. Multilayering of monolayers and nanotubes is energetically favorable at the LMP2 level for both C and BN, while HF and DFT are not able to reproduce this behavior for CH systems. The work highlights the importance of utilizing methods capable of properly describing weak interactions in the investigation of dispersively‐bound systems such as the multilayered graphanes and the corresponding nanotubes.     

High level of ab initio and density functional theory computational study of structural and energetic properties of tetrafluorhydrazine rotamers

The HF, MP2, MP3, MP4, and QCISD ab initio methods were compared with local, hybrid, and gradient-corrected density functional theory (DFT) methods for computing structures and energies of N2F4 rotamers. In all DFT calculations 6-311 + G(2d) basis set was used. The generated structures energies of trans- and gauche-N₂F₄ rotamers, and their dissociation energies to nitrogen difluoride were compared with experimental data. Suitable hybrid and gradient-corrected DFT methods for determining structures and energies for these and similar molecular systems were discussed.     

Vibrational frequencies of hydrazoic acid and methyl azide: density functional theory study

Harmonic vibrational frequencies of HN3 and CH3N3 molecules and their several isotopomers are calculated using HF, MP2 and five popular density functional theory (DFT) methods. On the basis of the comparison between calculated and experimental results, assignments of fundamental vibrational modes arc examined. HF and MP2 results are in bad agreement with experimental values. Of the five DFT methods, BLYP reproduces the observed fundamental frequencies the most satisfactorily. Two hybrid DFT methods are found to yield frequencies generally higher than the observed fundamental frequencies. The results indicate that BLYP calculation is a very promising approach for understanding the observed spectral features.     

(57)Fe Mössbauer isomer shifts of heme protein model systems: electronic structure calculations

We report the results of density functional theory (DFT) calculations of the (57)Fe M?ssbauer isomer shifts (delta(Fe)) for a series of 24 inorganic, organometallic, and metalloprotein/metalloporphyrin model systems in S = 0, (1)/(2), 1, (3)/(2), 2, and (5)/(2) spin states. We find an excellent correlation between calculation and experiment over the entire 2.34 mm s(-1) range of isomer shifts: a 0.07-0.08 mm s(-1) rms deviation between calculation and experiment (corresponding to 3-4% of the total delta(Fe) range, depending on the functionals used) with R(2) values of 0.973 and 0.981 (p < 0.0001). The best results are obtained by using the hybrid exchange-correlation functional B3LYP, used previously for (57)Fe M?ssbauer quadrupole splittings and (57)Fe NMR chemical shifts and chemical shielding anisotropies. The relativistically corrected value of alpha, alpha(rel), converges with the large basis set used in this work, but the exact values vary somewhat with the methods used: -0.253 a(0)(3) mm s(-1) (Hartree-Fock; HF); -0.316 a(0)(3) mm s(-1) (hybrid HF-DFT; B3LYP), or -0.367 a(0)(3) mm s(-1) (pure DFT; BPW91). Both normal and intermediate spin state isomer shifts are well reproduced by the calculations, as is the broad range of delta(Fe) values: from [Fe(VI)O(4)](2-) (-0.90 mm s(-1) expt; -1.01 mm s(-1) calc) to KFe(II)F(3) (1.44 mm s(-1) expt; 1.46 mm s(-1) calc). Molecular orbital analyses of all inorganic solids as well as all organometallic and metalloporphyrin systems studied reveal that there are three major core MO contributions to rho(tot)(0), the total charge density at the iron nucleus (and hence delta(Fe)), that do not vary with changes in chemistry, while the valence MO contributions are highly correlated with delta(Fe) (R(2) = 0.915-0.938, depending on the functionals used), and the correlation between the valence MO contributions and the total MO contribution is even better (R(2) = 0.965-0.976, depending on the functionals used). These results are of general interest since they demonstrate that DFT methods now enable the accurate prediction of delta(Fe) values in inorganic, organometallic, and metalloporphyrin systems in all spin states and over a very wide range of delta(Fe) values with a very small rms error.     

Assessment of theoretical methods for the calculation of methyl cation affinities

The methyl cation affinity (MCA; 298 K) of a variety of neutral and anionic bases has been examined computationally with a wide variety of theoretical methods. These include high-level composite procedures such as W1, G3, G3B3, and G2, conventional ab initio methods such as CCSD(T) and MP2, as well as a selection of density functional theory (DFT) methods. Experimental results for a variety of small model systems are well reproduced with practically all these methods, and the performance of DFT based methods are far superior in comparison to their MP2 analogs for these small models. For larger model, systems including motifs frequently encountered in organocatalysts, the performance deteriorates somewhat for DFT methods, while it improves significantly for MP2, rendering the former methods unreliable for common organic bases. Thus, MP2 calculations performed in combination with basis sets such as 6-31+G(2d, p) or larger, appear to offer a practical and reliable approach to compute MCAs of organic bases.