Spin-unrestricted calculations in quantum chemistry

The unrestricted complete active space self-consistent field (UCASSCF ) function is defined, and a proof that a UCASSCF eigenfunction of the spin operator S ² is a CASSCF function is given. The spin-contamination for an unrestricted Hartree–Fock (UHF ) function is evaluated by using Araki angle operators, and the UHF function is then projected on the restricted open-shell Hartree–Fock (ROHF ) space. The present analysis has deep consequences since it implies that the only non-spin-contaminated UHF functions are the ROHF functions. This is illustrated in a calculation of the spin density of He. © 1993 John Wiley & Sons, Inc.     

A note on density matrix extrapolation and multiple solutions of the unrestricted Hartree–Fock equations

Unrestricted Hartree–Fock (UHF) SCF–MO calculations on the doublet reaction surface for the addition of methylidyne (CH) to ethylene (C₂H₄) using the standard extrapolation techniques of the GAUSSIAN 70 program show erratic behavior. On the other hand, the potential energy surface calculated without extrapolation of the density matrix and by using the final density matrix of a neighboring point as the initial guess for the density matrix for the new point gave a smooth potential curve without any kinks or erratic pattern. Therefore, the density extrapolation technique should be used with particular caution in UHF calculations.     

钒硫团簇V2S2+、V3S4+的结构和稳定性

用ab initio分子轨道方法(RHF,UHF)和密度泛函(DFT)方法研究了团簇V2S2+、V3S4+的各种可能的几何构型和电子结构,所得理论计算能较好地解释有关实验结果.     

Rotationally invariant ab initio evaluation of Coulomb and exchange parameters for DFT+U calculations

Conventional density functional theory (DFT) fails for strongly correlated electron systems due to large intra-atomic self-interaction errors. The DFT+U method provides a means of overcoming these errors through the use of a parametrized potential that employs an exact treatment of quantum mechanical exchange interactions. The parameters that enter into this potential correspond to the spherically averaged intra-atomic Coulomb (U) and exchange (J) interactions. Recently, we developed an ab initio approach for evaluating these parameters on the basis of unrestricted Hartree-Fock (UHF) theory, which has the advantage of being free of self-interaction errors and does not require experimental input [Mosey and Carter, Phys. Rev. B 76, 155123 (2007)]. In this work, we build on that method to develop a more robust and convenient ab initio approach for evaluating U and J. The new technique employs a relationship between U and J and the Coulomb and exchange integrals evaluated using the entire set of UHF molecular orbitals (MOs) for the system. Employing the entire set of UHF MOs renders the method rotationally invariant and eliminates the difficulty in selecting unambiguously the MOs that correspond to localized states. These aspects overcome two significant deficiencies of our earlier method. The new technique is used to evaluate U and J for Cr(2)O(3), FeO, and Fe(2)O(3). The resulting values of U-J are close to empirical estimates of this quantity for each of these materials and are also similar to results of constrained DFT calculations. DFT+U calculations using the ab initio parameters yield results that are in good agreement with experiment. As such, this method offers a means of performing accurate and fully predictive DFT+U calculations of strongly correlated electron materials.     

EHF theory of chemical reactions V. Nature of manganese–oxygen bonds by hybrid density functional theory (DFT) and coupled‐cluster (CC) methods

Hybrid density functional theory (DFT) and post‐Hartree–Fock methods are compared by depicting potential energy curves of the O–O dissociation of hydroperoxide and the M–O dissociation of transition‐metal oxides. The former approach includes BLYP, B2LYP, B3LYP, and more general hybrid DFT methods, while the unrestricted Hartree–Fock (UHF) coulpled‐cluster (UCC) SD(T) method is considered as the latter approach. The hybrid DFT methods can reproduce the potential curve of the O–O dissociation process and the dissociation energy of HOOH by UCCSD(T). The methods are also useful for depicting potential curves of copper oxide (CuO) and manganese oxide (MnO), and reproduce the experimental M–O binding energies. The nature of Mn–O bonds in the naked Mn–O, Mn–O porphyrine system and model complexes, XH₃Mn(IV)O₂Mn(IV)H₃Y (X,Y=O,H), are examined in relation to the possible mechanisms of oxygenation reactions. It is found that the radical character of Mn–O bonds increases with the increase of the oxidation number of the Mn ion in these systems. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

On the nature of electron correlation in C60

The ground state restricted Hartree Fock (RHF) wave function of C(60) is found to be unstable with respect to spin symmetry breaking, and further minimization leads to a significantly spin contaminated unrestricted Hartree Fock (UHF) solution ( = 7.5, 9.6 for singlet and triplet, respectively). The nature of the symmetry breaking in C(60) relative to the radicaloid fullerene, C(36), is assessed by energy lowering of the UHF solution, , and the unpaired electron number. We conclude that the high value of each of these measures in C(60) is not attributable to strong correlation behavior as is the case for C(36). Instead, their origin is from the collective effect of relatively weak, global correlations present in the π space of both fullerenes. Second order perturbation (MP2) calculations of the singlet triplet gap are significantly more accurate with RHF orbitals than UHF orbitals, while orbital optimized opposite spin second order correlation (O2) performs even better.     

Rapid estimation of activation enthalpies for cytochrome-P450-mediated hydroxylations

Cytochrome P450 (CYP) enzymes play a critical role in detoxication and bioactivation of xenobiotics; thus, the ability to predict the biotransformation rates and regioselectivity of CYP enzymes toward substrates is an important goal in toxicology and pharmacology. Here, we present the use of the semiempirical quantum chemistry method SAM1 to rapidly estimate relative activation enthalpies (ΔH^?) for the hydroxylation of aliphatic carbon centers of various substrates. The ΔH^? were determined via a reaction path calculation, in the reverse direction (RRP), using the iron‐hydroxo‐porphine intermediate and the substrate radical. The SAM1 ΔH^? were calculated via unrestricted Hartree‐Fock (UHF) and configuration interaction (CI) formalisms for both the doublet and quartet spin states. The SAM1 RRP ΔH^?, after subtracting a correction factor, were compared with density functional theory (DFT) B3LYP activation energies for two sets of substrates and showed R² ranging from 0.69 to 0.89, and mean absolute differences ranging from 1.2 ± 1.0 to 1.7 ± 1.5 kcal/mol. SAM1 UHF and CI RRP calculation times were, on average, more than 200 times faster than those for the corresponding forward reaction path DFT calculations. Certain key transition‐state (TS) geometry measurements, such as the forming O···H bond length, showed good correlation with the DFT values. These results suggest that the SAM1 RRP approach can be used to rapidly estimate the DFT activation energy and some key TS geometry measurements and can potentially be applied to estimate substrate hydroxylation rates and regioselectivity by CYP enzymes. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2011     

Estimating the activation energy of the displacement of Mg atoms in the channels of B<Subscript>25</Subscript>C<Subscript>4</Subscript>Mg<Subscript>1.42</Subscript> crystals

The activation energy of displacement of Mg atoms through channels of B₂₅C₄Mg_1.42 crystals is estimated using quantum chemical calculations (DFT (B3LYP potential), RHF, and UHF methods, 3-21G basis set) of the element of the structure modeling the channel and location of Mg atoms in it. The changes in the activation energy at the replacement of Mg atoms by Na and Li atoms were estimated. The greatest decreasing in the activation energy was detected for Li atoms. The obtained results can be regarded as a theoretical background for development of conducting systems based on B₂₅C₄Mg_1.42 crystals.     

钴硫团簇ConSn+-1(n=2,3)的结构和稳定性

用ab initio分子轨道方法(RHF,UHF)和密度泛函(DFT)方法研究了团簇Co2S+,Co3S2+的各种可能的几何构型和电子结构,并计算了相应的较稳定构型的振动光谱,发现Co2S+和Co3S2+团簇最稳定结构均具有C,对称性.对团簇的成键作用机理进行了理论分析.     

Performance of density functionals for calculation of reductive ring-opening reaction energies of Li<Superscript>+</Superscript>-EC and Li<Superscript>+</Superscript>-VC

Reaction energies were determined for reductive ring-opening reactions of Li⁺-coordinated ethylene carbonate (EC) and vinylene carbonate (VC) by using various density functional theory (DFT) and ab-initio methods applying the basis sets up to Dunnings aug-cc-pVQZ. The methods examined include the local density functional (SVWN), the pure gradient-corrected density functionals (BLYP and BPW91), and the hybrid density functionals (B3LYP, B1LYP, B3PW91, and mPW1PW91). Comparison of the DFT results with ab-initio results indicates that the mPW1PW91 approach introduced by Adamo and Barone, is superior to all the other DFT methods (including B3LYP). The performance of more cost-effective Pople-type basis sets ranging from 6-31G(d,p) to 6-311++G(3df,3pd) was assessed at DFT levels of theory by calibrating them with the aug-cc-pVQZ results     

Exchange and correlation energy in density functional theory

Several different versions of density functional theory (DFT) that satisfy Hohenberg–Kohn theorems are characterized by different definitions of a reference or model state determined by an N‐electron ground state. A common formalism is developed in which exact Kohn–Sham equations are derived for standard Kohn–Sham theory, for reference‐state density functional theory, and for unrestricted Hartree–Fock (UHF) theory considered as an exactly soluble model Hohenberg–Kohn theory. A natural definition of exchange and correlation energy functionals is shown to be valid for all such theories. An easily computed necessary condition for the locality of exchange and correlation potentials is derived. While it is shown that in the UHF model of DFT the optimized effective potential (OEP) exchange satisfies this condition by construction, the derivation shows that this condition is not, in general, sufficient to define an exact local exchange potential. It serves as a test to eliminate proposed local potentials that are not exact for ground states. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 521–525, 2000     

Consequences of spin contamination in unrestricted calculations on open-shell species: effect of Hartree-Fock and Møller-Plesset contributions in hybrid and double-hybrid density functional theory approaches

The extent of spin contamination in unrestricted versions of pure, hybrid and double-hybrid density functional theory (DFT) methods, and its consequences, as manifested in the difference between unrestricted and restricted energies (U - R), has been investigated for 22 homolytic bond dissociation reactions. In accordance with previous studies, increasing the amount of Hartree-Fock (HF) exchange in unrestricted hybrid DFT procedures leads to an increase in the extent of spin contamination. However, in unrestricted double-hybrid DFT procedures, which include both a proportion of HF exchange and a perturbative correlation contribution (MP2), the opposing behavior of UHF and UMP2 with respect to spin contamination leads to smaller differences between the energies predicted by unrestricted and restricted variants. For example, for the most spin-contaminated radicals, a 30-100 kJ mol(-1) |U - R| difference at the HF and MP2 levels is reduced to just 0-5 kJ mol(-1) with the double-hybrid functionals. The double-hybrid UDFT procedures can thus benefit from the inclusion of UHF and UMP2 contributions without incurring to the same extent the problems associated with spin contamination.     

Accurate Structure and Bonding Description of the Transition Metal‐Disulfur Monoxide Complexes [(PMe3)2M(S2O)] (M = Ni,Pd, Pt): Grimme Dispersion Corrected DFT Study

Geometry and bonding energy analysis of M–S₂O bonds in the metal‐disulfur monoxide complexes [(PMe₃)₂M(S₂O)] of nickel, palladium, and platinum were investigated at DFT, DFT‐D3, and DFT‐D3(BJ) methods using three different functionals (BP86, PBE, and TPSS). The TPSS/DFT‐D3(BJ) yields better geometry, while the BP86 geometry is least accurate for studied complexes. The geometry of platinum complex optimized at TPSS/DFT‐D3(BJ) level is in excellent agreement with the available experimental values. The M–S bonds are shorter than the M–S(O) bonds. The Mayer bond orders suggest the presence of M–S and M–S(O) single bonds. Both the M–S and M–S(O) bond lengths vary with the density functionals as TPSS‐D3(BJ) < TPSS < PBE < BP86. The Hirshfeld charge distribution indicates that the overall charge flows from metal fragment to [S₂O]. The Ni–S₂O bond has greater degree of covalent character than the ionic. The contribution of dispersion interactions is large in computing accurate bond dissociation energies between the interacting fragments. The BDEs are largest for the functional TPSS and smallest for the functional BP86. The DFT‐D3 dispersion corrections to the BDEs between the metal fragments [(PMe₃)₂M] and ligand fragment [(S₂O)] for the TPSS functional are in the range 7.1–7.3 kcal · mol^–1, which are smaller than the corresponding DFT‐D3(BJ) dispersion corrections (9.4–10.6 kcal · mol^–1).     

Chirality and spin density: Ab initio and density functional approaches

The spin distribution in a stable nitroxide biradical that shows ferromagnetic interactions in the solid phase has been studied at three levels of theory: First, at the UHF level; then, including correlation effects in UMP 2 calculations; and finally, the results are compared with the spin density obtained using the local density functional (LDF ) approximation. It is shown that LDF spin densities are closer to UMP 2 than to UHF predictions; the difference between the UHF and the (UMP 2, LDF ) results points to a redistribution of the spin repartition between N and O due to electronic correlation. For planar conformations of the NO group, there is symmetric distribution (D_2d) of the spin density on the adamantane skeleton. For nonplanar nitroxides, the molecule is chiral (C₂), which results in a breakdown of the spin transmission on part of the adamantane cage. © 1993 John Wiley & Sons, Inc.     

Exchange interaction mechanisms in 1,3,5,7-tetramethyl-2,6-diazaadamantane <Emphasis Type="Italic">N,N’</Emphasis>-dioxyl biradical

The exchange interaction parameters were calculated and the spin density distribution over the organic skeleton of the 1,3,5,7-tetramethyl-2,6-diazaadamantane N,N’-dioxyl biradical was studied based on the results of quantum chemical modeling of the biradical structure by the DFT method using various hybrid functionals (UB3LYP, LC-wPBE, UCAM-B3LYP, UHSEH1PBE) with the 6-311++G(2d,2p) basis set and by the UHF method with the same basis set. The characteristics of the direct orbital overlap between the N atoms of the two nitroxide groups were determined. The values of the J constant, obtained using different calculation methods, were found to be similar to each other. It was established that there is ferromagnetic exchange interaction between the radical sites in the system in question, which occurs predominantly according to the spin polarization mechanism in the 2,6-diazaadamantane core, and the various spin density transfer pathways through the C atoms of the organic skeleton were found to be nonequivalent. The direct overlap of the upper singly-occupied МОs with localization on the nitroxide groups led to a noticeable additional contribution of the antiferromagnetic exchange interaction. Despite the latter factor, the total contribution of these two mechanisms (spin polarization and direct through-space exchange) resulted in the triplet ground state in the biradical studied.     

Assessing the Viability of the Methylsulfinyl Radical-Ozone Reaction

Although integral to remote marine atmospheric sulfur chemistry, the reaction between methylsulfinyl radical (CH₃SO) and ozone poses challenges to theoretical treatments. The lone theoretical study on this reaction reported an unphysically large barrier of 66 kcal mol⁻¹ for abstraction of an oxygen atom from O₃ by CH₃SO. Herein, we demonstrate that this result stems from improper use of MP2 with a single-reference, unrestricted Hartree-Fock (UHF) wavefunction. We characterized the potential energy surface using density functional theory (DFT), as well as multireference methodologies employing a complete active-space self-consistent field (CASSCF) reference. Our DFT PES shows, in contrast to previous work, that the reaction proceeds by forming an addition adduct [CH₃S(O₃)O] in a deep potential well of 37 kcal mol⁻¹. An O−O bond of this adduct dissociates via a flat, low barrier of 1 kcal mol⁻¹ to give CH₃SO₂+O₂. The multireference computations show that the initial addition of CH₃SO+O₃ is barrierless. These results provide a more physically intuitive and accurate picture of this reaction than the previous theoretical study. In addition, our results imply that the CH₃SO₂ formed in this reaction can readily decompose to give SO₂ as a major product, in alignment with the literature on CH₃SO reactions.     

Density functional theory study of UO<Stack> <Subscript>2</Subscript> <Superscript>2+</Superscript> </Stack> solvation in 1-butyl-3-methylimidazolium chloride

Structural characteristics and energies of [UO₂Cl₄(BMIm)_n]^(n–2)+ (n = 1-4) solvation complexes have been studied by the density functional theory (DFT) method in the SVWN5 local functional approximation.     

Molecular structure investigation of Z-3N(2-ethoxyphenyl)-2-N′(2-ethoxyphenyl)-imino-thiazolidin-4-one by <Emphasis Type="Italic">ab initio</Emphasis>, DFT and X-ray diffraction methods

We report here the synthesis of the Z-3N(2-ethoxyphenyl)-2-N′(2-ethoxyphenyl)-imino-thiazolidin-4-one compound. The crystal structure is determined by X-ray diffraction. The compound crystallizes in the monoclinic system with the space group P2_1/n and cell parameters: a = 9.4094(10) Å, b = 9.3066(10) Å, c = 20.960(2) Å, β = 99.0375(10)°, V = 1812.7(3) ų and Z = 4. The structure is refined to final R = 0.05 for 2083 observed reflections. The molecule in the crystal exhibits the intermolecular hydrogen bonds of C–H…O, C–H…N, and C–H…S types. Ab initio calculations are also performed at Hartree–Fock (HF) and density functional theory (DFT) levels. The full HF and DFT geometry optimization is carried out using the 6-31G(d,p) basis set. The observed molecular structure is compared with that calculated by both HF and DFT methods. The optimized geometry of the titled compound is found to be consistent with the structure determined by X-ray diffraction.     

Synthesis,spectroscopic characterization,crystal structure determination and DFT calculations of [Au(Me<Subscript>2</Subscript>phen)Br<Subscript>2</Subscript>][AuBr<Subscript>2</Subscript>]

New mixed valence gold(III/I) salt containing two complexes [Au(Me₂phen)Br₂][AuBr₂] (1) was prepared from the reaction of AuBr₃ and 5,6-dimethyl-1,10-phenanthroline (Me₂phen) in a mixture of methanol and acetonitrile. Suitable crystals of 1 for X-ray diffraction measurement were obtained by slow evaporation of the resulted red solution at room temperature. This complex was characterized by spectral methods (IR, UV–Vis and ¹H NMR), elemental analysis and single-crystal X-ray diffraction. The X-ray structural analysis indicated that the asymmetric unit of 1 contains one [Au(Me₂phen)Br₂]⁺ cation and two half anions of [AuBr₂]^ˉ. Furthermore, the packing diagram of this complex, 3-D structure stabilized by intermolecular Au…Br and Au…π interactions and intermolecular C–H···Br hydrogen bonds. The experimental investigations on complex have been accompanied computationally by the density functional theory (DFT) and time-dependent DFT calculations. The nature of the Au–N bonds was investigated using quantum theory of atoms in molecules. Moreover, natural bond orbital analysis carried out to obtain hyper-conjugative interactions and electron delocalization on the complex.