Role of electron correlation in the polydeprotonation of benzene to form trianions

Computations for anion, dianions, and trianions of benzene are carried out to study the role of electron correlation in the polydeprotonation of benzene leading to benzene trianions both in the singlet and triplet states. The computations, while assessing the use of polarization and diffuse functions, are performed with Møller–Plesset second‐order (MP2) perturbation theory and coupled‐cluster theory up to the level of CCSD(T)/6‐311++G(d,p)//MP2/6‐311++G(d,p), and with density functional theory (DFT) employing a hybrid, B3LYP, and a meta‐hybrid, M05‐2X, exchange‐correlation functionals with Gaussian basis set 6‐311++G(d,p) and correlation consistent basis set aug‐cc‐pVDZ. The deprotonation energies, including zero‐point energy correction, of benzene anion and dianions are found to be highly sensitive to the quantum mechanical method and the basis set used. The formation of dianions and trianions, where the anionic centers lie adjacent to each other, is observed with unusual behavior in the deprotonation energy and the geometrical parameters obtained from the different level of the theories. The two exchange‐correlation functionals compared show contrasting and unusual results for the trianionic species particularly for the triplet states, even if the diffuse functions are included in the basis set. Besides this, the ortho‐dianion and 1,3,5‐trianion are predicted to be ground‐state triplet at CCSD(T)/6‐311++G(d,p)//MP2/6‐311++G(d,p) and DFT/M05‐2X/6‐311++G(d,p) levels, whereas DFT/B3LYP/6‐311++G(d,p) predicts meta‐dianion and 1,2,3‐trianion to be ground‐state triplet where all the anionic centers lie adjacent to each other. Copyright © 2014 John Wiley & Sons, Ltd.     

Quantum Monte Carlo assessment of density functionals for π-electron molecules: ethylene and bifuran

ABSTRACT

We perform all-electron, pure-sampling quantum Monte Carlo (QMC) calculations on ethylene and bifuran molecules. The orbitals used for importance sampling with a single Slater determinant are generated from Hartree-Fock and density functional theory (DFT). Their fixed-node energy provides an upper bound to the exact energy. The best performing density functionals for ethylene are BP86 and M06, which account for 99% of the electron correlation energy. Sampling from the π-electron distribution with these orbitals yields a quadrupole moment comparable to coupled cluster CCSD(T) calculations. However, these, and all other density functionals, fail to agree with CCSD(T) while sampling from electron density in the plane of the molecule. For bifuran, as well as ethylene, a correlation is seen between the fixed-node energy and deviance of the QMC quadrupole moment estimates from those calculated by DFT. This suggests that proximity of DFT and QMC densities correlates with the quality of the exchange nodes of the DFT wave function for both systems.     

Chlorination of ammonia and aliphatic amines by Cl2: DFT study of medium and substituent effects

The mechanism of chlorination of ammonia and aliphatic amines by Cl₂ was studied by quantum‐chemical calculations using a series of DFT functionals. Three different reaction pathways were considered for the reaction between Cl₂ and NH₃ in the gas phase. Several intermediates and transition state structures, not described earlier, were located on the corresponding potential energy surface. It is calculated that the reaction field effects (SCIPCM) on the chlorination is much less pronounced than the effect of a specific solvent interaction which was modeled by an explicit water molecule. It is also found that the calculated energy barrier and the reaction free energy of the chlorination of different amines are dependent on the alkyl‐substituent effects. With increase in the basicity of amine, the chlorination reaction becomes more feasible. Calculated geometries of intermediates and overall reaction energetics are significantly influenced by the method for a treatment of electron correlation (DFT vs. MP2), and by the fraction of HF exchange (χ) in DFT functionals. With increase in the χ in the corresponding functional, the DFT results approach those obtained at the MP2 level, and are closer to experimental values, as well. Copyright © 2008 John Wiley & Sons, Ltd.     

A coupled cluster treatment of intramonomer electron correlation within symmetry-adapted perturbation theory: benchmark calculations and a comparison with a density-functional theory description

Symmetry-adapted perturbation theory (SAPT) with intramonomer electron correlation described by coupled cluster theory limited to single and double excitations was applied to 21 noncovalent complexes in their minimum geometries. The resulting benchmark contributions to the interaction energy were utilized to examine the accuracy of a more approximate variant of the SAPT method, where interacting molecules are described by density functional theory (DFT) with different functionals, like LDA, PBE, B3LYP, PBE0, M05, M05-2X, M06, and M06-2X (in all cases the asymptotic correction for the exchange-correlation functional has been utilized). Average errors for individual energy components of SAPT(DFT) are not larger than 10% for best functionals under study. Among the tested functionals PBE0, M05, and B3LYP should be especially recommended for the SAPT(DFT) approach. The M06 functional gives the largest errors with respect to SAPT(CCSD) and should not be used for describing intramonomer correlation in SAPT.     

Left-right correlation energy

We first attempt to determine a local exchange functional E_x[p] which accurately reproduces the Hartree-Fock (HF) energies of the 18 first and second row atoms. E_x[p is determined from p and |δp|, and we find that we can improve significantly upon Becke's original generalized gradient approximation functional (commonly called B88X) by allowing the coefficient of the Dirac exchange term to be optimized (it is argued that molecules do not behave like the uniform electron gas). We call this new two parameter exchange functional OPTX. We find that neither δ p or t = Σ δ _i |² improve the fit to these atomic energies. These exchange functionals include not only exchange, but also left-right correlation. It is therefore proposed that this functional provides a definition for exchange energy plus left-right correlation energy when used in Kohn-Sham (KS) calculations. We call this energy the Kohn-Sham exchange (or KSX) energy. It is shown that for nearly all molecules studied these KSX energies are lower than the corresponding HF energies, thus giving values for the non-dynamic correlation energy. At stretched geometries, the KSX energies are always lower than the HF energies, and often substantially so. Furthermore all bond lengths from the KSX calculations are longer than HF bond lengths and experimental bond lengths, which again demonstrates the inclusion of left-right correlation effects in the functional. For these reasons we prefer to split the correlation energy into two parts: left-right correlation energy and dynamic correlation energy, arguing that the usage of the words ‘non-dynamic’ or ‘static’ or ‘near-degeneracy’ is less meaningful. We recognize that this definition of KSX is not precise, because the definition of a local E_x[p] can never be precise. We also recognize that these ideas are not new, but we think that their importance has been insufficiently recognized in functional determination. When we include third row atoms in our analysis, we are unable to find a local exchange functional which is a substantial improvement over B88X for the reproduction of HF energies. This must arise from the effects of the core orbitals, and therefore we do not consider that this detracts from the improved accuracy of OPTX. We report some MCSCF calculations constructed from bonding-antibonding configurations, from which we attempt to calculate ab initio left-right correlation. There is only moderate agreement between the two approaches. Finally we combine the OPTX functional with established correlation functionals (LYP, P86, P91) to form OLYP, OP86 and OP91; OLYP is a great improvement on BLYP for both energy and structure, and OP86, OP91 are an improvement over BP86, BP91 for structure. The importance of the exchange functional for molecular structure is therefore underlined.     

Application of density-functional perturbation theory to calculate nonlinear polarizabilities of helium-like systems

Density-based perturbation theory within the Hohenberg-Kohn (HK) formalism of density functional theory (DFT), developed recently by us, is employed to calculate hyperpolarizabilities of helium-like ions from their ground-state densities obtained from their respective Hylleraas wavefunctions. The only approximation made is that of the local density (LDA) for exchange and correlation. Use of densities — instead of wavefunctions — in density-based perturbation theory together with simple approximate energy functionals makes our calculations much simpler than those based on wavefunctions. They lead, however, to accurate results.     

Practical failures from the inclusion of exact exchange: how much exact exchange is appropriate?

The influence of exact exchange incorporated into exchange—correlation functionals on the predictions of relative energies, structures, electronic states, and vibrational spectra is examined numerically. Failures of widely used hybrid exchange—correlation functionals due to either the physical unacceptability of including exact exchange or an unbalanced mixing of exact exchange are considered. One set of examples involves tetraatomic chalcogen clusters and charge transfer complexes between diatomic chalcogens and diatomic oxygen. Poor energetic predictions from Hartree-Fock rule against the inclusion of exact exchange into the exchange—correlation functionals for these systems with significant left—right electron correlation effects. The energies of the conformers of [10]annulene are considered from an unusual viewpoint, namely, the empirical adjustment of the admixture of exact exchange to match the predictions of very high level theoretical methods. For this annulene with insignificant left-right electron correlation effects, a greater (50%) percentage of exact exchange should be included. The relationship of symmetry breaking to the inclusion of exact exchange is examined for seven linear radicals, OXO (X = B, Al, Ga, In, TI). AIOS, and OAIS. exchange—correlation functionals generate symmetry adapted solutions at the expense of an unusual ordering of the Kohn-Sham orbitals, which can cause uncharacteristic electronic states, incorrect vibrational spectra, and poorer predictions of energetics. These effects are greater when exact exchange is included. In all the examples considered, the appropriate focus for a detailed discussion of molecular properties involves consideration of the effects of exact exchange.     

Benchmark CCSD(T) and DFT study of binding energies in Be7 − 12: in search of reliable DFT functional for beryllium clusters

We present a computational study of the stability of small homonuclear beryllium clusters Be_{7 ? 12} in singlet electronic states. Our predictions are based on highly correlated CCSD(T) coupled cluster calculations. Basis set convergence towards the complete basis set limit as well as the role of the 1s core electron correlation are carefully examined. Our CCSD(T) data for binding energies of Be_{7 ? 12} clusters serve as a benchmark for performance assessment of several density functional theory (DFT) methods frequently used in beryllium cluster chemistry. We observe that, from Be₁₀ clusters on, the deviation from CCSD(T) benchmarks is stable with respect to size, and fluctuating within 0.02 eV error bar for most examined functionals. This opens up the possibility of scaling the DFT binding energies for large Be clusters using CCSD(T) benchmark values for smaller clusters. We also tried to find analogies between the performance of DFT functionals for Be clusters and for the valence-isoelectronic Mg clusters investigated recently in Truhlar's group. We conclude that it is difficult to find DFT functionals that perform reasonably well for both beryllium and magnesium clusters. Out of 12 functionals examined, only the M06-2X functional gives reasonably accurate and balanced binding energies for both Be and Mg clusters.     

Density functional theory study on the magnetic properties of Co3O4 with normal spinel structure

The magnetic properties of Co₃O₄ with a normal spinel structure were investigated via the full potential linearized augmented plane wave (FP-LAPW) method based on density functional theory (DFT). The exchange and correlation effects between electrons were treated with a standard generalized gradient approximation (GGA) from Perdew–Burke–Ernzerhof (PBE), as a function of the on-site Coulomb U term, the GGA−PBE+U method, and a B3PW91 hybrid functional with different Hartree–Fock exchange admixtures. Were calculated all of these exchange–correlation (XC) functionals both with and without spin–orbit coupling (SOC). The objective for these calculations was to predict the ground-state magnetic structure of Co₃O₄ crystal using different XC functionals and to investigate the influence that SOC had on these results. All of our calculations confirmed that the collinear antiferromagnetic (AFM) order was energetically more favorable than the ferromagnetic (FM) one, which agrees with experimental findings. This conclusion was not influenced by the XC functional type employed or whether the spin–orbit effect was used. Thus, the present work does not confirm the recent DFT plane wave pseudopotential results that when including spin–orbit effects, the calculations determined that the collinear FM state had lower energy than the AFM one.     

Analysis of multi-configuration density functional theory methods: theory and model application to bond-breaking

We consider the extension of the standard single-determinant Kohn–Sham method to the case of a multi-configuration auxiliary wave function. By applying the rigorous Kohn–Sham method to this case, we construct the proper interacting and auxiliary energy functionals. Following the Hohenberg–Kohn theorem for both energy functionals, we derive the corresponding multi-configuration Kohn–Sham equations, based on a local effective potential. At the end of the analysis we show that, at the ground state, the auxiliary wavefunction must collapse into a single-determinant wave function, equal to the regular KS wavefunction. We also discuss the stability of the wavefunction in multi-configuration density functional theory methods where the auxiliary system is partially interacting, and the remaining (residual) correlation is evaluated as a functional of the density. As an example showing both the challenges and the possibilities, we implement such a procedure for the perfect pairing wavefunction, using a residual correlation functional that is based on the Lee–Yang–Parr functional, and present results for an elementary bond-breaking process.     

Fractional-charge and fractional-spin errors in range-separated density-functional theory

ABSTRACT

We investigate fractional-charge and fractional-spin errors in range-separated density-functional theory (DFT). Specifically, we consider the range-separated hybrid (RSH) method which combines long-range Hartree-Fock (HF) exchange with a short-range semilocal exchange-correlation density functional, and the RSH+MP2 method which adds long-range, second-order Møller-Plesset (MP2) correlation. Results on atoms and molecules show that the fractional-charge errors obtained in RSH are much smaller than in the standard Kohn-Sham (KS) scheme applied with semilocal or hybrid approximations, and also generally smaller than in the standard HF method. The RSH+MP2 method tends to have smaller fractional-charge errors than standard MP2 for the most diffuse systems, but larger fractional-charge errors for the more compact systems. Even though the individual contributions to the fractional-spin errors in the H atom coming from the short-range exchange and correlation density-functional approximations are smaller than the corresponding contributions for the full-range exchange and correlation density-functional approximations, RSH gives fractional-spin errors that are larger than in the standard KS scheme and only slightly smaller than in standard HF. Adding long-range MP2 correlation only leads to infinite fractional-spin errors. This work clarifies the successes and limitations of range-separated DFT approaches for eliminating self-interaction and static-correlation errors.     

The treatment of the spin coupling in the bonding of NO to the Ni-doped MgO (100) surface

The results are reported of density functional theory (DFT) and explicitly correlated wave-function (CASSCF and CASPT2) calculations on the bonding of NO with the Ni-doped MgO(100) surface. The surface is represented by means of a cluster of ions embedded in point charges. A comparison is made between unrestricted (spin polarized) and spin restricted approaches. While the geometry of the surface complex is described in quite an accurate way by a spin unrestricted DFT approach, e.g., using the B3LYP functional, the spin distribution does not correspond to that of the real physical situation. In fact, the spin polarized DFT treatment shows three unpaired electrons, two with spin up and one with spin down, while EPR experiments show clearly the existence of a single spin localized on an Ni 3d shell. A spin restricted B3LYP treatment, on the other hand, gives a correct spin distribution and geometry but fails in reproducing the adsorption energy. Other exchange-correlation functionals behave in a similar or even worse way. The CASPT2 results, by contrast, are in substantial agreement with the experiment, showing the importance of treating on the same footing the spin and electron correlation as well as the multi-configuration character of the wavefunction.     

Single-particle energies and density of states in density functional theory

Time-dependent density functional theory (TD-DFT) is commonly used as the foundation to obtain neutral excited states and transition weights in DFT, but does not allow direct access to density of states and single-particle energies, i.e. ionisation energies and electron affinities. Here we show that by extending TD-DFT to a superfluid formulation, which involves operators that break particle-number symmetry, we can obtain the density of states and single-particle energies from the poles of an appropriate superfluid response function. The standard Kohn– Sham eigenvalues emerge as the adiabatic limit of the superfluid response under the assumption that the exchange– correlation functional has no dependence on the superfluid density. The Kohn– Sham eigenvalues can thus be interpreted as approximations to the ionisation energies and electron affinities. Beyond this approximation, the formalism provides an incentive for creating a new class of density functionals specifically targeted at accurate single-particle eigenvalues and bandgaps.     

氘代甲烷几何构型及物性的量子化学研究

用HF/6-31G^**、密度泛函方法B3LYP/31G^**、二级微扰MP2/6-31G^**、四级微扰MP4/6-31G^**方法对甲烷和氘代甲烷进行几何构型全优化,并将优化的结果与实验值进行比较.用上述4种方法对甲烷和氘代甲烷分子进行分子的振动基频计算.密度泛函、二级微扰、四级微扰优于HF/6-31G^**,尤其是密度泛函、四级微扰方法.密度泛函方法所用的机时远小于微扰方法.不同方法计算所得的氘代甲烷振动频率值与实验值的最大误差为10.4%,最小误差为2.0%.