Benchmarking approximate density functional theory for s/d excitation energies in 3d transition metal cations

Holthausen has recently provided a comprehensive study of density functional theory for calculating the s/d excitation energies of the 3d transition metal cations. This study did not include the effects of scalar relativistic effects, and we show here that the inclusion of scalar relativistic effects significantly alters the conclusions of the study. We find, contrary to the previous study, that local functionals are more accurate for the excitation energies of 3d transition method cations than hybrid functionals. The most accurate functionals, of the 38 tested, are SLYP, PBE, BP86, PBELYP, and PW91.     

Relativistic effects on geometry and electronic structure of small Pdn species (n=1, 2, 4)

Relativistic effects on the properties of small neutral Pd_n species (n=1, 2, 4) and Pd₂⁻ have been examined for the first time at the all‐electron level by performing scalar‐relativistic and nonrelativistic density functional calculations using a gradient‐corrected density functional. Relativistic effects are found to be important: They lead to a contraction of bond lengths, increase of vibrational frequencies, and a significant enhancement of binding energies. While relativistic effects are quite uniform for several states of Pd₄, they vary for the states examined for Pd₂, leading to a change of ground state due to relativity. The calculated relativistic properties of Pd₂ and Pd₂⁻ are in good agreement with available experimental data from mass spectrometry and photoelectron spectroscopy. For Pd₄ three‐dimensional structures are found to be preferred to planar ones and many nearly isoenergetic isomers exist. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 74: 405–416, 1999     

Cyanide adsorbed on coinage metal electrodes: A relativistic density functional investigation

The adsorptive properties of cyanide (CN⁻) on coinage metal (M) electrodes (M=Cu, Ag, Au) have been investigated using a relativistic density functional method. The way to model the electrochemical potential applied to the electrodes is to consider the systems in the presence of a perturbative external field F. The field-perturbative approach is proven to be a suitable method in interpreting the observed spectral shifts with electrode potential. The calculated potential-dependent shifts of ω_{M(SINGLE BOND)CN} and ω_{C(SINGLE BOND)M} are similar for the three metals, in agreement with experiment observations. The relativistic effects are required to account for the similarity in the frequency shifts of ω_{M(SINGLE BOND)CN}. The calculated vibrational tuning rates dω_{C(SINGLE BOND)N}/dF are 6.61×10⁻⁷, 6.61×10⁻⁷, and 5.64×10⁻⁷ cm⁻¹/(V/cm) for M=Cu, Ag, and Au, respectively. The coupling of the M(SINGLE BOND)CN and C(SINGLE BOND)N internal modes contributes significantly (about 25%) to the size of the frequency shifts Δω_{C(SINGLE BOND)N} of the ligand. The effect of electric fields on the metal(SINGLE BOND)CN⁻ bonding is also investigated. It is shown that changes in the magnitude of CN⁻ to the metal donation and M(SINGLE BOND)CN bond strength occur under the influence of the electric field. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 67: 175–185, 1998     

Synthesis and characterization of new five-coordinate platinum nitrosyl derivatives: density functional theory study of their electronic structure

The neutral, five-coordinate platinum nitrosyl compounds [Pt(C(6)F(5))(3)(L)(NO)] (2) [L=CNtBu (2 a), NC(5)H(4)Me-4 (2 b), PPhMe(2) (2 c), PPh(3) (2 d) and tht (2 e)] have been prepared by the reaction of [NBu(4)][Pt(C(6)F(5))(3)(L)] (1) with NOClO(4) in CH(2)Cl(2). The ionic compound [N(PPh(3))(2)][Pt(C(6)F(5))(4)(NO)] (4) has been prepared in a similar way starting from the homoleptic species [N(PPh(3))(2)](2)[Pt(C(6)F(5))(4)] (3). Compounds 2 and 4 are all diamagnetic with [PtNO](8) electronic configuration and show nu(NO) stretching frequencies at around 1800 cm(-1). The crystal and molecular structures of 2 c and 4 have been established by X-ray diffraction methods. The coordination environment for the Pt center in both compounds can be described as square pyramidal (SPY-5). Bent nitrosyl coordination is observed in both cases with Pt-N-O angles of 120.1(6) and 130.2(7) degrees for 2 c and 4, respectively. The bonding mechanism of the nitrosyl ligand coordinated to various model [Pt(II)R(4)](2-) (R=H, Me, Cl, CN, C(6)F(5) or C(6)Cl(5)) and [Pt(C(6)F(5))(3)(L)](-) (L=CNMe, PH(3)) systems has been studied by density functional calculations at the B3LYP level of theory, using the SDD basis set. The R(4)Pt-NO and (C(6)F(5))(3)(L)Pt-NO interactions generally involve two components: i) a direct Pt-NO bonding interaction and ii) multicenter-bonding interactions between the N atom of the NO ligand and the donor atoms of the R and L ligands. Moreover, with the more complex R groups, C(6)F(5) or C(6)Cl(5), a third component has been found to arise, which involves multicenter electrostatic interactions between the positively charged NO ligand and the negatively charged halo-substituents in the ortho-position of the C(6)X(5) groups (X=F, Cl). The contribution of each component to the Pt-NO bonding in R(4)Pt-NO and (C(6)F(5))(3)(L)Pt-NO compounds seems to be modulated by the electronic and steric effects of the R and L ligands.     

Associative versus dissociative binding of CO to 4d transition metal trimers: A density functional study

Density functional calculations were performed to determine equilibrium geometrical structures, transition states and relative energies for M(3) clusters (M = Nb, Mo, Tc, Ru, Rh, Pd, Ag) reacting with CO, leading to proposed reaction pathways. For the Nb(3), Mo(3), and Tc(3) clusters, the lowest energy structure correlates to dissociated CO, with the C and O atoms bound on opposite sides of the metal triangle. For all other trimers, the lowest energy structures maintain the CO moiety. In the case of Pd(3) and Ag(3) the dissociated geometries lie higher in energy than the sum of the separated reactants. In most cases, several multiplicities were found to be similar in energy and for Mo(3)CO and Pd(3)CO singlet-triplet minimum energy crossing points were identified. In the case of Rh(3)CO, minimum energy crossing points for the doublet, quartet, and sextet reaction pathways were determined and compared. The electron densities of pertinent M(3)CO species were investigated using Natural Bond Order calculations. It was found that the effect of the metal trimer on the energy of the pure p-type pi* antibonding orbital of carbon monoxide directly correlates with the occurrence of CO dissociation.     

Analytical energy gradient evaluation in relativistic and nonrelativistic density functional calculations

The expressions of analytical energy gradients in density functional theory and their implementation in programs are reported. The evaluation of analytical energy gradients can be carried out in the fully 4-component relativistic, approximate relativistic, and nonrelativistic density functional calculations under local density approximation or general gradient approximation with or without frozen core approximation using different basis sets in our programs. The translational invariance condition and the fact that the one-center terms do not contribute to the energy gradients are utilized to improve the calculation accuracy and to reduce the computational effort. The calculated results of energy gradients and optimized geometry as well as atomization energies of some molecules by the analytical gradient method are in very good agreement with results obtained by the numerical derivative method.     

A screened hybrid density functional study on energetic complexes: Metal carbohydrazide nitrates

The molecular geometry, electronic structure and thermochemistry of a series of metal carbohydrazide nitrates were investigated using the Heyd–Scuseria–Ernzerhof (HSE) screened hybrid density functional. The results show that Ca, Sr, and Ba complexes have additional coordinated oxygen atoms from the nitrate ion, which differ obviously from Cu, Ni, Co, and Mg complexes in terms of the geometric structure. Detailed NBO analyses clearly indicate that the metal–ligand interactions in Cu, Ni, and Co complexes are covalent, whereas those of Mg, Ca, Sr, and Ba complexes are ionic in nature. Furthermore, the donor–acceptor interactions result in a reduction of occupancies of σ_{C? O} and σ_{N? H} orbitals. Consequently, the bond lengths increase and the bond orders decrease. Finally, the calculated heats of formation predict that the ionic alkaline‐earth metal carbohydrazide nitrates are more stable than the covalent transition metal carbohydrazide nitrates. It agrees well with the available experimental thermal stabilities, indicating that the metal–ligand bonding character plays an important role in the stabilities of these energetic complexes. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Molecular structure and vibrational spectra of phenobaraitone by density functional theory and ab initio hartree-Fock calculations

Quantum chemistry calculations have been performed using Gaussian03 program to compute optimized geometry, harmonic vibrational frequency along with intensities in IR and Raman spectra at RHF/6-31++G** and B3LYP/6-31++G** levels for phenobarbitone (C₁₂H₁₂N₂O₃) in the ground state. The scaled harmonic vibrational frequencies have been compared with experimental FT-IR and FT-Raman spectra. Theoretical vibrational spectra of the title compound were interpreted by means of potential energy distributions (PEDs) using MOLVIB program. A detailed interpretation of the infrared spectra of the title compound is reported. On the basis of the agreement between the calculated and observed results, the assignments of fundamental vibrational modes of phenobarbitone were examined and some assignments were proposed. The theoretical spectrograms for FT-IR and FT-Raman spectra of the title compound have been constructed.     

Yb、YbO电子激发态的相对论含时密度泛函理论研究

本文用基于精确二分量哈密顿（exact two—component Hamiltonian）的相对论含时密度泛函理论（time-dependent relativistic density functional theory）计算了Yb和YbO的电子激发态,并利用对称性、自然原子轨道对激发态性质和归属进行了详细分析,所得结果支持实验对YbO基态与激发态的指认．     

Benchmark Calculations on the Atomization Enthalpy, Geometry and Vibrational Frequencies of UF6 with Relativistic DFT Methods

Benchmark calculations on the molar atomization enthalpy, geometry, and vibrational frequencies of uranium hexafluoride （UF6） have been performed by using relativistic density functional theory （DFT） with various levels of relativistic effects, different types of basis sets, and exchange-correlation functionals. Scalar relativistic effects are shown to be critical for the structural properties. The spin-orbit coupling effects are important for the calculated energies, but are much less important for other calculated ground-state properties of closed-shell UF6. We conclude through systematic investigations that ZORA- and RECP-based relativistic DPT methods are both appropriate for incorporating relativistic effects. Comparisons of different types of basis sets （Slater, Gaussian, and plane-wave types） and various levels of theoretical approximation of the exchange-correlation functionals were also made.     

Reactions of chromium,molybdenum and tungsten carbonyls with a tetradentate schiff base

Interaction of metal carbonyls M(CO)₆ (M?=?Cr, Mo and W) with the tetradentate Schiff base bis(salicylaldehyde)phenylenediimine (salphenH₂) was studied in THF. Under reduced pressure, reaction of salphenH₂ with M(CO)₆ (M?=?Cr, Mo) yielded Cr(CO)₂(salphen) 1 and MoO(CO)(salphen) 2. The complexes MoO₂(salphenH)₂ 3 and W₂O₆(salphenH₂) 4 were isolated from reactions in air. All the complexes were characterized by elemental analysis, mass spectrometry and IR and ¹H?NMR spectroscopy. Spectroscopic studies of the reported complexes revealed the proposed structures. The UV-vis spectra of the complexes in different solvents showed bands due to either metal-to-ligand or ligand-to-metal charge transfer. Thermal properties of the chromium and molybdenum complexes were investigated by thermogravimetric techniques.     

Exploring odd-even effects of simple oligomer-like DRCNnT series: a study based on density functional theory/time-dependent density functional theory calculations

Odd-even effects of short-circuit current density and power conversion efficiency (PCE) are an interesting phenomenon in some organic solar cells. Although some explanations have been given, why they behave in such a way is still an open question. In the present work, we investigate a set of acceptor-donor-acceptor simple oligomer-like small molecules, named the DRCNnT (n = 5-9) series, to give an insight into this phenomenon because the solar cells based on them have high PCE (up to 10.08%) and show strong odd-even effects in experiments. By modeling the DRCNnT series and using density functional theory, we have studied the ground-state electronic structures of the DRCNnT (n = 5-9) series in condensed phase. The calculated results reproduce the experimental trends well. Furthermore, we find that the exciton-binding energies of the DRCNnT series may be one of the key parameters to explain this phenomenon because they also show odd-even effects. In addition, by studying the effects of alkyl branch and terminal group on odd-even effects of dipole moment, we find that eliminating one or two alkyl branches does not break the odd-even effects of dipole moments, but eliminating one or two terminal groups does. Finally, we conclude that removing one alkyl branch close to the terminal group of DRCN5T can decrease highest occupied molecular orbital (HOMO) energy (thus increasing open circuit voltage) and increase dipole moment (thus enhancing charge separation and short-circuit current). This could be a new and simple method to increase the PCE of DRCN5T-based solar cells.     

Interaction of copernicium with gold: Assessment of applicability of simple density functional theories

Interactions of Cn (element 112) atom with small Au clusters are studied using accurate ab initio scalar relativistic coupled cluster method for correlation treatment and two‐component relativistic density functional theory (RDFT) to take account of spin‐dependent relativistic effects. The results demonstrate the failure of RDFT with simple generalized‐gradient and hybrid functionals in describing Cn–Au bonds in complex systems. © 2013 Wiley Periodicals, Inc.     

Electronic structure and spectroscopic properties of 6‐aminophenanthridine and its derivatives: Insights from density functional theory

6‐Aminophenanthridine (6AP) and its derivatives show important biological activities as antiprion compounds and inhibitors of the protein folding activity of the ribosome. Both of these activities depend on the RNA binding property of these compounds, which has been recently characterized by fluorescence spectroscopy. Hence, fundamental insights into the photophysical properties of 6AP compounds are highly important to understand their biological activities. In this work, we have calculated electronic structures and optical properties of 6AP and its three derivatives 6AP8CF₃, 6AP8Cl, and 6APi by density functional theory (DFT) and time‐dependent density functional theory (TDDFT). Our calculated spectra show a good agreement with the experimental absorption and fluorescence spectra, and thus, provide deep insights into the optical properties of the compounds. Furthermore, comparing the results obtained with four different hybrid functionals, we demonstrate that the accuracy of the functionals varies in the order B3LYP > PBE0 > M062X > M06HF. © 2015 Wiley Periodicals, Inc.     

Modeling a halogen dance reaction mechanism: A density functional theory study

Since the discovery of the halogen dance (HD) reaction more than 60 years ago, numerous insights into the mechanism have been unveiled. To date however, the reaction has not been investigated from a theoretical perspective. Density functional theory (DFT) was used to model the potential energy surface linking the starting reagents to the lithiated products for each step in the mechanism using a thiophene substrate. It was found that the lithium‐halogen exchange mechanism is critical to understand the HD mechanism in detail and yielded the knowledge that S_N2 transition states (TS) are favored over the four‐center type for the lithium‐bromine exchange steps. The overall driving force for the HD is thermodynamics, while the kinetic factors tightly control the reaction path through temperature. The S_N2 lithium‐bromide TS are barrierless, except the second, which is the limiting step. Finally, the model for the HD is discovered to be a pseudo‐clock type, due to a highly favorable bromide catalysis step and the reformation of 2‐bromothiophene. © 2016 Wiley Periodicals, Inc.     

Benchmarking approximate density functional theory. I. s/d excitation energies in 3d transition metal cations

The performance of a number of different implementations of density functional theory (DFT) for predicting the s/d interconfigurational energies of the 3d transition metal cations is investigated. Systematic comparisons of computed results with experimental data indicate that gradient corrected correlation functionals, like the LYP GGA, efficiently correct the flaws of the LDA, but reveal shortcomings in the treatment of exchange by currently available GGAs. The admixture of exact exchange in hybrid functionals eventually leads to largely reduced errors. Several basis sets available for the 3d elements are tested in combination with the B3LYP functional. Finally, the influence of variations of the admixture of exact exchange is systematically tested. The results reveal that computed s/d excitation energies obtained for the individual ions depend in markedly different ways on the amount of exact exchange admixture and that there is no single optimal and transferable exchange parameter to create a hybrid functional that yields improved results for all ions alike. Several of the recently devised functionals perform as good as or slightly better than the B3LYP functional in the present study. But given the fact that the B3LYP functional has been identified as the most successful DFT method in an overwhelming number of systematic investigations in very many areas of chemical research, there is no persuasive motivation to recommend its replacement by one of the other functionals, as much less is known about their robustness.     

Density functional computations of 99Ru chemical shifts: relativistic effects, influence of the density functional, and study of solvent effects on fac-[Ru(CO)3I3]-

Solvent effects on the 99Ru NMR chemical shift of the complex fac-[Ru(CO)3I3]- are investigated computationally using density functional theory. Further, benchmark calculations of the 99Ru shift for a set of ten Ru complexes have been performed in order to calibrate the computational model and to determine the importance of relativistic effects on the 99Ru nuclear magnetic shielding and on the chemical shift. A computational model for fac-[Ru(CO)3I3]- that includes both explicit solvent molecules and a continuum model is shown to yield the best agreement with experiment. Relativistic corrections are shown to be of minor importance for determining 99Ru chemical shifts. On the other hand, the nature of the density functional is of importance. In agreement with literature data for ligand trends of 99Ru chemical shifts, the chemical shift range for different solvents is also best reproduced by a hybrid functional.     

Vinylidene carbonylation at a manganese-iron complex: A density functional study of mechanism

Treating the phenylvinyldene manganese complex Cp(CO)₂MnC¹C²HPh, 1, with [Fe(CO)₄] yields the binuclear μ-vinylidene complex Cp(CO)₂MnFe(μ-C¹C²HPh)(CO)₄, 2, that further isomerizes to the carbonylated product η⁴-[Cp(CO)₂MnC¹(CO)C²HPh]Fe(CO)₃, 3. In a computational study of the mechanism using a hybrid density functional method, we considered two stereoisomers for species 2 and 3 where the phenyl group at center C² is oriented in cis (E form) or trans (Z form) fashion to the Cp(CO)₂Mn unit. Isomers 2E and 2Z were calculated to be degenerate whereas the experimentally detected species 3E is 8 kcal/mol more stable than its isomer 3Z. The two-step pathway 1 → 2Z → 3E was calculated to be the lowest-energy route with the highest activation barrier at 12 kcal/mol. The activation energy of the alternative single-step pathway 1 → 3E is 19 kcal/mol. We rationalized the stabilization of the ground state of 3E and the transition states leading to or starting from isomer 2Z as conjugation effect between the Mn-CC metallaallene fragment and the co-planar phenyl ring.