Density functional theory calculations of the lowest energy quintet and triplet states of model hemes: role of functional, basis set, and zero-point energy corrections

We investigated the effect of several computational variables, including the choice of the basis set, application of symmetry constraints, and zero-point energy (ZPE) corrections, on the structural parameters and predicted ground electronic state of model 5-coordinate hemes (iron(II) porphines axially coordinated by a single imidazole or 2-methylimidazole). We studied the performance of B3LYP and B3PW91 with eight Pople-style basis sets (up to 6-311+G*) and B97-1, OLYP, and TPSS functionals with 6-31G and 6-31G* basis sets. Only hybrid functionals B3LYP, B3PW91, and B97-1 reproduced the quintet ground state of the model hemes. With a given functional, the choice of the basis set caused up to 2.7 kcal/mol variation of the quintet-triplet electronic energy gap (DeltaEel), in several cases, resulting in the inversion of the sign of DeltaEel. Single-point energy calculations with triple-zeta basis sets of the Pople (up to 6-311G++(2d,2p)), Ahlrichs (TZVP and TZVPP), and Dunning (cc-pVTZ) families showed the same trend. The zero-point energy of the quintet state was approximately 1 kcal/mol lower than that of the triplet, and accounting for ZPE corrections was crucial for establishing the ground state if the electronic energy of the triplet state was approximately 1 kcal/mol less than that of the quintet. Within a given model chemistry, effects of symmetry constraints and of a "tense" structure of the iron porphine fragment coordinated to 2-methylimidazole on DeltaEel were limited to 0.3 kcal/mol. For both model hemes the best agreement with crystallographic structural data was achieved with small 6-31G and 6-31G* basis sets. Deviation of the computed frequency of the Fe-Im stretching mode from the experimental value with the basis set decreased in the order: nonaugmented basis sets, basis sets with polarization functions, and basis sets with polarization and diffuse functions. Contraction of Pople-style basis sets (double-zeta or triple-zeta) affected the results insignificantly for iron(II) porphyrin coordinated with imidazole. Poor performance of a "locally dense" basis set with a large number of basis functions on the Fe center was observed in calculation of quintet-triplet gaps. Our results lead to a series of suggestions for density functional theory calculations of quintet-triplet energy gaps in ferrohemes with a single axial imidazole; these suggestions are potentially applicable for other transition-metal complexes.     

Comparison of density functionals for the study of the high spin low spin gap in Fe(III) spin crossover complexes

A detailed investigation of the accuracy of different quantum mechanical methods for the study of iron(III) spin crossover complexes is presented. The energy spin state gap between the high and low spin states; ΔE (HS‐LS) of nine iron(III) quinolylsalicylaldiminate complexes were calculated with nine different DFT functionals, then compared. DFT functionals: B3LYP, B3LYP‐D3, B3LYP*, BH&HLYP, BP86, OLYP, OPBE, M06L, and TPSSh were tested with six basis sets: 3‐21G*, dgdzvp, 6‐31G**, cc‐pVDZ, Def2TZVP, and cc‐pVTZ. The cations from the X‐ray crystal structures of [Fe(qsal‐OMe)₂]Cl·MeCN·H₂O, [Fe(qsal‐OMe)₂]Cl·2MeOH·0.5H₂O, [Fe(qsal‐OMe)₂]BF₄·MeOH, [Fe(qsal‐OMe)₂]NCS·CH₂Cl₂, [Fe(qsal‐F)₂]NCS, [Fe(qsal‐Cl)₂]NCS·MeOH, [Fe(qsal‐Br)₂]NCS·MeOH, [Fe(qsal‐I)₂]OTf·MeOH, and [Fe(qsal)₂]NCS?CH₂Cl₂ were used as starting structures. The results show that B3LYP, B3LYP‐D3, OLYP, and OPBE with a 6‐31G**, Def2TZVP, and cc‐pVTZ basis set give reasonable results of ΔE (HS‐LS) compared with the experimental data. The enthalpy of [Fe(qsal‐I)₂]⁺ calculated with an OLYP functional and cc‐pVTZ basis set (1.48 kcal/mol) most closely matches the experimental data (1.34 kcal/mol). B3LYP* yields an enthalpy of 5.92 kcal/mol suggesting it may be unsuitable for these Fe(III) complexes, mirroring recent results by Kepp (Inorg . Chem ., 2016, 55 , 2717–2727).     

硝酸甲与硝酸乙酯的结构、振动频率和热力学性质的密度函数 理论(DFT)研究

用密度函数理论(DFT)的BLYP和B3LYP方法,取6-31G,6-31G^*,6-31G^*^*,6-311G,6-311G^*和6-311G^*^*六种基组,对硝酸甲酯和硝酸乙酯的几何构型和红外振动频率进行了计算研究.结果表明,B3LYP方法在采用极化基组(6-31G^*,6-31G^*^*,6-311G^*和6-311G^*^*)时计算得到的结果均较好,适用于硝酸酯类化合物的研究.而BLYP方法无论采用何种基组均不适用;运用校正后的B3LYP/6-31G^*频率(校正因子0.975)计算得到的热力学性质(C^o~p,H^o和S^o)与实验结果较吻合。     

Theoretical calculation and prediction for experimental design to obtain spin crossover complexes

DFT methods were utilized to study SCO complexes. [Fe(2btz)₂(NCX)₂] (2btz = 2,2′‐bithiazoline, X = S ( 1 ) and Se ( 2 )), [Fe(phen)₂(NCX)₂] (phen = 1,10‐phenantroline, X = S ( 3 ) and Se ( 4 )), and [Fe(bpy)₂(NCS)₂] ( 5 ) (bpy = 2,2′‐bipyridine) compounds, which have experimentally shown SCO behavior, were calculated. B3LYP, B3LYP*, OPBE, and OLYP with 6‐31G* and 6‐311 + G** basis sets were employed to calculate the ΔE_HS/LS energy gap as a clue to find complexes with SCO behavior. It is found that calculated result by B3LYP* with c₃ = 0.14 and OPBE methods and 6‐31G* basis set are in agreement with experimentally observed SCO complexes. Then, newly designed Fe(N‐N)₂(X)₂ complexes, where N‐N are bidentate nitrogen donor chelating ligands and X= SCN^‐, SeCN^‐, Cl^‐, Br^‐, I^‐, were chosen to see their potential to be SCO compounds. ΔE_HS/LS for potential SCO complexes are estimated from 0.8 to 6.5 kcal/mol in B3LYP* and 0.6–5.7 kcal/mol in OPBE. These calculations suggest [Fe(bpy)₂(NCSe)₂], [Fe(5dmbpy)₂(NCS)₂], and [Fe(3‐BrPhen)₂(NCSe)₂] compounds have the ability to show SCO behavior. © 2016 Wiley Periodicals, Inc.     

水溶液中铵离子pKa值的理论计算

在HF/6-31+G*和B3LYP/6-31+G*水平上, 采用导体极化连续模型(CPCM)及UAKS孔穴计算了11种铵离子在水溶剂中的溶剂化自由能, 与实验值相比较, 平均误差和标准偏差分别为0.17, 12.04和0.96, 10.96 kJ/mol. 结合B3LYP/6-31+G*水平上的11种铵离子气相质子转移反应自由能, 得到了水溶剂中的绝对pKa值, 计算结果与实验数据吻合得很好, 相应的平均误差和标准偏差分别为0.05, 1.50和0.45, 1.40 pKa单位. 可见, 采用CPCM-UAKS模型能够较为精确地计算铵离子型化合物的绝对pKa值.     

CnBδ(δ=0, ±1; n =1～6)团簇的结构、稳定性和光谱

采用密度泛函理论(DFT)的B3LYP方法,在6-31G*和6-311＋G(3df)水平上对C_nB(n=1～6)团簇及其阴离子和阳离子的几何构型和电子结构进行了优化和振动频率计算.得到了C_nB(n=1～6)团簇的电离能,绝热电子亲合势以及C_nB^δ(δ=0,±1)团簇的能隙.结果表明C_nB^－(n=1～6)团簇的基态构型均为线形,这与等电子的C_n簇合物的结构是一致的; C_nB(n=1～6)团簇的基态构型中,除C₂B为不对称的三角形,C₆B为具有C_2v对称性的环状结构外,其余均为线形结构.阳离子团簇中n=2、3、6的基态结构具有C_2v对称性外,其它几个均为线形结构.从几何参数和振动频率上发现,采用密度泛函B3LYP方法在6-311＋G(3df)和6-31G*两种基组上计算得到的键长参数和振动频率非常接近,说明B3LYP方法在计算C_nB簇合物结构参数上对于基组的选择是不太敏感的.通过对C_nB(n=1～6)的光电子能谱性质的研究发现,C₄B容易获得一个电子形成阴离子团簇,但失去一个电子是很困难的,这与实验上观测到的结果非常吻合.     

DFT法研究3-羟基丙烯醛的双键旋转异构反应机理

利用密度泛函理论(DFT)分别在B3LYP/6-31G**和B3LYP/6-311＋＋G**的计算水平上优化了基态3-羟基丙烯醛分子在双键旋转异构反应过程中的平衡态以及过渡态的几何构型，分析了反应过程中键参数的变化，计算了该反应的内禀反应坐标(IRC)，发现在重排反应途径上存在一个四元环骨架的中间体.通过振动分析对平衡态和过渡态进行了确认，并得到了零点能.计算结果表明，基态3-羟基丙烯醛分子的双键旋转异构反应经过两步完成，第一步反应位垒稍高，第二步反应位垒较低，存在着发生重排反应的可能性.     

Theoretical Study of Heterocyclic Nitro Compounds for Use as Novel Explosives and Propellants

The heats of formation (HOFs) of heterocyclic nitro compounds were obtained by using a density functional theory B3LYP method with 6‐31G* and 6‐311+G** basis sets. The isodesmic reactions designed for the evaluation of HOFs keep most of the basic ring structures of the title compounds and thus ensure the credibility of the results. The values of HOFs are 567.90, 874.29 and 975.83 kJ/mol at the B3LYP/6‐31G* level for hexanitrohexazaadamantane ( A ), nonanitrononaza‐tetracyclo[7.3.1.1^3,7.1^5,11] pentadecane ( B ) and tetranitrotetrazacubane ( C ) respectively. The predicted detonation velocities of the title compounds are larger than, and detonation pressures are much larger than that of the widely used 1,3,5,7‐tetranitro‐1,3,5,7‐tetraazacyclooctane (HMX). The dissociation energy for the weakest C‐N bonds in the cage skeleton of the title compounds are 137‐144 kJ/mol at the B3LYP/6‐31G* level.     

Computational studies on carbohydrates: I. Density functional ab initio geometry optimization on maltose conformations

Ab initio geometry optimization was carried out on 10 selected conformations of maltose and two 2‐methoxytetrahydropyran conformations using the density functional denoted B3LYP combined with two basis sets. The 6‐31G* and 6‐311++G** basis sets make up the B3LYP/6‐31G* and B3LYP/6‐311++G** procedures. Internal coordinates were fully relaxed, and structures were gradient optimized at both levels of theory. Ten conformations were studied at the B3LYP/6‐31G* level, and five of these were continued with full gradient optimization at the B3LYP/6‐311++G** level of theory. The details of the ab initio optimized geometries are presented here, with particular attention given to the positions of the atoms around the anomeric center and the effect of the particular anomer and hydrogen bonding pattern on the maltose ring structures and relative conformational energies. The size and complexity of the hydrogen‐bonding network prevented a rigorous search of conformational space by ab initio calculations. However, using empirical force fields, low‐energy conformers of maltose were found that were subsequently gradient optimized at the two ab initio levels of theory. Three classes of conformations were studied, as defined by the clockwise or counterclockwise direction of the hydroxyl groups, or a flipped conformer in which the ψ‐dihedral is rotated by ∼180°. Different combinations of ω side‐chain rotations gave energy differences of more than 6 kcal/mol above the lowest energy structure found. The lowest energy structures bear remarkably close resemblance to the neutron and X‐ray diffraction crystal structures. © 2000 John Wiley & Sons, Inc. * J Comput Chem 21: 1204–1219, 2000     

吲哚分子振动光谱的密度泛函理论研究

用多种密度泛函理论(DFT)方法(BLYP/6-31G^*^*,B3LYP/6-31G^*^*,B3PW91/6-31G^*^*和SVWN/6-31G^*^*)对吲哚分子的平衡几何构型进行了优化。在优化构型的基础上计算了吲哚分子的谐力场、振动基频和红外光谱强度。计算得到的振动频率与实验值比较平均偏差对四种计算方法(BLYP/6-31G^*^*,P3LYP/6-31G^*^*,B3PW91/6-31G^*^*和SVWN/6-31G^*^*)分别为16.3,40.5,45.1和26.4cm^-^1。BLYP/6-31G^*^*理论力场被用于吲哚分子的简正坐标分析计算中。根据振动率的势能分布(PEDs)对此分子的振动基频进行了理论归属。     

Understanding selenocysteine through conformational analysis,proton affinities,acidities and bond dissociation energies

Density functional methods have been employed to characterize the gas phase conformations of selenocysteine. The 33 stable conformers of selenocysteine have been located on the potential energy surface using density functional B3LYP/6‐31+G* method. The conformers are analyzed in terms of intramolecular hydrogen bonding interactions. The proton affinity, gas phase acidities, and bond dissociation energies have also been evaluated for different reactive sites of selenocysteine for the five lowest energy conformers at B3LYP/6‐311++G*//B3LYP/6‐31+G* level. Evaluation of these intrinsic properties reflects the antioxidant activity of selenium in selenocysteine. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

线型碳链PC2nP的结构和电子光谱的密度泛函理论研究

应用密度泛函理论,在B3LYP/6-31G**和B3LYP/6-311G**水平上优化得到了线型簇合物PC2nP(n=1-10)的基态平衡几何构型,计算了它们的谐振动频率.在基态平衡构型下,利用含时密度泛函理论,计算得到了簇合物PC2nP(n=1-10)的垂直激发能和相应的振子强度,导出了激发能与体系大小n的解析关系式.     

二氯亚甲基锗烯与乙烯环加成反应机理的理论研究

The mechanism of a cycloaddition reaction between singlet dichloromethylene germylene and ethylene has been investigated with B3LYP/6-31G＊ method, including geometry optimization and vibrational analysis for the involved stationary points on the potential energy surface. Energies for the involved conformations were calculated by CCSD（T）//B3LYP/6-31G＊ method. On the basis of the surface energy profile obtained with CCSD（T）// B3LYP/6-31G＊ method for the cycloaddition reaction between singlet dichloromethylene germylene and ethylene, it can be predicted that the dominant reaction pathway is that an intermediate INT1 is firstly formed between the two reactants through a barrier-free exothermic reaction of 61.7 kJ/mol, and the intermediate INT1 then isomerizes to an active four-membered ring product P2.1 via a transition state TS2, an intermediate INT2 and a transition state TS2.1, in which energy barriers are 57.7 and 42.2 kJ/mol, respectively.     

Investigation of the use of B3LYP zero-point energies and geometries in the calculation of enthalpies of formation

The use of B3LYP/6–31G^* zero-point energies and geometries in the calculation of enthalpies of formation has been investigated for the enlarged G2 test set of 148 molecules [J. Chem. Phys. 106 (1997) 1063]. A scale factor of 0.96 for the B3LYP zero-point energies gives an average absolute deviation nearly the same as scaled HF/6–31G^* zero-point energies for G2, G2(MP2), and B3LYP/6–311 + G(3df,2p) enthalpies. A scale factor of 0.98, which has been recommended in some studies, increases the average absolute deviation by about 0.2 kcal/mol. Geometries from B3LYP/6–31G^* are found to do as well as MP2/6–31G^* geometries in the calculation of the enthalpies of formation.     

Theoretical studies on the effects of methods and parameterization on the calculated free energy of hydration for small molecules

Free energies of hydration (FEH) have been computed for 13 neutral and nine ionic species as a difference of theoretically calculated Gibbs free energies in solution and in the gas phase. In‐solution calculations have been performed using both SCIPCM and PCM polarizable continuum models at the density functional theory (DFT)/B3LYP and ab initio Hartree–Fock levels with two basis sets (6‐31G* and 6‐311++G**). Good linear correlation has been obtained for calculated and experimental gas‐phase dipole moments, with an increase by ～30% upon solvation due to solute polarization. The geometry distortion in solution turns out to be small, whereas solute polarization energies are up to 3 kcal/mol for neutral molecules. Calculation of free energies of hydration with PCM provides a balanced set of values with 6‐31G* and 6‐311++G** basis sets for neutral molecules and ionic species, respectively. Explicit solvent calculations within Monte Carlo simulations applying free energy perturbation methods have been considered for 12 neutral molecules. Four different partial atomic charge sets have been studied, obtained by a fit to the gas‐phase and in‐solution molecular electrostatic potentials at in‐solution optimized geometries. Calculated FEH values depend on the charge set and the atom model used. Results indicate a preference for the all‐atom model and partial charges obtained by a fit to the molecular electrostatic potential of the solute computed at the SCIPCM/B3LYP/6‐31G* level. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

A simple model for metal cation-phosphate interactions in nucleic acids in the gas phase: Alkali metal cations and trimethyl phosphate

Threshold collision-induced dissociation techniques are employed to determine the bond dissociation energies (BDEs) of complexes of alkali metal cations to trimethyl phosphate, TMP. Endothermic loss of the intact TMP ligand is the only dissociation pathway observed for all complexes. Theoretical calculations at the B3LYP/6-31G* level of theory are used to determine the structures, vibrational frequencies, and rotational constants of neutral TMP and the M+(TMP) complexes. Theoretical BDEs are determined from single point energy calculations at the B3LYP/6-311+G(2d,2p) level using the B3LYP/6-31G* optimized geometries. The agreement between theory and experiment is reasonably good for all complexes except Li+(TMP). The absolute M+-(TMP) BDEs are found to decrease monotonically as the size of the alkali metal cation increases. No activated dissociation was observed for alkali metal cation binding to TMP. The binding of alkali metal cations to TMP is compared with that to acetone and methanol.     

Characterization of Paramagnetic Reactive Intermediates: Predicting the NMR Spectra of Iron(IV)–Oxo Complexes by DFT

The relative energies of spin states of several iron(IV)–oxo complexes and related species have been calculated with DFT methods by employing the B3LYP* functional. We show that such calculations can predict the correct ground spin state of Fe^IV complexes and can then be used to determine the ¹H NMR spectra of all spin states; the spectral features are remarkably different, hence calculated paramagnetic ¹H NMR spectra can be used to support the structure elucidation of numerous paramagnetic complexes. Applications to a number of stable and reactive iron(IV)–oxo species are described.     

The reaction of triplet flavin with indole. A study of the cascade of reactive intermediates using density functional theory and time resolved infrared spectroscopy

As a model for riboflavin, lumiflavin was investigated using density functional theory methods (B3LYP/6-31G* and B3LYP/6-31+G**) with regard to the proposed cascade of intermediates formed after excitation to the triplet state, followed by electron-transfer, proton-transfer, and radical[bond]radical coupling reactions. The excited triplet state of the flavin is predicted to be 42 kcal/mol higher in energy than the singlet ground state, and the pi radical anion lies 45.1 kcal/mol lower in energy than the ground-state flavin and a free electron in the gas phase. The former value compares to a solution-phase triplet energy of 49.8 kcal/mol of riboflavin. For the radical anion, the thermodynamically favored position to accept a proton on the flavin ring system is at N(5). A natural population analysis also provided spin density information for the radicals and insight into the origin of the relative stabilities of the six different calculated hydroflavin radicals. The resulting 5H-LF* radical can then undergo radical[bond]radical coupling reactions, with the most thermodynamically stable adduct being formed at C(4'). Vibrational spectra were also calculated for the transient species. Experimental time-resolved infrared spectroscopic data obtained using riboflavin tetraacetate are in excellent agreement with the calculated spectra for the triplet flavin, the radical anion, and the most stable hydroflavin radical.