Atom-atom partitioning of total (super)molecular energy: the hidden terms of classical force fields

Classical force fields describe the interaction between atoms that are bonded or nonbonded via simple potential energy expressions. Their parameters are often determined by fitting to ab initio energies and electrostatic potentials. A direct quantum chemical guide to constructing a force field would be the atom-atom partitioning of the energy of molecules and van der Waals complexes relevant to the force field. The authors used the theory of quantum chemical topology to partition the energy of five systems [H2, CO, H2O, (H2O)2, and (HF)2] in terms of kinetic, Coulomb, and exchange intra-atomic and interatomic contributions. The authors monitored the variation of these contributions with changing bond length or angle. Current force fields focus only on interatomic interaction energies and assume that these purely potential energy terms are the only ones that govern structure and dynamics in atomistic simulations. Here the authors highlight the importance of self-energy terms (kinetic and intra-atomic Coulomb and exchange).     

Comparing ab initio density-functional and wave function theories: the impact of correlation on the electronic density and the role of the correlation potential

The framework of ab initio density-functional theory (DFT) has been introduced as a way to provide a seamless connection between the Kohn-Sham (KS) formulation of DFT and wave-function based ab initio approaches [R. J. Bartlett, I. Grabowski, S. Hirata, and S. Ivanov, J. Chem. Phys. 122, 034104 (2005)]. Recently, an analysis of the impact of dynamical correlation effects on the density of the neon atom was presented [K. Jankowski, K. Nowakowski, I. Grabowski, and J. Wasilewski, J. Chem. Phys. 130, 164102 (2009)], contrasting the behaviour for a variety of standard density functionals with that of ab initio approaches based on second-order M?ller-Plesset (MP2) and coupled cluster theories at the singles-doubles (CCSD) and singles-doubles perturbative triples [CCSD(T)] levels. In the present work, we consider ab initio density functionals based on second-order many-body perturbation theory and coupled cluster perturbation theory in a similar manner, for a range of small atomic and molecular systems. For comparison, we also consider results obtained from MP2, CCSD, and CCSD(T) calculations. In addition to this density based analysis, we determine the KS correlation potentials corresponding to these densities and compare them with those obtained for a range of ab initio density functionals via the optimized effective potential method. The correlation energies, densities, and potentials calculated using ab initio DFT display a similar systematic behaviour to those derived from electronic densities calculated using ab initio wave function theories. In contrast, typical explicit density functionals for the correlation energy, such as VWN5 and LYP, do not show behaviour consistent with this picture of dynamical correlation, although they may provide some degree of correction for already erroneous explicitly density-dependent exchange-only functionals. The results presented here using orbital dependent ab initio density functionals show that they provide a treatment of exchange and correlation contributions within the KS framework that is more consistent with traditional ab initio wave function based methods.     

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.     

Ab initio prediction of the vibrational spectrum of the hydrogen bonded complex O2N...HONO2

The changes in the structural parameters and vibrational characteristics (vibrational frequencies, infrared intensities and Raman activities) arising from the hydrogen bonding between NO(2) and HONO(2) have been studied employing ab initio 6-31G(d, p)/UHF and 6-31+G(d, p)/UHF, and B3LYP/6-31G(d, p) calculations. The charge rearrangement upon hydrogen bonding have been, estimated using the Mulliken population analyses. It was established that the complexation between NO(2) and HONO(2) leads to changes in the structural parameters and the vibrational characteristics of the monomers. The most sensitive to the hydrogen bond formation are the vibrational characteristics of the normal modes of the monomer bonds participating in the hydrogen bonding. The predicted shifts in the vibrational frequencies by ab initio and B3LYP/6-31G(d, p) calculations are in very good agreement with the experimentally observed, which is an evidence for the reliance of the studied structure.     

Ab initio derivation of multi-orbital extended Hubbard model for molecular crystals

From configuration interaction (CI) ab initio calculations, we derive an effective two-orbital extended Hubbard model based on the gerade (g) and ungerade (u) molecular orbitals (MOs) of the charge-transfer molecular conductor (TTM-TTP)I(3) and the single-component molecular conductor [Au(tmdt)(2)]. First, by focusing on the isolated molecule, we determine the parameters for the model Hamiltonian so as to reproduce the CI Hamiltonian matrix. Next, we extend the analysis to two neighboring molecule pairs in the crystal and we perform similar calculations to evaluate the inter-molecular interactions. From the resulting tight-binding parameters, we analyze the band structure to confirm that two bands overlap and mix in together, supporting the multi-band feature. Furthermore, using a fragment decomposition, we derive the effective model based on the fragment MOs and show that the staking TTM-TTP molecules can be described by the zig-zag two-leg ladder with the inter-molecular transfer integral being larger than the intra-fragment transfer integral within the molecule. The inter-site interactions between the fragments follow a Coulomb law, supporting the fragment decomposition strategy.     

DFT performance for the hole transfer parameters in DNA π stacks

Recently, we showed that unoccupied Kohn‐Sham (KS) orbitals stemming from DFT calculations of a neutral system can be used to derive accurate estimates of the free energy and electronic couplings for excess electron transfer in DNA (Félix and Voityuk, J Phys Chem A 2008, 112, 9043). In this article, we consider the propagation of radical cation states (hole transfer) through DNA π‐stacks and compare the performance of different exchange‐correlation functionals to estimate the hole transfer (HT) parameters. Two different approaches are used: (1) calculations that use occupied KS orbitals of neutral π stacks of nucleobases, and (2) the time‐dependent DFT method which is applied to the radical cation states of these stacks. Comparison of the calculated parameters with the reference data suggests that the best results are provided by the KS scheme with hybrid functionals (B3LYP, PBE0, and BH&HLYP). The TD DFT approach gives significantly less accurate values of the HT parameters. In agreement with high‐level ab initio results, the KS scheme predicts that the hole in π stacks is confined to a single nucleobase; in contrast, the spin‐unrestricted DFT method considerably overestimates the hole delocalization in the radical cations. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

On the vibrational spectra and structural parameters of methyl, silyl, and germyl azide from theoretical predictions and experimental data

The infrared and Raman spectra of methyl, silyl, and germyl azide (XN3 where X=CH3, SiH3 and GeH3) have been predicted from ab initio calculations with full electron correlation by second order perturbation theory (MP2) and hybrid density function theory (DFT) by the B3LYP method with a variety of basis sets. These predicted data are compared to previously reported experimental data and complete vibrational assignments are provided for all three molecules. It is shown that several of the assignments recently proposed [J. Mol. Struct. (Theochem.) 434 (1998) 1] for methyl azide are not correct. Structural parameters for CH3N3 and GeH3N3 have been obtained by combining the previously reported microwave rotational constants with the ab initio MP2/6-311+G(d,p) predicted values. These "adjusted r0" parameters have very small uncertainties of +/-0.003 A for the XH distances and a maximum of +/-0.005 A for the heavy atom distances and +/-0.5 degrees for the angles. The predicted distance for the terminal NN bond which is nearly a triple bond is much better predicted by the B3LYP calculations, whereas the fundamental frequencies are better predicted by the scaled ab initio calculations. The results are discussed and compared to those obtained for some similar molecules.     

The computation of the potential energy surface for H2 + OH → H2O + H using ab initio and density functional theory methods

The reaction energy profile for H₂ + OH → H + H₂O was computed using HF, MP2, MP4, QCISD, G1, G2, and G2MP2 ab initio methods. In addition, the B3LYP, B3P86, B3PW91, BLYP, BP291, and SVWN density functional theory (DFT) methods were also used. All the ab initio methods, with the exception of the G series, produced much higher activation barriers and heats of reaction than the experimental values. On the other hand, the DFT methods produced negative forward and reverse barriers which were too low, with the exception of the hybrid DFT methods. The G2 ab initio method generated energies which deviated from the experimental values by ∼ 1 kcal/mol and therefore should be considered a very accurate computational method. The hybrid DFT methods produced positive forward reaction barriers with energies that were 2–4 kcal/mol lower than the experimental values. The geometries of the transition state and energies computed by the ab initio and DFT methods were compared. These results suggest that, in the hybrid exchange functional, the portion of the Slater exchange term should be increased. This may be the reason why the computed energies were too low. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 62: 639–644, 1997     

CASCI-DFT study of the phenalenyl radical system

We present ab initio complete-active-space configuration interaction (CASCI) density functional theory (DFT) study of the phenalenyl radical systems. Our approach employed in this study is based on the assumption that one-electron per one phenalenyl unit is responsible for magnetic properties of the phenalenyl radical dimeric compounds and that the residual correlation effects can be covered by DFT correlation potential for CASCI[2,2] wavefunction. The effective exchange integrals and lowest-lying excited energies of several phenalenyl dimeric compounds are calculated by CASCI[2,2]-DFT method. The implication of the computational results are discussed in relation with those of spin unrestricted Hartree–Fock (UHF), hybrid DFT, and pure DFT, and the experimental ones.     

On the variation of magnetic susceptibility of a molecular crystal with temperature: the 2,4,6-triphenylverdazyl system

Magnetic susceptibilities of spin-1/2 systems of orthorhombic and higher crystal symmetries have been numerically investigated while taking possible anisotropy in the coupling constants along different crystal axes into account. The work relies on the magnon-based theory of ferromagnetic (FM) and antiferromagnetic (AFM) crystal systems of types FFF, AFF, AAF, and AAA [J. Chem. Phys. 111, 9009 (1999)]. The AAF crystal, in particular, shows interesting changes in the temperature dependence of magnetic susceptibility when the ferromagnetic exchange coupling constant is varied. We especially show that the susceptibility anomalies of molecular crystals fit naturally within the framework of the extended magnon-theoretical formalism, and do not necessarily imply a FM --> AFM or a reverse phase transition. A real system, molecular crystal of 2,4,6-triphenylverdazyl (2,4,6-TPV), has been investigated here. It was previously interpreted as an AAF system from observed susceptibility data [Tomiyoshi et al., Phys. Rev. B 49, 16031 (1994)]. The trend of the temperature dependence of magnetic susceptibility studied in the present work also indicates that the crystal belongs to the AAF category with a less prominent FM exchange coupling constant. To reinforce our conclusions, we have adopted a two-pronged strategy. First, the geometry of the 2,4,6-TPV monomer has been optimized here by ab initio unrestricted Hartree-Fock (UHF) calculations using the STO-3G basis set. The optimized geometry is almost planar. A subsequent calculation has been carried out with the phenyl rings twisted out of the plane of the nitrogen atoms. The STO-3G optimized geometry, and the same geometry except for the twisted phenyl rings, have been used to perform ab initio coupled-cluster (UCCSD-T) calculations with the same basis, and UHF as well as density-functional (UB3LYP) calculations using the 6-31G basis set. The calculated data can easily rationalize the twists while the species remains in crystal. The magnetic category of the crystal has been unambiguously confirmed as AFA from ab initio UHF and UB3LYP calculations of the total energy in different spin states of dimers and trimers along the crystal axes. The computed energy values, however, fail to yield accurate estimates of the exchange coupling constants Ja, Jb, and Jc, because the latter are on the order of 1kBK corresponding to energy differences on the order of 10(-6) hartree between different spin states. In the second approach, the observed features of the susceptibility minimum and maximum have been used to determine the best values of the exchange coupling constants from the theoretical formulas for an anisotropic AFA crystal. The AFM (Ja and Jc) and FM (Jb) exchange coupling constants and the Neel temperature (TN) found from this analysis correspond to Ja + Jc = -1.05 kBK, Jb = 1.35 kBK, and TN = 1.75 K. The calculated J values significantly differ from those estimated from a linear Heisenberg chain model, but generate a susceptibility versus temperature graph that mimics the experimental plot.     

Intramolecular SN2 reaction caused by photoionization of benzene chloride-NH3 complex: direct ab initio molecular dynamics study

Ionization processes of chlorobenzene-ammonia 1:1 complex (PhCl-NH3) have been investigated by means of full dimensional direct ab initio molecular dynamics (MD) method, static ab initio calculations, and density functional theory (DFT) calculations. The static ab initio and DFT calculations of neutral PhCl-NH3 complex showed that one of the hydrogen atoms of NH3 orients toward a carbon atom in the para-position of PhCl. The dynamics calculation for ionization of PhCl-NH3 indicated that two reaction channels are competitive with each other as product channels: one is an intramolecular SN2 reaction expressed by a reaction scheme [PhCl-NH3]+-->SN2 intermediate complex-->PhNH3++Cl, and the other is ortho-NH3 addition complex (ortho complex) in which NH3 attacks the ortho-carbon of PhCl+ and the trajectory leads to a bound complex expressed by (PhCl-NH3)+. The mechanism of the ionization of PhCl-NH3 is discussed on the basis of the theoretical results.     

An ab initio SCF + CI study of the SH3 and SF3 radicals

The symmetric sulfuranyl radicals SH₃ and SF₃ are studied by means of ab initio SCF + CI calculations. All geometries are optimized at the UHF level using analytical gradients. SH₃ is found to be a transition state corresponding to a hydrogen exchange reaction, whereas SF₃ is stable with respect to decomposition to SF₂ + F.     

Intermolecular electrostatic energies using density fitting

A method is presented to calculate the electron-electron and nuclear-electron intermolecular Coulomb interaction energy between two molecules by separately fitting the unperturbed molecular electron density of each monomer. This method is based on the variational Coulomb fitting method which relies on the expansion of the ab initio molecular electron density in site-centered auxiliary basis sets. By expanding the electron density of each monomer in this way the integral expressions for the intermolecular electrostatic calculations are simplified, lowering the operation count as well as the memory usage. Furthermore, this method allows the calculation of intermolecular Coulomb interactions with any level of theory from which a one-electron density matrix can be obtained. Our implementation is initially tested by calculating molecular properties with the density fitting method using three different auxiliary basis sets and comparing them to results obtained from ab initio calculations. These properties include dipoles for a series of molecules, as well as the molecular electrostatic potential and electric field for water. Subsequently, the intermolecular electrostatic energy is tested by calculating ten stationary points on the water dimer potential-energy surface. Results are presented for electron densities obtained at four different levels of theory using two different basis sets, fitted with three auxiliary basis sets. Additionally, a one-dimensional electrostatic energy surface scan is performed for four different systems (H2O dimer, Mg2+-H2O, Cu+-H2O, and n-methyl-formamide dimer). Our results show a very good agreement with ab initio calculations for all properties as well as interaction energies.     

An ab initio study based on a finite nucleus model for isotope fractionation in the U(III)-U(IV) exchange reaction system

Isotope fractionation in the U(III)-U(IV) reaction system was investigated by a series of atomic relativistic ab initio calculations using the multiconfigurational Dirac-Coulomb Hartree-Fock method. To evaluate the nuclear volume effect on the fractionation, the Fermi statistical distribution function was adopted for nuclear charge density. The isotope fractionation coefficient epsilon resulting from the nuclear volume difference was evaluated from the total electronic energies of U3+ and U4+, based on the theoretical equation proposed by Bigeleisen [J. Am. Chem. Soc. 118, 3676 (1996)]. The calculated fractionation coefficient epsilon in the present work for the isotopic pair 235U and 238U at 293 K is 0.0031, which is quite close to the experimentally observed value of 0.0027. Discussion is extended to the nuclear volume effects on isotopic fractionations in the Pu(III)-Pu(IV) and Eu(II)-Eu(III) exchange systems.     

The determination of intrinsic reaction coordinates by density functional theory

The first implementation of the intrinsic reaction coordinate (IRC ) method within the density functional theory (DFT ) framework is presented. The implementation has been applied to four different types of chemical reactions represented by the isomerization process, HCN ? HNC (A); the S_N2 process, H^? + CH₄ ? CH₄ + H^? (B); the exchange process, H˙ + HX ? HX + H˙ (X ? F,Cl) (C); and the elimination process, C₂H₅Cl ? C₂H₄ + HCl (D). The present study presents for each process optimized structures and calculated harmonic vibrational frequencies for the reactant(s), the transition state, and the product(s) along with the IRC path connecting the stationary points. The calculations were carried out within the local density approximation (LDA ) as well as the LDA/NL scheme where the LDA energy expression is augmented by Perdew's and Becke's nonlocal (NL ) corrections. The LDA and LDA/NL results are compared with each other as well as the best available ab initio calculations and experimental data. For reaction (D), ab initio calculations based on MP 2 geometries and MP 4SDTQ energies have been added due to the lack of accurate published post-HF calculations on this process. A detailed discussion is provided on the efficiency of the IRC algorithms, the relative accuracy of the DFT and ab initio schemes, as well as the reaction mechanisms of the four reactions. It is concluded that the LDA/NL scheme affords the same accuracy as does the MP 4 method. The post-HF methods seem to overestimate activation energies, whereas the corresponding LDA/NL estimates are too low. The LDA activation energies are even lower than the LDA/NL counterparts. The incorporation of the IRC method into the DFT framework provides a promising and reliable tool for probing the chemical reaction path on the potential energy surfaces, even for large-size systems. IRC calculations by ab initio methods of an accuracy similar to the LDA/NL scheme, such as the MP 4 scheme, are not feasible. © John Wiley & Sons, Inc.     

Structure of Au8: planar or nonplanar?

We have studied the structures and stabilities of Au6 and Au8 at the density-functional theory (DFT) and ab initio correlated levels of theory. For Au8, our ab initio calculations predict the lowest Au8 isomer to be planar, in line with the DFT calculations.     

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.