Correlation effects in EOM-CCSD for the excited states: evaluated by AIM localization index (LI) and delocalization index (DI)

We have extended the evaluation and interpretation of QTAIM (quantum theory of atoms in molecules) localization and delocalization indices lambda (LI) and delta (DI) to electronic excited states by studying ground states (at HF and CCSD levels) and excited states (at CIS and EOM-CCSD) of H2C=CH2, HCCH, H2C=O, H2C=S, CO2, CS2, and SO2. These molecules undergo extensive geometrical changes upon the excitation to the valence adiabatic excited singlet state. The importance of Coulomb correlation effects was demonstrated by comparing the LIs and DIs at none-correlated levels (HF and CIS) and those at correlated levels (CCSD and EOM-CCSD). In interpreting the changes in the magnitudes of the LIs and DIs, we made use of simple molecular orbital and Walsh-diagram analyses. Coulomb correlation is important in determining the magnitude of the LIs and DIs and obtaining geometries that are close to experiment.     

Ab initio calculation of torsion and inversion barriers of the amino group in aminopyrimidines

Calculations of the barriers to internal rotation and inversion of the amino group in substituted pyrimidines have been performed. Torsion and inversion barriers were determined by several ab initio methods: HF, HF/MP2, MP4, CISD, QCISD, QCISD(T), CCSD, and CCSD(T). DFT method also employed. Dependencies of the calculated barrier heights on the basis set and the electron correlation level and on the substitution position of the nitrogen atom in the ring were studied. We have determined that for certain molecules relatively low level calculations may eventually provide adequate results, but in general, higher level calculations are necessary.     

Hybrid correlation models based on active-space partitioning: seeking accurate O(N5) ab initio methods for bond breaking

Moller-Plesset second-order (MP2) perturbation theory remains the least expensive standard ab initio method that includes electron correlation, scaling as O(N5) with the number of molecular orbitals N. Unfortunately, when restricted Hartree-Fock orbitals are employed, the potential energy curves calculated with this method are of little use at large interatomic separations because of the divergent behavior of MP2 in these regions. In our previous study [J. Chem. Phys. 122, 234110 (2005)] we combined the MP2 method with the singles and doubles coupled cluster (CCSD) method to produce a hybrid method that retains the computational scaling of MP2 and improves dramatically the shape of the MP2 curves. In this work we expand the hybrid methodology to several other schemes. We investigate a new, improved MP2-CCSD method as well as a few other O(N5) methods related to the Epstein-Nesbet pair correlation theory. Nonparallelity errors across the dissociation curve as well as several spectroscopic constants are computed for BH, HF, H2O, CH+, CH4, and Li2 molecules with the 6-31G* basis set and compared with the corresponding full configuration interaction results. We show that among the O(N5) methods considered, our new hybrid MP2-CCSD method is the most accurate and significantly outperforms MP2 not only at large interatomic separations, but also near equilibrium geometries.     

Electron affinities of metals computed by density functional theory and ab initio methods

An extensive computational study of the meal electron affinity was performed using the ab initio and density functional theory (DFT) methods. HF, MP2, MP3, MP4, QCISD, and QCISD(T) was used as computational methods, while the hybrid, local, and nonlocal DFT methods with the LYP, P86, PW91, and VWN correlation functionals were used. Two basis sets, one small and applicable to almost all metals (LanL2DZ) and one large [6-311 + + G(3df, 3 pd)] used only for small metals, were employed. The computed results were compared with the experimental data and the capabilities of the DFT methods to perform this study were discussed. © 1997 John Wiley & Sons, Inc.     

Density functional theory and post-Hartree-Fock studies on molecular structure and harmonic vibrational spectrum of formaldehyde

Density functional theory (DFT) with the Becke's three-parameter exchange correlation functional and the functional of Lee, Yang and Parr, gradient-corrected functionals of Perdew, and Perdew and Wang [the DFT(B3LYP), DFT(B3P86) and DFT(B3PW91) methods, respectively], and several levels of conventional ab initio post-Hartree-Fock theory (second- and fourth-order perturbation theory M?ller-Plesset MP2 and MP4(SDTQ), coupled cluster with the single and double excitations (CCSD), and CCSD with perturbative triple excitation [CCSD(T)], configuration interaction with the single and double excitations [CISD], and quadratic configuration interaction method [QCISD(T)], using several basis sets [ranging from a simple 6-31G(d,p) basis set to a 6-311+ +G(3df, 2pd) one], were applied to study of the molecular structure (geometrical parameters, rotational constants, dipole moment) and harmonized infrared (IR) spectrum of formaldehyde (CH₂O). High-level ab initio methods CCSD(T) and QCISD(T) with the 6-311+ +G(3df, 2pd) predict correctly molecular parameters, vibrational harmonic wavenumbers and the shifts of the harmonic IR spectrum of ¹²CH₂ ¹⁶O upon isotopic substitution. Received: 30 January 1997 / Accepted: 7 May 1997     

Ab initio and DFT benchmark study for nucleophilic substitution at carbon (SN2@C) and silicon (SN2@Si)

To obtain a set of consistent benchmark potential energy surfaces (PES) for the two archetypal nucleophilic substitution reactions of the chloride anion at carbon in chloromethane (S(N)2@C) and at silicon in chlorosilane (S(N)2@Si), we have explored these PESes using a hierarchical series of ab initio methods [HF, MP2, MP4SDQ, CCSD, CCSD(T)] in combination with a hierarchical series of six Gaussian-type basis sets, up to g polarization. Relative energies of stationary points are converged to within 0.01 to 0.56 kcal/mol as a function of the basis-set size. Our best estimate, at CCSD(T)/aug-cc-pVQZ, for the relative energies of the [Cl(-), CH(3)Cl] reactant complex, the [Cl-CH(3)-Cl](-) transition state and the stable [Cl-SiH(3)-Cl](-) transition complex is -10.42, +2.52, and -27.10 kcal/mol, respectively. Furthermore, we have investigated the performance for these reactions of four popular density functionals, namely, BP86, BLYP, B3LYP, and OLYP, in combination with a large doubly polarized Slater-type basis set of triple-zeta quality (TZ2P). Best overall agreement with our CCSD(T)/aug-cc-pVQZ benchmark is obtained with OLYP and B3LYP. However, OLYP performs better for the S(N)2@C overall and central barriers, which it underestimates by 2.65 and 4.05 kcal/mol, respectively. The other DFT approaches underestimate these barriers by some 4.8 (B3LYP) to 9.0 kcal/mol (BLYP).     

Molecular structure of the octatetranyl anion, C8H-: a computational study

The equilibrium molecular structure of the octatetranyl anion, C8H(-), which has been recently detected in two astronomical environments, is investigated with the aid of both ab initio post-Hartree-Fock and density functional theory (DFT) calculations. The model chemistry adopted in this study was selected after a series of benchmark calculations performed on molecular acetylene for which accurate gas-phase structural data are available. Geometry optimizations performed at the CCSD/6-311+G(2d,p), QCISD/6-311+G(2d,p), and MP4(SDQ)/6-311+G(2d,p) levels of theory yield for C8H(-) an interesting polyyne-type structure that defies the chemical formula displaying a simple alternation of triple and single carbon-carbon bonds, [:C[triple bond]C-C[triple bond]C-C[triple bond]C-C[triple bond]CH](1-). In the optimized geometry of C8H(-), as one proceeds from the naked carbon atom on one side of the chain to the CH unit on the opposite side of the chain, the short (formally triple) carbon-carbon bonds decrease in length from 1.255 to 1.213 A whereas the long (formally single) carbon-carbon bonds increase (albeit only slightly) in length from 1.362 to 1.378 A (CCSD results). In striking contrast, both MP2 and DFT (B3LYP and PBE0) calculations fail in reproducing the pattern of the carbon-carbon bond lengths obtained with the CCSD, QCISD, and MP4 methods. The structures of three shorter n-even chains, C(n)H(-) (n = 2, 4, and 6), along with those of four n-odd compounds (n = 3, 5, 7, and 9) are also investigated at the CCSD/6-311+G(2d,p) level of theory.     

Reaction of [Xe-F]+ with HI

The reaction behavior of [XeF][AsF₆] in solution toward hydrogen iodide, HI, was investigated, and Xe, HF, and [I₄][AsF₆]₂ were identified as the final reaction products. The reaction enthalpy of the gas-phase reaction ([XeF]⁺ + HI → [XeI]⁺ (¹Σ) + HF) was calculated at the optimized MP4(SDQ) geometries at the QCISD(TQ) level to be: ΔH0298 [QCISD(TQ)/LANL2DZ//MP4(SDQ)/LANL2DZ] = −63.3 kcal mol⁻¹. The [XeI]⁺ cation is bound only in the ¹Σ singlet state, and the triplet state (³Π) was shown to be essentially unbound at all levels of theory applied and very close in energy to the singlet state at equilibrium structure. According to the ab initio calculations, [XeI]⁺ can react with HI in a thermodynamically and spin-symmetry allowed reaction to yield the [XeI]⁺ (¹Σ) cation that may, after interconversion into the unbound triplet state, immediately dissociate into xenon (¹S) and I⁺ (³P). © 1997 John Wiley & Sons, Inc. Heteroatom Chem 8: 473–478, 1997     

Are the hydrogen bonds involving sulfur bases inverse or anomalous?

The hydrogen‐bonded complexes (HBCs) of H₂S, CH₂S, and CH₄S with H–F (hydrogen fluoride) were studied within the framework of the quantum theory of atoms in molecules at several theoretical levels (HF, B3LYP, MP2, and QCISD) with a wide range of basis sets. According to the integrated atomic populations obtained at correlated levels, the interacting hydrogen of the acid gains charge upon complexation, in sharp contrast to the conventional picture of hydrogen bonding, whereas the HF method yields a small loss of charge. The study of several H_nA…H_mD HBCs of hydrides, where A is the hydrogen‐acceptor atom and D is the atom bonded to the hydrogen donor, reveals this behavior is followed when the electronegativity of D significantly exceeds that of A. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Second-order Møller-Plesset perturbation energy obtained from divide-and-conquer Hartree-Fock density matrix

The density matrix (DM) obtained from Yang's [Phys. Rev. Lett. 66, 1438 (1991)] divide-and-conquer (DC) Hartree-Fock (HF) calculation is applied to the explicit second-order M?ller-Plesset perturbation (MP2) energy functional of the HF DM, which was firstly mentioned by Ayala and Scuseria [J. Chem. Phys. 110, 3660 (1999)] and was improved by Surján [Chem. Phys. Lett. 406, 318 (2005)] as DM-Laplace MP2. This procedure, termed DC-DM MP2, requires the HF DM of holes, for which we propose two evaluation schemes in DC manner. Numerical studies reveal that the DC-DM MP2 energy deviation from canonical MP2 is the same order of magnitude as DC-HF energy deviation from conventional HF whichever type of hole DM is adopted. It is also confirmed that the central processing unit time of DC-DM MP2 is less than that of DM-Laplace MP2 because the DC-HF DM is sparser than conventional DM.     

Computational study of the reaction of fluorine atom with acetone

The reaction of F(2P) with acetone has been studied theoretically using ab initio quantum chemistry methods and transition state theory. The potential energy surface was calculated at the G3MP2 level using the MP2/6-311G(d,p) optimized structures. Additionally, to ensure the accuracy of the calculations, optimizations with either larger basis set (e.g., MP2/G3MP2Large) or higher level electron correlation [e.g., CCSD/ 6-311G(d,p)] were also performed. It has been revealed that the F + CH3C(O)CH3 reaction proceeds via two pathways: (1) the direct hydrogen abstraction of acetone by F gives the major products HF + CH3C(O)CH2; (2) the addition of F atom to the >C=O double bond of acetone and the subsequent C-C bond cleavage gives the minor products CH3 + CH3C(O)F. All other product channels are of no importance due to the occurrence of significant barriers. Both abstraction and addition appear to be barrierless processes. Variational transition state model and multichannel RRKM theory were employed to calculate the temperature- and pressure-dependent rate constants and branching ratios. The predicted rate constants for the abstraction channel and the yields of HF + CH3C(O)CH3 and CH3 + CH3C(O)F are both in good agreement with the experimental data at 295 K and 700 Torr. A negative temperature dependence of the overall rate constants was predicted at temperatures below 500 K.     

Interaction of dihydrogen with small and light molecules

Second-order M?ller-Plesset (MP2) calculations (using the approximate resolution of the identity, RI-MP2), explicitly correlated MP2 (MP2-R12) calculations, and coupled-cluster calculations including all single and double excitations with a perturbative estimate of triple excitations [CCSD(T)] are performed to study the interaction of molecular hydrogen with the small molecules HF, H2O, NH3, and LiOH. Different adsorption positions are studied. In the cases of H2O and NH3, the most favorable configuration places H2 in an end-on fashion on the O or N atom, respectively. In the cases of HF and LiOH, the H2 molecule takes a side-on position on the H atom of HF or the Li atom. With respect to MP2 calculations in a triple-zeta basis, both the enlargement of the basis set and the extension of the correlation treatment (CCSD(T) vs MP2) increase the interaction energy. The basis set limit CCSD(T) estimates of the interaction energy of H2 with the HF, H2O, NH3, and LiOH molecules amount to 4.40, 2.67, 3.02, and 10.74 kJ mol-1, respectively. The interaction energy for the simultaneous interaction of H2 with two LiOH molecules does not significantly exceed the value obtained for the interaction with a single LiOH molecule. Furthermore, the interaction energies (by MP2) of H2 with glycine, the glycine dimer, and imidazolium chloride amount to 2.78, 5.00, and 6.30 kJ mol-1, respectively.     

密度泛函理论与Hartree-Fock方法混合处理中的稳态相关能校正

本文分析了通常的Hartree-Fock(HF)相关能定义和密度泛函理论(DFT)中的相关能定义的等价性条件。认为在参考电子密度与真实密度相差很大时两种定义是不等价的, 严格的DFT相关能比HF相关能(绝对值)要大。而在DFT与HF混合处理中得到的相关能比HF相关能(绝对值)要小, 两者之差相当于稳态相关能。实际计算表明, 通过合理地选择组态, 采用有限CI可以求得这一差值。本文描绘了双原子分子H2(X^1∑g^+), HF(X^1∑^+), N2(X^1∑g^+)的势能曲线, 结果比完全CISD和MP4的曲线还要好。H2的离解能是0.17a.u., 逼近实验值0.1747a.u..。     

Basis set limits of the second order Moller-Plesset correlation energies of water, methane, acetylene, ethylene, and benzene

We report second order Moller-Plesset (MP2) and MP2-F12 total energies on He, Ne, Ar, H(2)O, CH(4), C(2)H(2), C(2)H(4), and C(6)H(6), using the correlation consistent basis sets, aug-cc-pVXZ (X=D-7). Basis set extrapolation techniques are applied to the MP2 and MP2-F12/B methods. The performance of the methods is tested in the calculations of the atoms, He, Ne, and Ar. It is indicated that the two-point extrapolation of MP2-F12/B with the basis sets (X=5,6) is the most reliable. Similar accuracy is obtained using two-point extrapolated conventional MP2 with the basis sets (X=6,7). For the molecules investigated the valence MP2 correlation energy is estimated within 1 mE(h).     

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.     

Geometry, dipole moment, polarizability and first hyperpolarizability of polymethineimine: an assessment of electron correlation contributions

We have investigated the geometries as well as the longitudinal dipole moment (micro), polarizability (alpha), and first hyperpolarizability (beta) of polymethineimine oligomers using different approaches [Hartree-Fock (HF), second-order M?ller-Plesset (MP2), and hybrid density functional theory (DFT) methods (B3LYP and PBE0)] for evaluating the geometries and the nonlinear optical properties. It turns out that (i) HF and the selected DFT methods provide the incorrect sign for beta of short and medium size oligomers. (ii) The B3LYP and PBE0 electron correlation correction are too small for micro, too large for alpha, and for some oligomer lengths, they are in the wrong direction for beta. (iii) On the contrary to polyacetylene, the hybrid-DFT geometries are in poor agreement with MP2 geometries; the former showing much smaller bond length alternations.