Ab initio calculation of bowl, cage, and ring isomers of C20 and C20-

High-level ab initio calculations have been carried out to reexamine relative stability of bowl, cage, and ring isomers of C(20) and C(20)(-). The total electronic energies of the three isomers show different energy orderings, strongly depending on the hybrid functionals selected. It is found that among three popular hybrid density-functional (DF) methods B3LYP, B3PW91, PBE1PBE, and a new hybrid-meta-DF method TPSSKCIS, only the PBE1PBE method (with cc-pVTZ basis set) gives qualitatively correct energy ordering as that predicted from ab initio CCSD(T)/cc-pVDZ [CCSD(T)-coupled-cluster method including singles, doubles, and noniterative perturbative triples; cc-pVDZ-correlation consistent polarized valence double zeta] as well as from MP4(SDQ)/cc-pVTZ [MP4-fourth-order Moller-Plesset; cc-pVTZ-correlation consistent polarized valence triple zeta] calculations. Both CCSD(T) and MP4 calculations indicate that the bowl is most likely the global minimum of neutral C(20) isomers, followed by the fullerene cage and ring. For the anionic counterparts, the PBE1PBE calculation also agrees with MP4/cc-pVTZ calculation, both predicting that the bowl is still the lowest-energy structure of C(20)(-) at T=0 K, followed by the ring and the cage. In contrast, both B3LYP/cc-pVTZ and B3PW91/cc-pVTZ calculations predict that the ring is the lowest-energy structure of C(20)(-). Apparently, this good reliability in predicting the energy ordering renders the hybrid PBE method a leading choice for predicting relative stability among large-sized carbon clusters and other carbon nanostructures (e.g., finite-size carbon nanotubes, nano-onions, or nanohorns). The relative stabilities derived from total energy with Gibbs free-energy corrections demonstrate a changing ordering in which ring becomes more favorable for both C(20) and C(20)(-) at high temperatures. Finally, photoelectron spectra (PES) for the anionic C(20)(-) isomers have been computed. With binding energies up to 7 eV, the simulated PES show ample spectral features to distinguish the three competitive C(20)(-) isomers.     

How accurate is the density functional theory combined with symmetry-adapted perturbation theory approach for CH-pi and pi-pi interactions? A comparison to supermolecular calculations for the acetylene-benzene dimer

Five different orientations of the acetylene-benzene dimer including the T-shaped global minimum structure are used to assess the accuracy of the density functional theory combined with symmetry adapted perturbation theory (DFT-SAPT) approach in its density-fitting implementation (DF-DFT-SAPT) for the study of CH-pi and pi-pi interactions. The results are compared with the outcome of counterpoise corrected supermolecular calculations employing second-order M?ller-Plesset (MP2), spin-component scaled MP2 (SCS-MP2) and single and double excitation coupled cluster theory including perturbative triple excitations (CCSD(T)). For all considered orientations MP2 predicts much deeper potential energy curves with considerably shifted minima compared to CCSD(T) and DFT-SAPT. In spite of being an improvement over the results of MP2, SCS-MP2 tends to underestimate the well depth while DFT-SAPT, employing an asymptotically corrected hybrid exchange-correlation potential in conjunction with the adiabatic local density approximation for the exchange-correlation kernel, is found to be in excellent agreement with CCSD(T). Furthermore, DFT-SAPT provides a detailed understanding of the importance of the electrostatic, induction and dispersion contributions to the total interaction energy and their repulsive exchange corrections.     

高级量子化学从头计算法研究N2和H2O分子间相互作用

在MP2/6-311++G(3d,3p)电子相关校正水平上,对N₂和H₂O分子间可能存在的氢键复合物进行全自由度能量梯度优化,发现了一个接近于直线的弱氢键总能量极小结构(1),进一步在高级电子相关校正的MP4SDTQ和CCSD(T)水平,用6-311++G(3d,3p)基组加上(3s3p2d1f)键函数,用MP4和CCSD(T)计算的结构1的结合能分别为-5.061kJ/mol和-4.715kJ/mol.     

Isomer stability of N6C6H6 cages

Recent theoretical studies have identified carbon-nitrogen cages that are potentially stable high energy density materials (HEDM). One such molecule is an N(6)C(6)H(6) cage in which a six-membered ring of nitrogen is bonded to C(3)H(3) triangles on both sides. This molecule is based on the structure of the most stable N(12) cage, with six carbon atoms substituted into the structure. In the current study, several N(6)C(6)H(6) isomers (including the previously studied cage) are examined by theoretical calculations to determine which is actually the most stable. Stability will be evaluated from two points of view: (1) thermodynamic stability of one isomer versus another and (2) kinetic stability of each isomer as determined by the energetics of bond breaking. Density functional theory (B3LYP), perturbation theory (MP2 and MP4), and coupled-cluster theory (CCSD(T)) are used in this study, along with the correlation-consistent basis sets of Dunning. Trends in thermodynamic and kinetic stability are discussed.     

Stabilisation energy of C(6)H(6)...C(6)X(6) (X = F, Cl, Br, I, CN) complexes: complete basis set limit calculations at MP2 and CCSD(T) levels

Stabilisation energies of stacked structures of C(6)H(6)...C(6)X(6) (X = F, Cl, Br, CN) complexes were determined at the CCSD(T) complete basis set (CBS) limit level. These energies were constructed from MP2/CBS stabilisation energies and a CCSD(T) correction term determined with a medium basis set (6-31G**). The former energies were extrapolated using the two-point formula of Helgaker et al. from aug-cc-pVDZ and aug-cc-pVTZ Hartree-Fock energies and MP2 correlation energies. The CCSD(T) correction term is systematically repulsive. The final CCSD(T)/CBS stabilisation energies are large, considerably larger than previously calculated and increase in the series as follows: hexafluorobenzene (6.3 kcal mol(-1)), hexachlorobenzene (8.8 kcal mol(-1)), hexabromobenzene (8.1 kcal mol(-1)) and hexacyanobenzene (11.0 kcal mol(-1)). MP2/SDD** relativistic calculations performed for all complexes mentioned and also for benzene[dot dot dot]hexaiodobenzene have clearly shown that due to relativistic effects the stabilisation energy of the hexaiodobenzene complex is lower than that of hexabromobenzene complex. The decomposition of the total interaction energy to physically defined energy components was made by using the symmetry adapted perturbation treatment (SAPT). The main stabilisation contribution for all complexes investigated is due to London dispersion energy, with the induction term being smaller. Electrostatic and induction terms which are attractive are compensated by their exchange counterparts. The stacked motif in the complexes studied is very stable and might thus be valuable as a supramolecular synthon.     

Improvement of the coupled-cluster singles and doubles method via scaling same- and opposite-spin components of the double excitation correlation energy

There has been much interest in cost-free improvements to second-order M?ller-Plesset perturbation theory (MP2) via scaling the same- and opposite-spin components of the correlation energy (spin-component scaled MP2). By scaling the same- and opposite-spin components of the double excitation correlation energy from the coupled-cluster of single and double excitations (CCSD) method, similar improvements can be achieved. Optimized for a set of 48 reaction energies, scaling factors were determined to be 1.13 and 1.27 for the same- and opposite-spin components, respectively. Preliminary results suggest that the spin-component scaled CCSD (SCS-CCSD) method will outperform all MP2 type methods considered for describing intermolecular interactions. Potential energy curves computed with the SCS-CCSD method for the sandwich benzene dimer and methane dimer reproduce the benchmark CCSD(T) potential curves with errors of only a few hundredths of 1 kcal mol(-1) for the minima. The performance of the SCS-CCSD method suggests that it is a reliable, lower cost alternative to the CCSD(T) method.     

Theoretical study of oxidative additions of H2 and MeCN to a nickel(0) complex: significantly large correlation effects and characteristic features of the reaction

Oxidative addition of H2 to Ni(PH3)2 was theoretically studied as a prototype of nickel-catalyzed sigma-bond activation reaction, where CASSCF, CASPT2, CCSD(T), broken symmetry (Bs) MP2 to MP4(SDTQ), and DFT methods were employed. The CASPT2 method yields a reliable potential energy curve (PEC) when the active space consists of 10 electrons and 10 orbitals including five outer 3d' orbitals. The CCSD(T) method presents almost the same PEC as the CASPT2-calculated one, when either the ANO or the cc-pVTZ basis set is used for Ni. Bs-MP4(SDTQ)-calculated PEC is similar to those calculated by the CASPT2/ANO method, while the PEC is not smooth around the transition state. In the DFT calculation, ANO, cc-pVTZ, and triple-zeta quality basis sets (SDB) with Stuttgart-Dresden-Bonn effective core potentials (ECPs) must be used for Ni. The DFT-calculated reaction energy is somewhat smaller than the CASPT2- and CCSD(T)-calculated values, while B3PW91 and mPW1PW91 present moderately better energy changes than BLYP, B1LYP, and B3LYP. Oxidative addition of MeCN to Ni(PH3)2 was investigated by the DFT(B3PW91) and CCSD(T) methods. Almost the same activation barrier was calculated by these methods, when cc-pVTZ was employed for Ni. However, the DFT method moderately underestimates the binding energy of the reactant complex and the reaction energy compared to the CCSD(T) method. This oxidative addition exhibits interesting characteristic features, as follows: The barrier height relative to infinite separation is lower, and the product is more stable than those of the oxidative addition of C2H6. These differences are discussed in detail in terms of Ni-Me and Ni-CN bond energies and the participation of the CN pi* orbital to stabilization interaction in the transition state.     

Molecular calculations for HeH<Superscript>+</Superscript> with two-center correlated orbitals

A two-center correlated orbital approach was used to calculate the electronic ground state energy for the HeH⁺ molecular ion. The wavefunctions were constructed from the exact solution of the Schrödinger equation for the HeH⁺⁺ problem in prolate-spheroidal coordinates taken together with a Hylleraas type correlation factor. With a simple single term wavefunction, we obtained ground state energy of ?2.95308691 hartree without any variational parameters in the calculation. When a two-configuration-state wavefunction was used and effective charges were allowed to be adjusted, we found an energy of ?2.97384868 hartree, which is to be compared with ?2.97869074 hartree obtained by an 83 term configuration interaction wavefunction or ?2.97364338 hartree by an ab initio calculation (at the MP4(SDQ)/6-311++G(3df, 3dp) level) using the well-known “canned” code.     

Studies of neutral and ionic CuAr and CuKr van der Waals complexes

Ab initio calculations of the interaction potential between Cu (or Cu(+)) and Ar (or Kr) have been carried out. A range of theoretical methods, including Hartree-Fock (HF), Moeller-Plesset perturbation methods to second order (MP2), and single and double excitation coupled cluster methods, with the perturbational effect of triple excitations (CCSD(T)), were employed with relativistic pseudopotential basis sets. The effects of bond functions and diffuse polarization (f, g, h) functions were tested on the calculation of the weak intermolecular interactions. Potential energy curves were obtained for all four complexes by MP2 and CCSD(T) methods. For CuKr, even with the largest basis set used, a binding energy that is only 37% of the measured value was obtained. Possible reasons for the disagreement are discussed.     

SCF and localized orbitals in ethylene: MBPT/CC results and comparison with one-million configuration Cl

Many-body perturbation theory (MBPT) and coupled-cluster (CC) calculations are performed on the ethylene molecule employing canonical SCF and simple bond-orbital localized orbitals (LO). Full fourth-order MBPT [i.e. SDTQ MBPT(4)], CC doubles (CCD) and CC singles and doubles (CCSD) energies are compared with the over one-million configuration ‘bench-mark” Cl calculation of Saxe et al. Though the SCF and LO reference determinant energies differ by 0.29706 hartree, the CCSD energy difference is only 1.7 mhartrees (mh). Our most extensive SCF orbital calculation, CCSD plus fourth-order triples, is found to be lower in energy than the CI result by 5.3 mh.     

Quantum dynamics of vibrationally activated OH-CO reactant complexes

The MP2 complete basis set (CBS) limit for the binding energy of the two low-lying water octamer isomers of D2d and S4 symmetry is estimated at -72.7+/-0.4 kcal/mol using the family of augmented correlation-consistent orbital basis sets of double through quintuple zeta quality. The largest MP2 calculation with the augmented quintuple zeta (aug-cc-pV5Z) basis set produced binding energies of -73.70 (D2d) and -73.67 kcal/mol (S4). The effects of higher correlation, computed at the CCSD(T) level of theory, are estimated at <0.1 kcal/mol. The newly established MP2/CBS limit for the water octamer is reproduced quite accurately by the newly developed all atom polarizable, flexible interaction potential (TTM2-F). The TTM2-F binding energies of -73.21 (D2d) and -73.24 kcal/mol (S4) for the two isomers are just 0.5 kcal/mol (or 0.7%) larger than the MP2/CBS limit.     

Multireference coupled-cluster study of the symmetry breaking in the C2B radical

The potential energy surfaces (PESs) for both the ground and the excited electronic states of the C(2)B radical are investigated using various multireference (MR) coupled-cluster (CC) approaches. In the ground state case we employ the reduced MR (RMR) CC approach with singles (S) and doubles (D), the RMR CCSD method, as well as its RMR CCSD(T) version corrected for secondary triples, relying on various model spaces and basis sets. The reliability of this approach is also tested against the benchmark full configuration interaction results obtained for a small Dunning-Hay (DH) basis set. The results imply a clear preference for a cyclic structure which, however, breaks the C(2v) symmetry. This symmetry breaking manifests itself strongly at the level of the independent particle model, as represented by the restricted open-shell Hartree-Fock approximation, but the tendency toward symmetry breaking diminishes with the increasing size of the basis set employed as well as with the enhanced account of the correlation effects. It is likely to disappear in the complete basis set limit. The general model space CCSD method is then used to compute vertical excitation energies for a number of excited states as well as the cuts of the PES as the boron atom moves around the C(2) fragment. These results also explain why no symmetry breaking is found when relying on a spin contaminated unrestricted Hartree-Fock reference, as in the UMP2 method.     

Singlet-triplet energy separation of cyclobutylidene

Ab initio (MP2, CCSD(T)) and density functional theory (BLYP, B3LYP) calculations provide insight concerning novel aspects of structure and bonding in cyclobutylidene (1). Singlet cyclobutylidene ((1)1) adopts a bicyclobutane-like structure (C(s) symmetry) that includes a weak, transannular bonding interaction between the carbene carbon and the opposing CH(2) group. Conformational ring inversion in (1)1 occurs through a transition state of C(2)(v)() symmetry (TS(1)1) with an enthalpy barrier of approximately 3 kcal/mol. Stabilization afforded the singlet state by the transannular interaction appears to be largely offset by a loss of hyperconjugative stabilization from the adjacent C-H bonds. Triplet cyclobutylidene ((3)1) exhibits a C(2)(v)() structure and conventional bonding. The triplet state lies 5.9 kcal/mol above the singlet ground state at the CCSD(T)/TZP//CCSD(T)/DZP level of theory. The singlet-triplet energy gap of cyclobutylidene (-5.9 kcal/mol) lies between that of an acyclic analogue, dimethylcarbene (-1.6 kcal/mol), and a highly strained analogue, cyclopropylidene (-13.8 kcal/mol). The magnitude of the energy gap suggests that triplet cyclobutylidene ((3)1) will be thermally accessible under a variety of experimental conditions.     

Characterization of the potential energy surfaces of two small but challenging noncovalent dimers: (P2)2 and (PCCP)2

This work characterizes eight stationary points of the P₂ dimer and six stationary points of the PCCP dimer, including a newly identified minimum on both potential energy surfaces. Full geometry optimizations and corresponding harmonic vibrational frequencies were computed with the second‐order Møller–Plesset (MP2) electronic structure method and six different basis sets: aug‐cc‐pVXZ, aug‐cc‐pV(X+d)Z, and aug‐cc‐pCVXZ where X = T, Q. A new L‐shaped structure with C₂ symmetry is the only minimum for the P₂ dimer at the MP2 level of theory with these basis sets. The previously reported parallel‐slipped structure with C_2h symmetry and a newly identified cross configuration with D₂ symmetry are the only minima for the PCCP dimer. Single point energies were also computed using the canonical MP2 and CCSD(T) methods as well as the explicitly correlated MP2‐F12 and CCSD(T)‐F12 methods and the aug‐cc‐pVXZ (X = D, T, Q, 5) basis sets. The energetics obtained with the explicitly correlated methods were very similar to the canonical results for the larger basis sets. Extrapolations were performed to estimate the complete basis set (CBS) limit MP2 and CCSD(T) binding energies. MP2 and MP2‐F12 significantly overbind the P₂ and PCCP dimers relative to the CCSD(T) and CCSD(T)‐F12 binding energies by as much as 1.5 kcal mol^?1 for the former and 5.0 kcal mol^?1 for the latter at the CBS limit. The dominant attractive component of the interaction energy for each dimer configuration was dispersion according to several symmetry‐adapted perturbation theory analyses. © 2014 Wiley Periodicals, Inc.     

Theoretical study of Pt(PR3)(2)(AlCl3) (R = H, Me, Ph, or Cy) including an unsupported bond between transition metal and non-transition metal elements: geometry, bond strength, and prediction

The molecular structure and the binding energy of Pt(PR(3))(2)(AlCl(3)) (R = H, Me, Ph, or Cy) were investigated by DFT, MP2 to MP4(SDTQ), and CCSD(T) methods. The optimized structure of Pt(PCy(3))(2)(AlCl(3)) (Cy = cyclohexyl) by the DFT method with M06-2X and LC-BLYP functionals agrees well with the experimental one. The MP4(SDTQ) and CCSD(T) methods present similar binding energies (BE) of Pt(PH(3))(2)(AlCl(3)), indicating that these methods provide reliable BE value. The DFT(M06-2X)-calculated BE value is close to the MP4(SDTQ) and CCSD(T)-calculated values, while the other functionals present BE values considerably different from the MP4(SDTQ) and CCSD(T)-calculated values. All computational methods employed here indicate that the BE values of Pt(PMe(3))(2)(AlCl(3)) and Pt(PPh(3))(2)(AlCl(3)) are considerably larger than those of the ethylene analogues. The coordinate bond of AlCl(3) with Pt(PR(3))(2) is characterized to be the σ charge transfer (CT) from Pt to AlCl(3). This complex has a T-shaped structure unlike the well-known Y-shaped structure of Pt(PMe(3))(2)(C(2)H(4)), although both are three-coordinate Pt(0) complex. This T-shaped structure results from important participation of the Pt d(σ) orbital in the σ-CT; because the Pt d(σ) orbital energy becomes lower as the P-Pt-P angle decreases, the T-shaped structure is more favorable for the σ-CT than is the Y-shaped structure. [Co(alcn)(2)(AlCl(3))](-) (alcn = acetylacetoneiminate) is theoretically predicted here as a good candidate for the metal complex, which has an unsupported M-Al bond because its binding energy is calculated to be much larger than that of Pt(PCy(3))(2)(AlCl(3)).     

New nonsymmetric P(OH)3 species. Comparison with the C3 isomer and themochemistry at the DFT, MP2, and CCSD(T) levels of theory

Two new less-symmetric P(OH)3 isomers that are more stable than the C3 structure are found at the density functional theory (B3PW91, B3LYP), MP2, and CCSD(T) levels with the large aug-cc-pvdz/pvtz basis sets. The C1 and C3 structures are qualitatively different from those found for the As(OH)3 molecule. An additional lower lying P(OH)3 structure with Cs symmetry has been obtained. With the largest basis set the Cs isomer is predicted to be the most stable. However, the inclusion of zero-point-energy corrections induces an inversion between the Cs and C1 isomers, with the latter becoming the lowest energy structure at the highest correlated level. Increasing inclusion of electronic correlation effects reduces the energy difference between the C1 and Cs structures while the C1-C3 energy difference and C1-Cs interconversion barrier become larger. In all cases, energy differences and barrier heights are around 1 kcal/mol.     

Hybrid coupled-cluster and perturbation method for extended systems of one-dimensional periodicity

A hybrid of the coupled-cluster singles and doubles (CCSD) and second-order M?ller-Plesset perturbation (MP2) methods [M. Nooijen, J. Chem. Phys. 111, 10815 (1999); A. D. Bochevarov and C. D. Sherrill, ibid. 122, 234110 (2005); A. D. Bochevarov et al., ibid. 125, 054109 (2006)] is formulated and implemented for one-dimensional periodic extended systems, in which the excitation (T) amplitudes of active bands are determined iteratively by CCSD, while the T amplitudes of mixed active/inactive bands are held fixed at the first-order M?ller-Plesset perturbation values. The occupied and virtual bands near the Fermi level, which can cause instability in MP2 when they are (quasi-)degenerate, are selected as active bands to be treated by CCSD, which can, in principle, resist such instability. Two contraction schemes of the T amplitudes (Contractions A and B) are considered. Contraction A is the one proposed for molecules and used also for extended systems because it is efficient for CCSD, but not necessarily so for the hybrid CCSD/MP2. Contraction B is introduced to be more optimally efficient for the hybrid CCSD/MP2 by maximizing the number of intermediate quantities made of the inactive T amplitudes and molecular integrals, which do not vary during CCSD iterations and are computed only once, stored, and reused. In an application to trans-polyacetylene, a smooth transition of the results of the hybrid CCSD/MP2 is observed toward those of CCSD and MP2 by increasing and decreasing, respectively, the number of active bands. With the smallest active space, the hybrid CCSD/MP2 with Contractions A and B achieves a speedup by a factor of 360 and 520, respectively, relative to CCSD. When all of the occupied bands and about half of the virtual bands are active, the hybrid CCSD/MP2 can recover 98% of the CCSD correlation energy or half of the difference between CCSD and MP2 at less than a tenth of the usual CCSD cost.     

Infrared spectroscopy of ozone-water complex in a neon matrix

Matrix isolation infrared spectroscopy has been applied to study an ozone-water complex of atmospheric interest. The complex was identified in the spectral region of three normal modes of ozone and water. Ab initio calculation at MP4(SDQ), QCISD, and CCSD(T) levels indicates the existence of only one stable conformer, which accords with the present experimental result. This conformer belongs to the Cs symmetry group where two molecular planes of ozone and water are perpendicular to the Cs symmetry plane. The binding energy was calculated to be 1.89 kcal/mol at the CCSD(T)/6-311++G(3df,3pd)//CCSD(T)/6-311++G(d,p) level of theory. The formation constant and atmospheric abundance of the ozone-water complex are estimated using the thermodynamic and spectroscopic data obtained.