Explicit correlation and basis set superposition error: the structure and energy of carbon dioxide dimer

We have investigated the slipped parallel and t-shaped structures of carbon dioxide dimer [(CO(2))(2)] using both conventional and explicitly correlated coupled cluster methods, inclusive and exclusive of counterpoise (CP) correction. We have determined the geometry of both structures with conventional coupled cluster singles doubles and perturbative triples theory [CCSD(T)] and explicitly correlated cluster singles doubles and perturbative triples theory [CCSD(T)-F12b] at the complete basis set (CBS) limits using custom optimization routines. Consistent with previous investigations, we find that the slipped parallel structure corresponds to the global minimum and is 1.09 kJ mol(-1) lower in energy. For a given cardinal number, the optimized geometries and interaction energies of (CO(2))(2) obtained with the explicitly correlated CCSD(T)-F12b method are closer to the CBS limit than the corresponding conventional CCSD(T) results. Furthermore, the magnitude of basis set superposition error (BSSE) in the CCSD(T)-F12b optimized geometries and interaction energies is appreciably smaller than the magnitude of BSSE in the conventional CCSD(T) results. We decompose the CCSD(T) and CCSD(T)-F12b interaction energies into the constituent HF or HF CABS, CCSD or CCSD-F12b, and (T) contributions. We find that the complementary auxiliary basis set (CABS) singles correction and the F12b approximation significantly reduce the magnitude of BSSE at the HF and CCSD levels of theory, respectively. For a given cardinal number, we find that non-CP corrected, unscaled triples CCSD(T)-F12b/VXZ-F12 interaction energies are in overall best agreement with the CBS limit.     

Ab initio ground state phenylacetylene-argon intermolecular potential energy surface and rovibrational spectrum

We evaluate the phenylacetylene-argon intermolecular potential energy surface by fitting a representative number of ab initio interaction energies to an analytic function. These energies are calculated at a grid of intermolecular geometries, using the CCSD(T) method and the aug-cc-pVDZ basis set extended with a series of 3s3p2d1f1g midbond functions. The potential is characterized by two equivalent global minima where the Ar atom is located above and below the phenylacetylene plane at a distance of 3.5781 A? from the molecular center of mass and at an angle of 9.08° with respect to the axis perpendicular to the phenylacetylene plane and containing the center of mass. The calculated interaction energy is -418.9 cm(-1). To check further the potential, we obtain the rovibrational spectrum of the complex and the results are compared to the available experimental data.     

Ab initio structural and vibrational investigation of sulfuric acid monohydrate

We employ ab initio methods to find stable geometries and to calculate potential energy surfaces and vibrational wavenumbers for sulfuric acid monohydrate. Geometry optimizations are carried out with the explicitly correlated coupled-cluster approach that includes single, double, and perturbative triple excitations (CCSD(T)-F12a) with a valence double-ζ basis set (VDZ-F12). Four different stable geometries are found, and the two lowest are within 0.41 kJ mol(-1) (or 34 cm(-1)) of each other. Vibrational harmonic wavenumbers are calculated at both the density-fitted local spin component scaled second-order M?ller-Plesset perturbation theory (DF-SCS-LMP2) with the aug-cc-pV(T+d)Z basis set and the CCSD-F12/VDZ-F12 level. Water O-H stretching vibrations and two highly anharmonic large-amplitude motions connecting the three lowest potential energy minima are considered by limiting the dimensionality of the corresponding potential energy surfaces to small two- or three-dimensional subspaces that contain only strongly coupled vibrational degrees of freedom. In these anharmonic domains, the vibrational problem is solved variationally using potential energy surfaces calculated at the CCSD(T)-F12a/VDZ-F12 level.     

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.     

Xe-N2O复合物的分子间势能面和振转光谱的理论研究

采用CCSD(T)方法研究了范德华分子体系Xe—N2O复合物的势能面和振转光谱性质,研究表明,该势能面有两个极小点,分别对应T构型和线性Xe—ONN构型,采用离散变量表象和Lanczos算法计算了体系的振转能级,计算结果表明,CCSD(T)势能面支持97个振动束缚态,并对能级进行了指认,计算得到的Xe—N2O转动跃迁频率与实验值吻合得很好。     

On the accuracy of explicitly correlated coupled-cluster interaction energies--have orbital results been beaten yet?

The basis set convergence of weak interaction energies for dimers of noble gases helium through krypton is studied for six variants of the explicitly correlated, frozen geminal coupled-cluster singles, doubles, and noniterative triples [CCSD(T)-F12] approach: the CCSD(T)-F12a, CCSD(T)-F12b, and CCSD(T)(F12*) methods with scaled and unscaled triples. These dimers were chosen because CCSD(T) complete-basis-set (CBS) limit benchmarks are available for them to a particularly high precision. The dependence of interaction energies on the auxiliary basis sets has been investigated and it was found that the default resolution-of-identity sets cc-pVXZ/JKFIT are far from adequate in this case. Overall, employing the explicitly correlated approach clearly speeds up the basis set convergence of CCSD(T) interaction energies, however, quite surprisingly, the improvement is not as large as the one achieved by a simple addition of bond functions to the orbital basis set. Bond functions substantially improve the CCSD(T)-F12 interaction energies as well. For small and moderate bases with bond functions, the accuracy delivered by the CCSD(T)-F12 approach cannot be matched by conventional CCSD(T). However, the latter method in the largest available bases still delivers the CBS limit to a better precision than CCSD(T)-F12 in the largest bases available for that approach. Our calculations suggest that the primary reason for the limited accuracy of the large-basis CCSD(T)-F12 treatment are the approximations made at the CCSD-F12 level and the non-explicitly correlated treatment of triples. In contrast, the explicitly correlated second-order Mo?ller-Plesset perturbation theory (MP2-F12) approach is able to pinpoint the complete-basis-set limit MP2 interaction energies of rare gas dimers to a better precision than conventional MP2. Finally, we report and analyze an unexpected failure of the CCSD(T)-F12 method to deliver the core-core and core-valence correlation corrections to interaction energies consistently and accurately.     

Ab initio and analytic intermolecular potentials for Ar-CF4

Ab initio calculations at the CCSD(T) level of theory were performed to characterize the Ar + CF4 intermolecular potential. Potential energy curves were calculated with the aug-cc-pVTZ basis set, and with and without a correction for basis set superposition error (BSSE). Additional calculations were performed with other correlation consistent basis sets to extrapolate the Ar-CF4 potential energy minimum to the complete basis set (CBS) limit. Both the size of the basis set and BSSE have substantial effects on the Ar + CF4 potential. Calculations with the aug-cc-pVTZ basis set, and with a BSSE correction, appear to give a good representation of the BSSE corrected potential at the CBS limit. In addition, MP2 theory is found to give potential energies in very good agreement with those determined by the much higher level CCSD(T) theory. Two model analytic potential energy functions were determined for Ar + CF4. One is a fit to the aug-cc-pVTZ calculations with a BSSE correction. The second was derived by fitting an average BSSE corrected potential, which is an average of the CCSD(T)/aug-cc-pVTZ potentials with and without a BSSE correction. These analytic functions are written as a sum of two-body potentials and excellent fits to the ab initio potentials are obtained by representing each two-body interaction as a Buckingham potential.     

State of the art theoretical study and comparison to experiment for the phenol...argon complex

The phenol...argon complex was studied by means of various high level ab initio quantum mechanics methods and high resolution threshold ionization spectroscopy. The structure and stabilization energy of different conformers were determined. Stabilization energy of van der Waals bonded and H-bonded PhOH...Ar complex determined at CCSD(T) complete basis set (CBS) level for CP-RI-MP2/cc-pVTZ/Ar aug-cc-pVTZ geometries amount to 434 and 285 cm(-1). The CCSD(T)/CBS were constructed either as a sum of MP2/CBS interaction energy and CCSD(T) correction term [difference between CCSD(T) and MP2 correlation energies determined with medium basis set] or directly from CCSD(T)/aug-cc-pVDZ and aug-cc-pVTZ energies. Both schemes provide very similar values. Harmonic vibrational analysis revealed that the H-bonded structure does not represent energy minimum but first order transition structure. The respective imaginary vibrational mode (16 cm(-1)) connects two possible argon locations -- above and below the phenol aromatic ring. Including the DeltaZPVE, we obtained stabilization enthalpy at 0 K of 389 cm(-1). This value is marginally higher (25-35 cm(-1), 0.07-0.10 kcal/mol) than the experimental value. The determination of DeltaZPVE constitutes the most significant error and possible improvements should come from more accurate evaluation of the (nonharmonic) vibrational frequencies.     

Ab initio intermolecular potential-energy surface and microwave spectra for the Ne-OCS complex

An ab initio potential-energy surface for the Ne-OCS complex was calculated using the coupled-cluster singles and doubles with noniterative inclusion of connected triples [CCSD(T)] with a large basis set containing bond functions. The interaction energies were obtained by the supermolecular approach with the full counterpoise correction for the basis set superposition error. The CCSD(T) potential was found to have three minima corresponding to the T-shaped and the linear Ne-SCO and Ne-OCS structures. The two-dimensional discrete variable representation method was employed to calculate the rovibrational energy levels for five isotopomers Ne-OCS, (22)Ne-OCS, Ne-OC(34)S, Ne-O(13)CS, and Ne-(18)OCS. The calculated pure rotational transition frequencies for the vibrational ground state of the five isotopomers are in good agreement with the observed values. The corresponding microwave spectra show that the b-type transitions (deltaK(a)=+/-1) are significantly stronger than the a-type transitions (deltaK(a)=0).     

Theoretical study of the spectroscopically relevant parameters for the detection of HNP(q) and HPN(q) (q = 0, +1, -1) in the gas phase

High level ab initio electronic structure calculations at different levels of theory have been performed on HNP and HPN neutrals, anions, and cations. This includes standard coupled cluster CCSD(T) level with augmented correlation-consistent basis sets, internally contacted multi-reference configuration interaction, and the newly developed CCSD(T)-F12 methods in connection with the explicitly correlated basis sets. Core-valence correction and scalar relativistic effects were examined. We present optimized equilibrium geometries, harmonic vibrational frequencies, rotational constants, adiabatic ionization energies, electron affinities, vertical detachment energies, and relative energies. In addition, the three-dimensional potential energy surfaces of HNP(-1,0,+1) and of HPN(-1,0,+1) were generated at the (R)CCSD(T)-F12b∕cc-pVTZ-F12 level. The anharmonic terms and fundamentals were derived using second order perturbation theory. For HNP, our best estimate for the adiabatic ionization energy is 7.31 eV, for the adiabatic electron affinity is 0.47 eV. The higher energy isomer, HPN, is 23.23 kcal∕mol above HNP. HPN possesses a rather large adiabatic electron affinity of 1.62 eV. The intramolecular isomerization pathways were computed. Our calculations show that HNP(-) to HPN(-) reaction is subject to electron detachment.     

The Role of High Excitations in Constructing Sub-spectroscopic Accuracy Intermolecular Potential of He-HCN: Critically Examined by the High-Resolution Spectra with Resonance States

Interpreting high-resolution rovibrational spectra of weakly bound complexes commonly requires spectroscopic accuracy (<1 cm^-1) potential energy surfaces (PES). Constructing high-accuracy ab initio PES relies on the high-level electronic structure approaches and the accurate physical models to represent the potentials. The coupled cluster approaches including single and double excitations with a perturbational estimate of triple excitations (CCSD(T)) have been termed the "gold standard" of electronic structure theory, and widely used in generating intermolecular interaction energies for most van der Waals complexes. However, for HCN-He complex, the observed millimeter-wave spectroscopy with high-excited resonance states has not been assigned and interpreted even on the ab initio PES computed at CCSD(T) level of theory with the complete basis set (CBS) limit. In this work, an effective three-dimensional ab initio PES for HCN-He, which explicitly incorporates dependence on the Q₁ (C-H) normal-mode coordinate of the HCN monomer has been calculated at the CCSD(T)/CBS level. The post-CCSD(T) interaction energy has been examined and included in our PES. Analytic two-dimensional PESs are obtained by least-squares fitting vibrationally averaged interaction energies for v₁(C-H)=0, and 1 to the Morse/Long-Range potential function form with root-mean-square deviations (RMSD) smaller than 0.011 cm^-1. The role and significance of the post-CCSD(T) interaction energy contribution are clearly illustrated by comparison with the predicted rovibrational energy levels. With or without post-CCSD(T) corrections, the value of dissociation limit (D₀) is 8.919 or 9.403 cm^-1, respectively. The predicted millimeter-wave transitions and intensities from the PES with post-CCSD(T) excitation corrections are in good agreement with the available experimental data with RMS discrepancy of 0.072 cm^-1. Moreover, the infrared spectrum for HCN-He complex is predicted for the first time. These results will serve as a good starting point and provide reliable guidance for future infrared studies of HCN doped in (He)_n clusters.     

Potential-energy surface for the electronic ground state of NH3 up to 20,000 cm-1 above equilibrium

Ab initio coupled cluster calculations with single and double substitutions and a perturbative treatment of connected triple excitations [CCSD(T)] with the augmented correlation-consistent polarized valence triple-zeta aug-cc-pVTZ basis at 51 816 geometries provide a six-dimensional potential-energy surface for the electronic ground state of NH3. At 3814 selected geometries, CBS+ energies are obtained by extrapolating the CCSD(T) results for the aug-cc-pVXZ(X=T,Q,5) basis sets to the complete basis set (CBS) limit and adding corrections for core-valence correlation and relativistic effects. CBS** ab initio energies are generated at 51,816 geometries by an empirical extrapolation of the CCSD(T)/aug-cc-pVTZ results to the CBS+ limit. They cover the energy region up to 20,000 cm-1 above equilibrium. Parametrized analytical functions are fitted through the ab initio points. For these analytical surfaces, vibrational term values and transition moments are calculated by means of a variational program employing a kinetic-energy operator expressed in the Eckart-Sayvetz frame. Comparisons against experiment are used to assess the quality of the generated potential-energy surfaces. A "spectroscopic" potential-energy surface of NH3 is determined by a slight empirical adjustment of the ab initio potential to the experimental vibrational term values. Variational calculations on this refined surface yield rms deviations from experiment of 0.8 cm-1 for 24 inversion splittings and 0.4 (3.0) cm-1 for 34 (51) vibrational term values up to 6100 (10,300) cm-1.     

Ne-HCl势能面和振转光谱的理论研究

利用量子化学计算方法CCSD(T)和大基组aug-cc-pVTZ加键函数3_s3_p2_d对Ne-HCl体系的分子间势能面进行了理论研究.结果表明,势能面上有两个势阱,分别对应于线性Ne-ClH和Ne-HCl构型.通过精确求解核运动方程发现,该从头算势能面分别支持5个(对Ne-HCl)和7个(Ne-DCl)振动束缚态.计算得到的振转跃迁频率与实值值吻合.     

Computational study of the rovibrational spectrum of (OCS)2

In this paper, we report a new intermolecular potential energy surface and rovibrational transition frequencies and line strengths computed for the OCS dimer. The potential is made by fitting energies obtained from explicitly correlated coupled-cluster calculations and fit using an interpolating moving least squares method. The rovibrational Schroedinger equation is solved with a symmetry-adapted Lanczos algorithm and an uncoupled product basis set. All four intermolecular coordinates are included in the calculation. On the potential energy surface we find, previously unknown, cross-shaped isomers and also polar and non-polar isomers. The associated wavefunctions and energy levels are presented. To identify polar and cross states we use both calculations of line strengths and vibrational parent analysis. Calculated rotational constants differ from their experimental counterparts by less than 0.001 cm(-1).     

New accurate benchmark energies for large water clusters: DFT is better than expected

In this work, we use MP2 and coupled‐cluster with single, double, and perturbative triple excitations [CCSD(T)] as well as their corresponding explicitly correlated (F12) counterparts to compute the interaction energies of water icosamers. The incremental scheme is used to compute benchmark energies at the CCSD(T)/CBS(45) and CCSD(T)(F12*)/cc‐pVQZ‐F12 level of theory. The four structures, dodecahedron, edge sharing, face sharing, and fused cubes, are part of the WATER27 test set and therefore, highly accurate interaction energies are required. All methods applied in this work lead to new benchmark energies for these four systems. To obtain these values, we carefully analyze the convergence of the interaction energies with respect to the basis set. Furthermore, we investigate the influence of the basis set superposition error and the core‐valence correlation. The interaction energies are: dodecahedron ?198.6 kcal/mol, edge sharing ?209.7 kcal/mol, face sharing ?208.0 kcal/mol, and fused cubes ?208.0 kcal/mol. For water clusters, we recommend to use the PW6B95 density functional of Truhlar in combination with Grimme's dispersion correction (D3), as the mean absolute error is 0.9 and the root mean‐squared deviation is only 1.4 kcal/mol. © 2014 Wiley Periodicals, Inc.     

Ab initio ground- and excited-state intermolecular potential energy surfaces for the NO-Ne and NO-Ar van der Waals complexes

The ground- [NO(X(2)Π)] and excited-state [NO(A(2)Σ(+))] intermolecular potential energy surfaces (IPESs) of the NO-Ne and NO-Ar van der Waals complexes are evaluated using the RCCSD(T) spin-restricted coupled cluster method and d-aug-cc-pVQZ basis set extended with a set of 3s3p2d1f1g midbond functions. These bases are selected from the results of a systematic basis-set convergence study carried out for the NO(A(2)Σ(+))-Ar state. We fit the interaction energies to analytic functions and compare the results to those previously available. The NO-Ar (NO-Ne) IPESs are characterized by absolute minima of -120 and -75 cm(-1) (-58 and -5 cm(-1)) at the ground and first excited state, respectively, located close to the T-shaped geometries for the ground states and at linear dispositions in the case of the excited states. The potentials are further used in the evaluation of the rovibrational spectra of the complexes, and the results are compared to those available in the literature.     

卤素阴离子和取代苯间Anion-π作用强度的快速计算

A scheme that explicitly contains electrostatic, polarization, and dispersion interactions to rapidly simulate anion-π interactions is proposed and assessed by structural and energetic comparison with those produced via the complete basis set limit of the coupled-cluster singles and doubles plus perturbative triples [CCSD (T)/CBS] method for a set of X-…C₆H_6-nR_n complexes where X^-=F^-, Cl^-, Br^- and R=CN, F. We use the chemical bonds C≡N, C―F, and C―H of the substituted benzenes as bond dipoles. The electrostatic interactions are estimated by calculating the interactions between the charge of the anion and the bond dipole moments of the substituted benzene. The polarization interactions are described according to the variation of the magnitudes of the bond dipole moments with the local environment. The parameters needed are produced by fitting the high-quality CCSD (T)/CBS potential energy curves. Calculation results show that our scheme produces equilibrium intermolecular distances with a root-mean-square deviation of 0.004 nm and interaction energies with a root-mean-square deviation of 2.81 kJ·mol^-1 compared with the CCSD (T)/CBS results. The calculation results also show that our scheme reproduces the CCSD (T)/CBS potential energy curves well. These comparisons indicate the scheme proposed here is accurate and efficient, suggesting it may be a helpful tool to design and simulate relevant molecular materials.     

Theoretical spectroscopy of the N2HAr+ complex

The six-dimensional potential energy surface of the electronic ground state of N2HAr+ is determined by ab initio computations at the CCSD(T) level of theory. The potential energy surface is used to derive a set of spectroscopic data for N2HAr+ and N2DAr+ using second order perturbation theory. Full six-dimensional (6-D) rotation-vibration computations are also carried out using an analytical representation of the surface for J=0 and 1, in order to deduce the rovibrational spectra of N2HAr+ and its deuterated isotopomer. Our variationally determined anharmonic wavenumbers differ by less than 15 cm(-1) from the most accurate experimental values. Strong anharmonic resonances are found between the rovibrational levels of both cations even at low energies.     

A new ab initio intermolecular potential energy surface and predicted rotational spectra of the Ne-H2S complex

We report a new three-dimensional ab initio intermolecular potential energy surface for the Ne-H(2)S complex with H(2)S monomer fixed at its experimental average structure. Using the supermolecular approach, the intermolecular potential energies were evaluated at CCSD(T) (coupled cluster with single and double and perturbative triple excitations) level with large basis sets including bond functions. The full counterpoise procedure was employed to correct the basis set superposition error. The planar T-shaped global minimum is located at the intermolecular distance of 3.51 ? with a well depth of 71.57 cm(-1). An additional planar local minimum was found to be separated from the global minimum with an energy barrier of 23.11 cm(-1). In addition, two first-order and one second-order saddle points were also located. The combined radial discrete variable representation/angular finite basis representation method and the Lanczos algorithm were employed to evaluate the rovibrational energy levels for eight isotopic species of the Ne-H(2)S complexes. The rotational transition frequencies for the eight isotopomers were also determined for the ground and first vibrational excited states, which are all in very good agreement with the available experimental values.     

Ab initio potential energy surface and predicted microwave spectra for Ar--OCS dimer and structures of Arn--OCS (n = 2-14) clusters

An ab initio potential energy surface for the Ar--OCS dimer was calculated using the coupled-cluster singles and doubles with noniterative inclusion of connected triples [CCSD(T)] with a large basis set containing bond functions. The interaction energies were obtained by the supermolecular approach with the full counterpoise correction for the basis set superposition error. The CCSD(T) potential was found to have two minima corresponding to the T-shaped and the collinear Ar--SCO structures. The two-dimensional discrete variable representation method was employed to calculate the rovibrational energy levels for five isotopomers Ar--OCS, Ar--OC34S, Ar--O13CS, Ar--18OCS, and Ar--17OCS. The calculated pure rotational transition frequencies for the vibrational ground state of the five isotopomers are in good agreement with the observed values. The corresponding microwave spectra show that the b-type transitions (Delta Ka = +/-1) are significantly stronger than the a-type transitions (Delta Ka = 0). Minimum-energy structures of the Ar2--OCS trimer were been determined with MP2 optimization, whereas the minimum-energy structures of the Arn--OCS clusters with n = 3-14 were obtained with the pairwise additive potentials. It was found that there are two minima corresponding to one distorted tetrahedral structure and one planar structure for the ternary complex. The 14 nearest neighbor Ar atoms form the first solvation shell around the OCS molecule.