A universal state-selective approach to multireference coupled-cluster non-iterative corrections

A new form of the asymmetric energy functional for multireference coupled cluster (MRCC) theories is discussed from the point of view of an energy expansion in a quasidegenerate situation. The resulting expansion for the exact electronic energy can be used to define the non-iterative corrections to approximate MRCC approaches. In particular, we show that in the proposed framework the essential part of dynamic correlation can be encapsulated in the so-called correlation Hamiltonian, which in analogy to the effective Hamiltonian, is defined in the model space (M(0)). The proper parametrization of the exact/trial wavefunctions leads to the cancellation of the overlap-type numerators and to a connected form of the correlation Hamiltonian and size-extensive energies. Within this parametrization, when the trial wavefunctions are determined without invoking a specific form of the MRCC sufficiency conditions, the ensuing correction can be universally applied to any type of the approximate MRCC method. The analogies with other MRCC triples corrections to MRCC theories with singles and doubles (MRCCSD) are outlined. In particular, we discuss the approach, which in analogy to the Λ-Mk-MRCCSD(T) method [F. A. Evangelista, E. Prochnow, J. Gauss, H. F. Schaefer III, J. Chem. Phys. 132, 074107 (2010)], introduces an approximate form of the triply-excited clusters into the effective and correlation Hamiltonians. Since the discussed corrections can be calculated as a sum of independent reference-related contributions, possible parallel algorithms are also outlined.     

Calculation of electric dipole (hyper)polarizabilities by long-range-correction scheme in density functional theory: a systematic assessment for polydiacetylene and polybutatriene oligomers

The long-range correction (LC) for treating electron exchange in density functional theory, combined with the Becke-Lee-Yang-Parr (BLYP) exchange-correlation functional, was used to determine (hyper)polarizabilities of polydiacetylene/polybutatriene oligomers. In comparison with coupled-cluster calculations including single and double excitations as well as a perturbative treatment of triple excitations, our values indicate that the tendency of conventional functionals to result in a catastrophic overshoot for these properties is alleviated but not eliminated. No clear-cut preference for LC-BLYP over Hartree-Fock values is obtained. This analysis is consistent with the calculations of Sekino et al. [J. Chem. Phys. 126, 014107 (2007)] on polyacetylene and molecular hydrogen oligomers. Thus, the performance of LC-BLYP with regard to (hyper)polarizabilities of quasilinear conjugated systems is now well characterized.     

A global 12-dimensional ab initio potential energy surface and dynamical studies for the SiH4+H-->SiH3+H2 reaction

A global 12-dimensional ab initio interpolated potential energy surface (PES) for the SiH(4)+H-->SiH(3)+H(2) reaction is presented. The ab initio calculations are based on the unrestricted quadratic configuration interaction treatment with all single and double excitations together with the cc-pVTZ basis set, and the modified Shepard interpolation method of Collins and co-workers [K. C. Thompson et al., J. Chem. Phys. 108, 8302 (1998); M. A. Collins, Theor. Chem. Acc. 108, 313 (2002); R. P. A. Bettens and M. A. Collins, J. Chem. Phys. 111, 816 (1999)] is applied. Using this PES, classical trajectory and variational transition state theory calculations have been carried out, and the computed rate constants are in good agreement with the available experimental data.     

The open-shell interaction of He with the B 3Piu(0+) state of Br2: an ab initio study and its comparison with a diatomics-in-molecule perturbation model

The interaction of He with Br2 in electronically excited B 3Piu state is investigated using spin-unrestricted single and double coupled-cluster approach with noniterative perturbative treatment of triple excitations. Internal electrons of the Br atom are described by effective core pseudopotentials. The validity of this approach is analyzed by comparing the lowest 2Sigma+ and 2Pi electronic states of the HeBr molecule with those obtained in all electron calculations [J. Chem. Phys. 115, 10438 (2001)]. In this context, we examine the performance of different basis sets and saturation with bond functions. The comparison of theoretical blue-shifts with the experiment provides confidence about the present ab initio calculations. In addition, He-Br results of ab initio calculations at the same level are used to obtain approximate He-Br2 (3Piu) interactions in the framework of the diatomics-in-molecule first order perturbation theory (IDIM-PT1) [J. Chem. Phys. 104, 9913 (1996)]. Overall, the IDIM-PT1 model results show a good agreement with the ab initio ones, being the main difference the sensitivity to the elongation of the Br-Br bond.     

Spin-adapted open-shell time-dependent density functional theory. III. An even better and simpler formulation

The recently proposed spin-adapted time-dependent density functional theory (S-TD-DFT) [Z. Li and W. Liu, J. Chem. Phys. 133, 064106 (2010)] resolves the spin-contamination problem in describing singly excited states of high spin open-shell systems. It is an extension of the standard restricted open-shell Kohn-Sham-based TD-DFT which can only access those excited states due to singlet-coupled single excitations. It is also far superior over the unrestricted Kohn-Sham-based TD-DFT (U-TD-DFT) which suffers from severe spin contamination for those excited states due to triplet-coupled single excitations. Nonetheless, the accuracy of S-TD-DFT for high spin open-shell systems is still inferior to TD-DFT for well-behaved closed-shell systems. The reason can be traced back to the violation of the spin degeneracy conditions (SDC) by approximate exchange-correlation (XC) functionals. Noticing that spin-adapted random phase approximation (S-RPA) can indeed maintain the SDC by virtue of the Wigner-Eckart theorem, a hybrid ansatz combining the good of S-TD-DFT and S-RPA can immediately be envisaged. The resulting formalism, dubbed as X-TD-DFT, is free of spin contamination and can also be viewed as a S-RPA correction to the XC kernel of U-TD-DFT. Compared with S-TD-DFT, X-TD-DFT leads to much improved results for the low-lying excited states of, e.g., N(2)(+), yet with much reduced computational cost. Therefore, X-TD-DFT can be recommended for routine calculations of excited states of high spin open-shell systems.     

Quantum Monte Carlo calculations of the dissociation energy of the water dimer

We report diffusion quantum Monte Carlo (DMC) calculations of the equilibrium dissociation energy D(e) of the water dimer. The dissociation energy measured experimentally, D(0), can be estimated from D(e) by adding a correction for vibrational effects. Using the measured dissociation energy and the modern value of the vibrational energy Mas et al., [J. Chem. Phys. 113, 6687 (2000)] leads to D(e)=5.00+/-0.7 kcal mol(-1), although the result Curtiss et al., [J. Chem. Phys. 71, 2703 (1979)] D(e)=5.44+/-0.7 kcal mol(-1), which uses an earlier estimate of the vibrational energy, has been widely quoted. High-level coupled cluster calculations Klopper et al., [Phys. Chem. Chem. Phys. 2, 2227 (2000)] have yielded D(e)=5.02+/-0.05 kcal mol(-1). In an attempt to shed new light on this old problem, we have performed all-electron DMC calculations on the water monomer and dimer using Slater-Jastrow wave functions with both Hartree-Fock approximation (HF) and B3LYP density functional theory single-particle orbitals. We obtain equilibrium dissociation energies for the dimer of 5.02+/-0.18 kcal mol(-1) (HF orbitals) and 5.21+/-0.18 kcal mol(-1) (B3LYP orbitals), in good agreement with the coupled cluster results.     

Breakdown of the pseudopotential approximation for magnetizabilities and electric multipole moments. II. The importance of gauge invariance for large-core semi-local pseudopotentials

In a previous paper we pointed out that core contributions to the static magnetizability are non-negligible, and can therefore lead to erroneous results within the pseudopotential approximation [P. Schwerdtfeger, B. Assadollahzadeh, U. Rohrmann, R. Scha?fer, and J. R. Cheeseman, J. Chem. Phys. 134, 204102 (2011)]. In a recent paper van Wu?llen showed that additional terms arising from the gauge-invariant condition for the semi-local part of a pseudopotential operator can lead to non-negligible contributions to the magnetizability tensor, which are sensitive to the gauge origin and basis set chosen [C. van Wu?llen, J. Chem. Phys. 136, 114110 (2012)]. These terms were neglected in previous calculations as they were assumed to be small. In this paper we analyze the importance of the gauge-dependent semi-local pseudopotential correction term in detail for AuF and clusters of Sn showing that it leads indeed to very large corrections to the paramagnetic term for large-core pseudopotentials. Without this correction the results become very sensitive to the basis set applied. This now resolves some of the unusual large paramagnetic contributions reported before for both AuF and Sn(2).     

Assessment of a simple correction for the long-range charge-transfer problem in time-dependent density-functional theory

The failure of the time-dependent density-functional theory to describe long-range charge-transfer (CT) excitations correctly is a serious problem for calculations of electronic transitions in large systems, especially if they are composed of several weakly interacting units. The problem is particularly severe for molecules in solution, either modeled by periodic boundary calculations with large box sizes or by cluster calculations employing extended solvent shells. In the present study we describe the implementation and assessment of a simple physically motivated correction to the exchange-correlation kernel suggested in a previous study [O. Gritsenko and E. J. Baerends J. Chem. Phys. 121, 655 (2004)]. It introduces the required divergence in the kernel when the transition density goes to zero due to a large spatial distance between the "electron" (in the virtual orbital) and the "hole" (in the occupied orbital). A major benefit arises for solvated molecules, for which many CT excitations occur from solvent to solute or vice versa. In these cases, the correction of the exchange-correlation kernel can be used to automatically "clean up" the spectrum and significantly reduce the computational effort to determine low-lying transitions of the solute. This correction uses a phenomenological parameter, which is needed to identify a CT excitation in terms of the orbital density overlap of the occupied and virtual orbitals involved. Another quantity needed in this approach is the magnitude of the correction in the asymptotic limit. Although this can, in principle, be calculated rigorously for a given CT transition, we assess a simple approximation to it that can automatically be applied to a number of low-energy CT excitations without additional computational effort. We show that the method is robust and correctly shifts long-range CT excitations, while other excitations remain unaffected. We discuss problems arising from a strong delocalization of orbitals, which leads to a breakdown of the correction criterion.     

A nine-dimensional calculation of the vibrational OH stretching and HOH bending spectrum of the water trimer

We have studied the vibrational high-frequency spectrum of the water trimer computationally. We expand an earlier study [J. Chem. Phys. A 2009, 113, 9124-9132] where we approximated the water trimer as three individually vibrating water monomer units. Some intramolecular potential energy coupling terms are now included in the previous model. The six OH bond lengths and the three HOH bending angles are used as the internal coordinates. The kinetic energy operator is a sum of the kinetic energy operators of the monomer units. We use the coupled cluster method with single, double, and perturbative triple excitations method [CCSD(T)] with augmented correlation consistent polarized valence triple-ζ (aug-cc-pVTZ) basis set to calculate the potential energy surface (PES). The counterpoise correction is included in the one-dimensional part of the PES. We calculate the vibrational energy eigenvalues using the variational method. The corresponding eigenfunctions are used to obtain the absorption intensities.     

Interactions between anionic and neutral bromine and rare gas atoms

High-quality, ab initio potential energy functions are obtained for the interaction of bromine atoms and anions with atoms of the six rare gases (Rg) from He to Rn. The potentials of the nonrelativistic (2)Sigma(+) and (2)Pi electronic states arising from the ground-state Br((2)P)-Rg interactions are computed over a wide range of internuclear separations using a spin-restricted version of the coupled cluster method with single and double excitations and noniterative correction to triple excitations [RCCSD(T)] with an extrapolation to the complete basis set limit, from basis sets of d-aug-cc-pVQZ and d-aug-cc-pV5Z quality. These are compared with potentials derived previously from experimental measurements and ab initio calculations. The same approach is used also to refine the potentials of the Br(-)-Rg anions obtained previously [Buchachenko et al., J. Chem. Phys. 125, 064305 (2006)]. Spin-orbit coupling in the neutral species is included both ab initio and via an atomic approximation; deviations between two approaches that are large enough to affect the results significantly are observed only in the Br-Xe and Br-Rn systems. The resulting relativistic potentials are used to compute anion zero electron kinetic energy photoelectron spectra, differential scattering cross sections, and the transport coefficients of trace amounts of both anionic and neutral bromine in the rare gases. Comparison with available experimental data for all systems considered proves a very high precision of the present potentials.     

Higher excitations for an exponential multireference wavefunction Ansatz and single-reference based multireference coupled cluster Ansatz: application to model systems H(4), P(4), and BeH(2)

This article reports on the convergence of the exponential multireference wavefunction Ansatz (MRexpT) [J. Chem. Phys. 123, 84102 (2005)] and the single-reference based multireference coupled cluster Ansatz [J. Chem. Phys. 94, 1229 (1991)] with respect to higher cluster excitations. The approaches are applied to the H(4), P(4), and BeH(2) model systems according to the recently published analysis by Evangelista et al. [J. Chem. Phys. 125, 154113 (2006)]. The results show both MRexpT and SRMRCC to be highly accurate although SRMRCC shows problems due to its lack of Fermi vacuum invariance (symmetry breaking).     

Accelerating the convergence of the total energy evaluation in density functional theory calculations

A special feature of the Strutinsky shell correction method (SCM) [D. Ullmo et al., Phys. Rev. B 63, 125339 (2001)] and the recently proposed orbital-corrected orbital-free density functional theory (OO-DFT) [B. Zhou and Y. A. Wang, J. Chem. Phys. 124, 081107 (2006)] is that the second-order corrections are incorporated in the total energy evaluation. In the SCM, the series expansion of the total electronic energy is essentially the Harris functional with its second-order correction. Unfortunately, a serious technical problem for the SCM is the lack of the exact Kohn-Sham (KS) density rho KS(r) required for the evaluation of the second-order correction. To overcome this obstacle, we design a scheme that utilizes the optimal density from a high-quality density mixing scheme to approximate rho KS(r). Recently, we proposed two total energy density functionals, i.e., the Zhou-Wang-lambda (ZW lambda) and the Wang-Zhou-alpha (WZ alpha) functionals, for use in the OO-DFT method. If the two interpolation parameters, lambda and alpha, are chosen to allow the second-order errors of the ZW lambda and the WZ alpha functionals to vanish, these two functionals reduce to the Hohenberg-Kohn-Sham functional with its second-order correction. Again, the optimal density from a high-quality density mixing scheme is used to approximate rho KS(r) in the evaluation of lambda and alpha. This approach is tested in iterative KS-DFT calculations on systems with different chemical environments and can also be generalized for use in other iterative first-principles quantum chemistry methods.     

Excitation energies for a benchmark set of molecules obtained within time-dependent current-density functional theory using the Vignale-Kohn functional

In this article we explain how the existing linear response theory of time-dependent density-functional theory can be extended to obtain excitation energies in the framework of time-dependent current-density-functional theory. We use the Vignale-Kohn current-functional [G. Vignale and W. Kohn, Phys. Rev. Lett. 77, 2037 (1996)] which has proven to be successful for describing ultranonlocal exchange-correlation effects in the case of the axial polarizability of molecular chains [M. van Faassen, P. L. de Boeij, R. van Leeuwen, J. A. Berger, and J. G. Snijders, Phys. Rev. Lett. 88, 186401 (2002); J. Chem. Phys. 118, 1044 (2003)]. We study a variety of singlet excitations for a benchmark set of molecules. The pi(*)<--pi transitions obtained with the Vignale-Kohn functional are in good agreement with experiment and other theoretical results and they are in general an improvement upon the adiabatic local density approximation. In case of the pi(*)<--n transitions the Vignale-Kohn functional fails, giving results that strongly overestimate the experimental and other theoretical results. The benchmark set also contains some other types of excitations for which no clear failures or improvements are observed.     

Revisiting the Frenkel-Ladd method to compute the free energy of solids: the Einstein molecule approach

In this paper a new method to evaluate the free energy of solids is proposed. The method can be regarded as a variant of the method proposed by Frenkel and Ladd [J. Chem. Phys. 81, 3188 (1984)]. The main equations of the method can be derived in a simple way. The method can be easily implemented within a Monte Carlo program. We have applied the method to determine the free energy of hard spheres in the solid phase for several system sizes. The obtained free energies agree within the numerical uncertainty with those obtained by Polson et al. [J. Chem. Phys. 112, 5339 (2000)]. The fluid-solid equilibria has been determined for several system sizes and compared to the values published previously by Wilding and Bruce [Phys. Rev. Lett. 85, 5138 (2000)] using the phase switch methodology. It is shown that both the free energies and the coexistence pressures present a strong size dependence and that the results obtained from free energy calculations agree with those obtained using the phase switch method, which constitutes a cross-check of both methodologies. From the results of this work we estimate the coexistence pressure of the fluid-solid transition of hard spheres in the thermodynamic limit to be p*=11.54(4), which is slightly lower than the classical value of Hoover and Ree (p*=11.70) [J. Chem. Phys. 49, 3609 (1968)]. Taking into account the strong size dependence of the free energy of the solid phase, we propose to introduce finite size corrections, which allow us to estimate approximately the free energy of the solid phase in the thermodynamic limit from the known value of the free energy of the solid phase with N molecules. We have also determined the free energy of a Lennard-Jones solid by using both the methodology of this work and the finite size correction. It is shown how a relatively good estimate of the free energy of the system in the thermodynamic limit is obtained even from the free energy of a relatively small system.     

Development and applications of a unitary group adapted state specific multi-reference coupled cluster theory with internally contracted treatment of inactive double excitations

Any multi-reference coupled cluster (MRCC) development based on the Jeziorski-Monkhorst (JM) multi-exponential ansatz for the wave-operator Ω suffers from spin-contamination problem for non-singlet states. We have very recently proposed a spin-free unitary group adapted (UGA) analogue of the JM ansatz, where the cluster operators are defined in terms of spin-free unitary generators and a normal ordered, rather than ordinary, exponential parametrization of Ω is used. A consequence of the latter choice is the emergence of the "direct?term" of the MRCC equations that terminates at exactly the quartic power of the cluster amplitudes. Our UGA-MRCC ansatz has been utilized to generate both the spin-free state specific (SS) and the state universal MRCC formalisms. It is well-known that the SSMRCC theory requires suitable sufficiency conditions to resolve the redundancy of the cluster amplitudes. In this paper, we propose an alternative variant of the UGA-SSMRCC theory, where the sufficiency conditions are used for all cluster operators containing active orbitals and the single excitations with inactive orbitals, while the inactive double excitations are assumed to be independent of the model functions they act upon. The working equations for the inactive double excitations are thus derived in an internally contracted (IC) manner in the sense that the matrix elements entering the MRCC equations involve excitations from an entire combination of the model functions. We call this theory as UGA-ICID-MRCC, where ICID is the acronym for "Internally Contracted treatment of Inactive Double excitations." Since the number of such excitations are the most numerous, choosing them to be independent of the model functions will lead to very significant reduction in the number of cluster amplitudes for large active spaces, and is worth exploring. Moreover, unlike for the excitations involving active orbitals, where there is inadequate coupling between the model and the virtual functions in the SSMRCC equations generated from sufficiency conditions, our internally contracted treatment of inactive double excitations involves much more complete couplings. Numerical implementation of our formalism amply demonstrates the efficacy of the formalism.     

Explicitly correlated coupled-cluster theory using cusp conditions. II. Treatment of connected triple excitations

The coupled-cluster singles and doubles method augmented with single Slater-type correlation factors (CCSD-F12) determined by the cusp conditions (also denoted as SP ansatz) yields results close to the basis set limit with only small overhead compared to conventional CCSD. Quantitative calculations on many-electron systems, however, require to include the effect of connected triple excitations at least. In this contribution, the recently proposed [A. Ko?hn, J. Chem. Phys. 130, 131101 (2009)] extended SP ansatz and its application to the noniterative triples correction CCSD(T) is reviewed. The approach allows to include explicit correlation into connected triple excitations without introducing additional unknown parameters. The explicit expressions are presented and analyzed, and possible simplifications to arrive at a computationally efficient scheme are suggested. Numerical tests based on an implementation obtained by an automated approach are presented. Using a partial wave expansion for the neon atom, we can show that the proposed ansatz indeed leads to the expected (L(max)+1)(-7) convergence of the noniterative triples correction, where L(max) is the maximum angular momentum in the orbital expansion. Further results are reported for a test set of 29 molecules, employing Peterson's F12-optimized basis sets. We find that the customary approach of using the conventional noniterative triples correction on top of a CCSD-F12 calculation leads to significant basis set errors. This, however, is not always directly visible for total CCSD(T) energies due to fortuitous error compensation. The new approach offers a thoroughly explicitly correlated CCSD(T)-F12 method with improved basis set convergence of the triples contributions to both total and relative energies.     

Exploring the new three-dimensional ab initio interaction energy surface of the Ar-HF complex: rovibrational calculations for Ar-HF and Ar-DF with vibrationally excited diatoms

Several features and the performance of the recently published [P. Jankowski and M. Ziolkowski, Mol. Phys. 104, 2293 (2006)] three-dimensional intermolecular potential energy surface for the Ar-HF complex have been investigated. This full-dimensional surface has been obtained using the method of the local expansion of the exact interaction energy surface [P. Jankowski, J. Chem. Phys. 121, 1655 (2004)] in the Taylor series with respect to intramolecular coordinates. The interaction energies have been calculated with the coupled-cluster supermolecular method with single, double, and noniterative triple excitations. The convergence of the interaction energy with respect to the size of the basis set is discussed. The two-dimensional surfaces resulting from averaging of the full-dimensional surface over the intramolecular vibration of HF have been obtained and directly compared to the empirical H6(4,3,2) set of surfaces proposed by Hutson [J. Chem. Phys. 96, 6752 (1992)]. A very good agreement has been observed. The averaged potentials have been used to calculate the rovibrational energy levels of the Ar-HF and Ar-DF complexes and compared to the experimental data. The accuracy of rovibrational calculations achieved with the new surface is much better than with any of the ab initio surfaces available so far. Predictions of the rovibrational energy levels and spectroscopic constants have also been done for Ar-HF with HF in the v=4,5 vibrational states, and for Ar-DF and DF in the v=3,4 states. The full-dimensional surface studied in this paper is the first ab initio surface which is fully compatible with the empirical H6(4,3,2) surface proposed by Hutson.     

Counterdiabatic suppression of background state population in resonance leaking by controlling intermediate branching

The counterdiabatic principle [M. Demirplak and S. A. Rice, J. Phys. Chem. A 107, 9937 (2003)] is used in a pragmatic way to formulate a practical control strategy for perturbed population transfer. Interpreting the appearance of population in undesirable intruder or background states as phenomenological consequences of diabatic perturbations, such branching is suppressed as soon as it arises. By invoking a penalty term that is sensitive to any transitional population in undesirable levels, a correction field is created which effectively prevents diabatic behavior. This strategy is applied to the control of background state population in multiphoton excitations. For a model five-level system we show that leaking of a resonant three-photon transition to a background state can readily be suppressed by simple correction fields obtained from our intermediate-branching driven implementation of counterdiabatic control.     

High-level ab initio potential energy surfaces and vibrational energies of H2CS

Six-dimensional (6D) potential energy surfaces (PESs) of H(2)CS have been generated ab initio using the recently proposed explicitly correlated (F12) singles and doubles coupled cluster method including a perturbational estimate of connected triple excitations, CCSD(T)-F12b [T. B. Adler, G. Knizia, and H.-J. Werner, J. Chem. Phys. 127, 221106 (2007)] in conjunction with F12-optimized correlation consistent basis sets. Core-electron correlation, high-order correlation, scalar relativistic, and diagonal Born-Oppenheimer terms were included as additive high-level (HL) corrections. The resulting 6D PESs were represented by analytical functions which were used in variational calculations of the vibrational term values below 5000 cm(-1). The best PESs obtained with and without the HL corrections, VQZ-F12(*HL) and VQZ-F12?, reproduce the fundamental vibrational wavenumbers with mean absolute deviations of 1.13 and 1.22 cm(-1), respectively. A detailed analysis of the effects of the HL corrections shows how the VQZ-F12 results benefit from error cancellation. The present purely ab initio PESs will be useful as starting points for empirical refinements towards an accurate "spectroscopic" PES of H(2)CS.     

Low-energy rotational inelastic collisions of H(+) + CO system

The quantum mechanical state-to-state rotational excitation cross sections have been computed using the ab initio ground electronic state potential energy surface of the system [M. Mladenovic and S. Schmatz, J. Chem. Phys. 109, 4456 (1998)] computed at coupled-cluster single and double and triple perturbative excitations method using correlation-consistent polarized valence quadruple zeta basis set where the asymptotic potential have been computed using the dipole moment, quadrupole moment, and the molecular polarizability components and fitted to this interaction potential. The anisotropy of the surface has been analyzed in terms of the multipolar expansion coefficients for the rigid-rotor surface. The integral cross sections for rotational excitations have been computed by solving close-coupled equations at very low collision energies (5-200 cm(-1)) and the corresponding rates have been obtained for a range of low temperatures (5-175 K). The j = 0 → j(') = 1 rotational excitation cross section (and rate) is found to be the dominant followed by the j = 0 → j(') = 2 in these collision energies. The close-coupling, coupled-state, and infinite-order sudden approximations coupling calculations have been performed in the energy range of 0.1-1.0 eV using vibrational ground potential. The rotational cross sections have been obtained by performing computationally accurate close-coupling calculations at 0.1 eV using vibrationally averaged potential (ν = 1) and compared with the results of vibrational ground potential.