Basis Set Convergence Research Articles

Basis set convergence of the binding energies of strongly hydrogen-bonded atmospheric clusters.

We investigate the basis set convergence of second order Møller Plesset perturbation theory for the binding energies of 11 strongly hydrogen-bonded clusters relevant to the atmosphere. The binding energies are calculated both as the uncorrected (UC) value, as well as by employing the counterpoise (CP) and the Same Number Of Optimized Parameters (SNOOP) correction schemes, with and without explicit correlation (F12). We find that the use of the F12 corrections is of utter importance for obtaining converged binding energies. Without F12 corrections at least a quadruple-ζ basis set is generally required to yield errors below 1 kcal mol-1 compared to the complete basis set (CBS) limit. Using coupled cluster methods we obtain a best estimate of the CCSD(T) CBS limit of the binding energies of the considered clusters and compare it with approximate DLPNO-CCSD(T) and DFT methods. We identify a pragmatic approach, relying solely on a series of double-ζ basis set calculations, for obtaining results in remarkably good agreement with our CBS estimate.

Gauge-origin independent calculations of electric-field-induced second-harmonic generation circular intensity difference using London atomic orbitals

ABSTRACTWe present the first gauge-origin independent calculations of the circular intensity difference (CID) in electric-field-induced second-harmonic generation (EFISHG), including all contributions up to the electric-quadrupole–magnetic-dipole level. A recursive, open-ended response theory framework in combination with the use of London atomic orbitals allows us to ensure gauge-origin independent results. We apply this approach to study EFISHG-CID in a collection of chiral amino acids. We demonstrate that diffuse polarising basis functions are critical in order to obtain accurate CIDs, and that a basis set of at least aug-cc-pVTZ quality is needed in order to obtain results close to the basis-set limit. The use of London orbitals does not lead to significantly faster basis set convergence, although the improved basis set convergence allows the aug-cc-pVDZ basis set to be used with some confidence for larger molecules.

Thermochemistry and Geometries for Transition-Metal Chemistry from the Random Phase Approximation.

Performance of the random phase approximation (RPA) is tested for thermochemistry and geometries of transition-metal chemistry using various benchmarks obtained either computationally or experimentally. Comparison is made to popular (semi)local meta- and hybrid density functionals as well as to the second-order Møller-Plesset perturbation theory (MP2) and its spin-component-scaled derivatives. The benchmark sets include reaction energies, barrier heights, and dissociation energies of prototype bond-activation reactions, dissociation energies for a set of large transition-metal complexes, bond lengths and dissociation energies of metal hydride ions, and bond lengths and angles of a set of closed-shell first-row transition-metal complexes. The emphasis is on first-row transition-metal chemistry, though for energies, elements beyond the first-row are included. Attention is paid to the basis set convergence of RPA. For thermochemistry, RPA performs on par or better than the density functional theory (DFT) functionals presented and is significantly more accurate than MP2. The largest errors are observed in dissociation energies where the electronic environment is altered substantially. For structural parameters, very good results were obtained, and RPA meets the high quality of structures from DFT. In most cases, well-converged structures are obtained with basis sets of triple-zeta quality. MP2 optimized values can often not be obtained and are on average of inferior quality. Though chemical accuracy is not reached, the RPA method is a step forward toward a systematic, parameter-free, all-round method to describe transition-metal chemistry.

Density functional theory basis set convergence of sulfuric acid-containing molecular clusters

We investigate the basis set convergence of three density functionals (M06-2X, PW91, and ωB97X-D) with respect to the binding energy, thermal contribution to the Gibbs free energy, and optimized geometry. We apply correlation consistent, Pople-type, and polarization consistent basis sets with different amount of diffuse and polarization functions. Our test set contains six molecular cluster formation reactions which represent key noncovalent interactions in the atmosphere. In most cases partially augmented basis sets yield as accurate results as the fully augmented basis sets, with significant gain in computational efficiency. Relatively small basis sets are found to be sufficient to optimize geometries and to calculate thermal contributions to the Gibbs free energy. For binding energies, slightly bigger basis sets are needed to reach the complete basis set limit. The PW91 functional with the 6-311++G(3df,3pd) basis set gives a mean absolute error of 0.9kcal/mol in the binding energy, indicating that it has not reached the complete basis set limit. We estimate the effect of anharmonicity and derive scale factors to correct for it. When the lowest vibrational frequencies are treated separately, the errors arising from the anharmonicity of the remaining frequencies are small regardless of system size. We treated the low frequencies as free rotors and calculate thermal contributions to the Gibbs free energy using the quasi-harmonic approximation. We identify an error of a few percent of the total harmonic thermal contributions, which is larger than the error arising from vibrational anharmonicity.

Cold NH–NH collisions in a magnetic field: Basis set convergence versus sensitivity to the interaction potential

We explore the combined effect of the uncertainties due to the interaction potential and basis set convergence on low-temperature collisional properties of spin-polarized NH molecules in a magnetic field. We show that quantum scattering calculations with different rotational basis sets and λ-scaled interaction potentials produce qualitatively different ratios of elastic to inelastic cross sections for collision energies above 10−3 cm−1, leading to favorable (unfavorable) prospects for sympathetic cooling of NH molecules depending on the basis set cutoff parameter . The physical reason behind this effect is that the resonance widths, which determine the maximum variation of the scattering cross sections with λ, tend to depend strongly on . At ultralow collision energies, all basis sets produce highly uncertain (and statistically indistinguishable) elastic and inelastic cross sections; however, their ratio γ is much less sensitive to small variations of the interaction potential. Our results highlight the importance of basis set convergence in quantum scattering calculations and establish the existence of parameter regimes where unconverged calculations can still be used to make qualitatively accurate predictions of scattering observables.

Basis set convergence of CCSD(T) equilibrium geometries using a large and diverse set of molecular structures.

We examine the basis set convergence of the CCSD(T) method for obtaining the structures of the 108 neutral first- and second-row species in the W4-11 database (with up to five non-hydrogen atoms). This set includes a total of 181 unique bonds: 75 H-X, 49 X-Y, 43 X=Y, and 14 X≡Y bonds (where X and Y are first- and second-row atoms). As reference values, geometries optimized at the CCSD(T)/aug'-cc-pV(6+d)Z level of theory are used. We consider the basis set convergence of the CCSD(T) method with the correlation consistent basis sets cc-pV(n+d)Z and aug'-cc-pV(n+d)Z (n = D, T, Q, 5) and the Weigend-Ahlrichs def2-n ZVPP basis sets (n = T, Q). For each increase in the highest angular momentum present in the basis set, the root-mean-square deviation (RMSD) over the bond distances is decreased by a factor of ∼4. For example, the following RMSDs are obtained for the cc-pV(n+d)Z basis sets 0.0196 (D), 0.0050 (T), 0.0015 (Q), and 0.0004 (5) Å. Similar results are obtained for the aug'-cc-pV(n+d)Z and def2-n ZVPP basis sets. The double-zeta and triple-zeta quality basis sets systematically and significantly overestimate the bond distances. A simple and cost-effective way to improve the performance of these basis sets is to scale the bond distances by an empirical scaling factor of 0.9865 (cc-pV(D+d)Z) and 0.9969 (cc-pV(T+d)Z). This results in RMSDs of 0.0080 (scaled cc-pV(D+d)Z) and 0.0029 (scaled cc-pV(T+d)Z) Å. The basis set convergence of larger basis sets can be accelerated via standard basis-set extrapolations. In addition, the basis set convergence of explicitly correlated CCSD(T)-F12 calculations is investigated in conjunction with the cc-pVnZ-F12 basis sets (n = D, T). Typically, one "gains" two angular momenta in the explicitly correlated calculations. That is, the CCSD(T)-F12/cc-pVnZ-F12 level of theory shows similar performance to the CCSD(T)/cc-pV(n+2)Z level of theory. In particular, the following RMSDs are obtained for the cc-pVnZ-F12 basis sets 0.0019 (D) and 0.0006 (T) Å. Overall, the CCSD(T)-F12/cc-pVDZ-F12 level of theory offers a stellar price-performance ratio and we recommend using it when highly accurate reference geometries are needed (e.g., in composite ab initio theories such as W4 and HEAT).

On the convergence of zero-point vibrational corrections to nuclear shieldings and shielding anisotropies towards the complete basis set limit in water

ABSTRACTThe method and basis set dependence of zero-point vibrational corrections (ZPVCs) to nuclear magnetic resonance shielding constants and anisotropies has been investigated using water as a test system. A systematic comparison has been made using the Hartree–Fock, second-order Møller–Plesset perturbation theory (MP2), coupled cluster singles and doubles (CCSD), coupled cluster singles and doubles with perturbative triples corrections (CCSD(T)) and Kohn–Sham density functional theory with the B3LYP exchange-correlation functional methods in combination with the second-order vibrational perturbation theory (VPT2) approach for the vibrational corrections. As basis sets, the correlation consistent basis sets cc-pVXZ, aug-cc-pVXZ, cc-pCVXZ and aug-cc-pCVXZ with X = D, T, Q, 5, 6 and the polarisation consistent basis sets aug-pc-n and aug-pcS-n with n = 1, 2, 3, 4 were employed. Our results show that basis set convergence of the vibrational corrections is not monotonic and that very large basis sets are needed before a reasonable extrapolation to the basis set limit can be performed. Furthermore, our results suggest that coupled cluster methods and a decent basis set are required before the error of the electronic structure approach is lower than the inherent error of the VPT2 approximation.

Toward a W4-F12 approach: Can explicitly correlated and orbital-based ab initio CCSD(T) limits be reconciled?

In the context of high-accuracy computational thermochemistry, the valence coupled cluster with all singles and doubles (CCSD) correlation component of molecular atomization energies presents the most severe basis set convergence problem, followed by the (T) component. In the present paper, we make a detailed comparison, for an expanded version of the W4-11 thermochemistry benchmark, between, on the one hand, orbital-based CCSD/AV{5,6}Z + d and CCSD/ACV{5,6}Z extrapolation, and on the other hand CCSD-F12b calculations with cc-pVQZ-F12 and cc-pV5Z-F12 basis sets. This latter basis set, now available for H-He, B-Ne, and Al-Ar, is shown to be very close to the basis set limit. Apparent differences (which can reach 0.35 kcal/mol for systems like CCl4) between orbital-based and CCSD-F12b basis set limits disappear if basis sets with additional radial flexibility, such as ACV{5,6}Z, are used for the orbital calculation. Counterpoise calculations reveal that, while total atomization energies with V5Z-F12 basis sets are nearly free of BSSE, orbital calculations have significant BSSE even with AV(6 + d)Z basis sets, leading to non-negligible differences between raw and counterpoise-corrected extrapolated limits. This latter problem is greatly reduced by switching to ACV{5,6}Z core-valence basis sets, or simply adding an additional zeta to just the valence orbitals. Previous reports that all-electron approaches like HEAT (high-accuracy extrapolated ab-initio thermochemistry) lead to different CCSD(T) limits than "valence limit + CV correction" approaches like Feller-Peterson-Dixon and Weizmann-4 (W4) theory can be rationalized in terms of the greater radial flexibility of core-valence basis sets. For (T) corrections, conventional CCSD(T)/AV{Q,5}Z + d calculations are found to be superior to scaled or extrapolated CCSD(T)-F12b calculations of similar cost. For a W4-F12 protocol, we recommend obtaining the Hartree-Fock and valence CCSD components from CCSD-F12b/cc-pV{Q,5}Z-F12 calculations, but the (T) component from conventional CCSD(T)/aug'-cc-pV{Q,5}Z + d calculations using Schwenke's extrapolation; post-CCSD(T), core-valence, and relativistic corrections are to be obtained as in the original W4 theory. W4-F12 is found to agree slightly better than W4 with ATcT (active thermochemical tables) data, at a substantial saving in computation time and especially I/O overhead. A W4-F12 calculation on benzene is presented as a proof of concept.

Optical Rotation from Coupled Cluster and Density Functional Theory: The Role of Basis Set Convergence.

We have calculated the electronic optical rotation of seven molecules using coupled cluster singles-doubles (CCSD) and the second-order approximation (CC2) employing the aug-cc-pVXZ (X = D, T, or Q) basis sets. We have also compared to time-dependent density functional theory (TDDFT) by utilizing two functionals B3LYP and CAM-B3LYP and the same basis sets. Using relative and absolute error schemes, our calculations demonstrate that the CAM-B3LYP functional predicts optical rotation with the minimum deviations compared to CCSD at λ = 355 and 589.3 nm. Furthermore, our results illustrate that the aug-cc-pVDZ basis set provides the optical rotation in good agreement with the larger basis sets for molecules not possessing small-angle optical rotation at λ = 589.3 nm. We have also performed several two-point inverse power extrapolations for the basis set convergence, i.e., OR(∞) + AX(-n), using the CC2 model at λ = 355 and 589.3 nm. Our results reveal that a two-point inverse power extrapolation with the aug-cc-pVTZ and aug-cc-pVQZ basis sets at n = 5 provides optical rotation deviations similar to those of aug-cc-pV5Z with respect to the basis limit.

Finite-field calculation of static polarizabilities and hyperpolarizabilities ofIn+and Sr

The dipole polarizabilities, dipole hyperpolarizabilities, quadrupole moments, and quadrupole polarizabilities of the $5{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S$ and $5s5p\phantom{\rule{0.16em}{0ex}}{}^{3}{P}^{o}$ states of ${\mathrm{In}}^{+}$ and Sr are calculated by using the finite-field method. The electron correlation effect and the basis set convergence are investigated in the relativistic coupled-cluster and configuration interaction calculations in order to obtain polarizabilities of high accuracy. Comparative study of the fully and scalar relativistic calculations reveals the effect of the spin-orbit coupling on the dipole polarizabilities of ${\mathrm{In}}^{+}$ and Sr. The blackbody-radiation shifts of the clock transition $5{s}^{2}\phantom{\rule{0.16em}{0ex}}{}^{1}{S}_{0}\ensuremath{-}5s5fp\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{0}^{o}$ due to the dipole polarizabilities, quadrupole polarizabilities, and dipole hyperpolarizabilities are evaluated to be 0.017, $8.33\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$, and $1.93\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$ Hz for ${\mathrm{In}}^{+}$ and 2.09 and $5.82\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}$, and $1.69\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}$ Hz for Sr. The blackbody-radiation shifts from the quadrupole polarizabilities and dipole hyperpolarizabilities are significantly less than that from the dipole polarizabilities and therefore can be safely omitted for the quoted ${10}^{\ensuremath{-}18}$ uncertainty of the optical frequency standard of ${\mathrm{In}}^{+}$ and Sr.

Polarization contributions to intermolecular interactions revisited with fragment electric-field response functions.

The polarization energy in intermolecular interactions treated by self-consistent field electronic structure theory is often evaluated using a constraint that the atomic orbital (AO) to molecular orbital transformation is blocked by fragments. This approach is tied to AO basis sets, overestimates polarization energies in the overlapping regime, particularly in large AO basis sets, and lacks a useful complete basis set limit. These problems are addressed by the construction of polarization subspaces based on the responses of isolated fragments to weak electric fields. These subspaces are spanned by fragment electric-field response functions, which can capture effects up to the dipole (D), or quadrupole (DQ) level, or beyond. Schemes are presented for the creation of both non-orthogonal and orthogonal fragment subspaces, and the basis set convergence of the polarization energies computed using these spaces is assessed. Numerical calculations for the water dimer, water-Na(+), water-Mg(2+), water-F(-), and water-Cl(-) show that the non-orthogonal DQ model is very satisfactory, with small differences relative to the orthogonalized model. Additionally, we prove a fundamental difference between the polarization degrees of freedom in the fragment-blocked approaches and in constrained density schemes. Only the former are capable of properly prohibiting charge delocalization during polarization.

Open-ended recursive calculation of single residues of response functions for perturbation-dependent basis sets.

We present theory, implementation, and applications of a recursive scheme for the calculation of single residues of response functions that can treat perturbations that affect the basis set. This scheme enables the calculation of nonlinear light absorption properties to arbitrary order for other perturbations than an electric field. We apply this scheme for the first treatment of two-photon circular dichroism (TPCD) using London orbitals at the Hartree-Fock level of theory. In general, TPCD calculations suffer from the problem of origin dependence, which has so far been solved by using the velocity gauge for the electric dipole operator. This work now enables comparison of results from London orbital and velocity gauge based TPCD calculations. We find that the results from the two approaches both exhibit strong basis set dependence but that they are very similar with respect to their basis set convergence.

Benchmark calculations on the nuclear quadrupole-coupling parameters for open-shell molecules using non-relativistic and scalar-relativistic coupled-cluster methods.

Quantum-chemical computations of nuclear quadrupole-coupling parameters for 24 open-shell states of small molecules based on non-relativistic and spin-free exact two-component (SFX2C) relativistic equation-of-motion coupled-cluster (EOM-CC) as well as spin-orbital-based restricted open-shell Hartree-Fock coupled-cluster (ROHF-CC) methods are reported. Relativistic effects, the performance of the EOM-CC and ROHF-CC methods for treating electron correlation, as well as basis-set convergence have been carefully analyzed. Consideration of relativistic effects is necessary for accurate calculations on systems containing third-row (K-Kr) and heavier elements, as expected, and the SFX2C approach is shown to be a useful cost-effective option here. Further, it is demonstrated that the EOM-CC methods constitute flexible and accurate alternatives to the ROHF-CC methods in the calculations of nuclear quadrupole-coupling parameters for open-shell states.

Accurate Complete Basis Set Extrapolation of Direct Random Phase Correlation Energies.

The direct random phase approximation (dRPA) is a promising way to obtain improvements upon the standard semilocal density functional results in many aspects of computational chemistry. In this paper, we address the slow convergence of the calculated dRPA correlation energy with the increase of the quality and size of the popular Gaussian-type Dunning's correlation consistent aug-cc-pVXZ split valence atomic basis set family. The cardinal number X controls the size of the basis set, and we use X = 3-6 in this study. It is known that even the very expensive X = 6 basis sets lead to large errors for the dRPA correlation energy, and thus complete basis set extrapolation is necessary. We study the basis set convergence of the dRPA correlation energies on a set of 65 hydrocarbon isomers from CH4 to C6H6. We calculate the iterative density fitted dRPA correlation energies using an efficient algorithm based on the CC-like form of the equations using the self-consistent HF orbitals. We test the popular inverse cubic, the optimized exponential, and inverse power formulas for complete basis set extrapolation. We have found that the optimized inverse power based extrapolation delivers the best energies. Further analysis showed that the optimal exponent depends on the molecular structure, and the most efficient two-point energy extrapolations that use X = 3 and 4 can be improved considerably by considering the atomic composition and hybridization states of the atoms in the molecules. Our results also show that the optimized exponents that yield accurate X = 3 and 4 extrapolated dRPA energies for atoms or small molecules might be inaccurate for larger molecules.

Convergence of normal mode variational calculations of methane spectra: Theoretical linelist in the icosad range computed from potential energy and dipole moment surfaces

Accurate basis set convergence of first-principles predictions of rotationally resolved spectra at high energy range is a common challenging issue for variational methods. In this paper, a detailed convergence study for the methane spectra is presented both for vibrational and rotational degrees of freedom as well as for intensities. For this purpose, we use our previously reported nine-dimensional potential energy and dipole moment surfaces of the methane molecule [Nikitin et al. Chem Phys Lett 2011;501:179–86; 2013;565:5–11]. Vibration–rotation calculations were carried out using variational normal mode approach with a full account of the Td symmetry. The aim was to obtain accurate theoretical methane line lists for the wavenumber range beyond currently available spectra analyses. The focus of this paper is the complicated icosad range (6280–7900cm−1) containing 20 bands and 134 sub-bands where over 90% of experimental lines still remain unassigned. We provide variational line lists converged to a “spectroscopic precision” for icosad transitions for T=80K and T=296K. The first one contains 70300 lines and the second one 286170 lines with the intensity cut-off 10−29cm−1/(moleculecm−2) with Jmax=18. An average error in line positions of theoretical predictions up to J=15 is estimated as 0.2–0.5cm−1 from the comparisons with currently analyzed bands. Ab initio line strength calculations give the integrated intensity 4.37×10−20cm−1/(moleculecm−2) at T=80K for the sum of all icosad bands. This is to be compared to the integrated intensity 4.36×10−20cm−1/(moleculecm−2) of the experimental icosad line list recorded in Grenoble University [Campargue et al., J Mol Spectrosc 2013;291:16–22] using very sensitive laser techniques. The shapes of absorption bands are also in a good qualitative agreement with experimental spectra.

Relativistic coupled-cluster calculations on XeF6: Delicate interplay between electron-correlation and basis-set effects

A systematic relativistic coupled-cluster study is reported on the harmonic vibrational frequencies of the O(h), C(3v), and C(2v) conformers of XeF6, with scalar-relativistic effects efficiently treated using the spin-free exact two-component theory in its one-electron variant (SFX2C-1e). Atomic natural orbital type basis sets recontracted for the SFX2C-1e scheme have been shown to provide rapid basis-set convergence for the vibrational frequencies. SFX2C-1e as well as complementary pseudopotential based computations consistently predicts that both O(h) and C(3v) structures are local minima on the potential energy surface, while the C(2v) structure is a transition state. Qualitative disagreement between the present results for the O(h) structure and those from CCSD(T)-F12b calculations [Peterson et al., J. Phys. Chem. A 116, 9777 (2012)], which yielded a triply degenerate imaginary frequency for the O(h) structure, is attributed here to the high sensitivity of the computed harmonic frequencies of the t(1u) bending modes to the basis-set effects of triples contributions.

Explicitly correlated ring-coupled-cluster-doubles theory.

The connection between the random-phase approximation and the ring-coupled-cluster-doubles method bridges the gap between density-functional and wave-function theories and the importance of the random-phase approximation lies in both its broad applicability and this linking role in electronic-structure theory. In this contribution, we present an explicitly correlated approach to the random-phase approximation, based on the direct ring-coupled-cluster-doubles ansatz, which overcomes the problem of slow basis-set convergence, inherent to the random-phase approximation. Benchmark results for a test set of 106 molecules and a selection of 10 organic complexes from the S22 test set demonstrate that convergence to within 99% of the basis-set limit is reached for triple-zeta basis sets for atomisation energies, while quadruple-zeta basis sets are required for interaction energies. Corrections due to single excitations into the complementary auxiliary space reduce the basis-set incompleteness error by one order of magnitude, while contributions due to the coupling of conventional and geminal amplitudes are in general negligible. We find that a non-iterative explicitly correlated correction to first order in perturbation theory exhibits the best ratio of accuracy to computational cost.

Estimating the CCSD basis-set limit energy from small basis sets: basis-set extrapolations vs additivity schemes

Coupled cluster calculations with all single and double excitations (CCSD) converge exceedingly slowly with the size of the one-particle basis set. We assess the performance of a number of approaches for obtaining CCSD correlation energies close to the complete basis-set limit in conjunction with relatively small DZ and TZ basis sets. These include global and system-dependent extrapolations based on the A + B/Lα two-point extrapolation formula, and the well-known additivity approach that uses an MP2-based basis-set-correction term. We show that the basis set convergence rate can change dramatically between different systems(e.g.it is slower for molecules with polar bonds and/or second-row elements). The system-dependent basis-set extrapolation scheme, in which unique basis-set extrapolation exponents for each system are obtained from lower-cost MP2 calculations, significantly accelerates the basis-set convergence relative to the global extrapolations. Nevertheless, we find that the simple MP2-based basis-set additivity scheme outperforms the extrapolation approaches. For example, the following root-mean-squared deviations are obtained for the 140 basis-set limit CCSD atomization energies in the W4-11 database: 9.1 (global extrapolation), 3.7 (system-dependent extrapolation), and 2.4 (additivity scheme) kJ mol–1. The CCSD energy in these approximations is obtained from basis sets of up to TZ quality and the latter two approaches require additional MP2 calculations with basis sets of up to QZ quality. We also assess the performance of the basis-set extrapolations and additivity schemes for a set of 20 basis-set limit CCSD atomization energies of larger molecules including amino acids, DNA/RNA bases, aromatic compounds, and platonic hydrocarbon cages. We obtain the following RMSDs for the above methods: 10.2 (global extrapolation), 5.7 (system-dependent extrapolation), and 2.9 (additivity scheme) kJ mol–1.

Small and efficient basis sets for the evaluation of accurate interaction-induced linear and non-linear electric properties in model hydrogen-bonded complexes

Interaction-induced electric dipole moment, polarisability and first hyperpolarisability are investigated in model hydrogen-bonded clusters built of hydrogen fluoride molecules organised in three linear chains parallel to each other. The properties are evaluated within the finite field approach, using the second order Møller–Plesset method, and the LPol-m (m = ds, dl) and the optical rotation prediction (ORP) basis sets. These bases and correlation method are selected after a systematic basis set and correlation method convergence study carried out on the smallest of the complexes and taking properties obtained with Dunning's bases and the coupled cluster singles and doubles (CCSD) and the CCSD including connected triple corrections (CCSD(T)) methods as reference. Results are analysed in terms of many-body and cooperative effects.

An efficient method for energy levels calculation using full symmetry and exact kinetic energy operator: tetrahedral molecules.

A simultaneous use of the full molecular symmetry and of an exact kinetic energy operator (KEO) is of key importance for accurate predictions of vibrational levels at a high energy range from a potential energy surface (PES). An efficient method that permits a fast convergence of variational calculations would allow iterative optimization of the PES parameters using experimental data. In this work, we propose such a method applied to tetrahedral AB4 molecules for which a use of high symmetry is crucial for vibrational calculations. A symmetry-adapted contracted angular basis set for six redundant angles is introduced. Simple formulas using this basis set for explicit calculation of the angular matrix elements of KEO and PES are reported. The symmetric form (six redundant angles) of vibrational KEO without the sin(q)(-2) type singularity is derived. The efficient recursive algorithm based on the tensorial formalism is used for the calculation of vibrational matrix elements. A good basis set convergence for the calculations of vibrational levels of the CH4 molecule is demonstrated.