CCSDT Level Research Articles

Tightening the Screws: The Importance of Tight d Functions in Coupled-Cluster Calculations up to the CCSDT(Q) Level

It is well established that the basis set convergence of the correlation consistent (cc-pVnZ) basis sets depends on the presence of high-exponent "tight" d functions in the basis set for second-row atoms. The effect has been linked to low-lying 3d virtual orbitals approaching the valence shell. However, since most of this effect is captured at the self-consistent field level, the effect of tight d functions in high-level coupled-cluster calculations has not been extensively studied. Here, we construct an extensive data set of 45 second-row species to examine the effect of tight d functions in CCSD, CCSD(T), CCSDT, and CCSDT(Q) calculations in conjunction with basis sets of up to sextuple-ζ quality. The selected set of molecules covers the gamut from systems where the tight d functions play a relatively minor role (e.g., SiH, SH, SiF, PF3, HOCl, Cl2, and C2Cl2) to challenging systems containing a central second-row atom bonded to many oxygen or fluorine atoms (e.g., PF5, SF6, SO3, ClO3, and HClO4) and systems containing many second-row atoms (e.g., P4, S4, CCl4, and C2Cl6). In conjunction with the cc-pVDZ basis set, we find chemically significant contributions to the total atomization energies (TAEs) of up to ∼2 kcal/mol at the CCSD level, ∼1 kcal/mol at the (T) level, and contributions of up to ∼0.1 kcal/mol for the post-CCSD(T) components. The effects of the tight d functions are diminished with the size of the basis set; however, they are still chemically significant at the CCSD and (T) levels. For example, with the cc-pVTZ basis set, we obtain contributions to the TAEs of up to ∼1.5 and ∼0.3 kcal/mol at the CCSD and (T) levels, respectively, and with the cc-pVQZ basis set, we obtain contributions of up to ∼1.0 and ∼0.2 kcal/mol at the CCSD and (T) levels, respectively. We also find that a simple natural bond orbital population analysis of the 3d orbitals of the second-row atom provides a useful a priori indicator of the magnitude of the effect of tight d functions on post-CCSD(T) contribution to the TAEs in oxide and fluoride systems. These results are particularly important in the context of high-level composite ab initio methods capable of confident benchmark accuracy in thermochemical predictions.

A Mountaineering Strategy to Excited States: Revising Reference Values with EOM-CC4.

In the framework of the computational determination of highly accurate vertical excitation energies in small organic compounds, we explore the possibilities offered by the equation-of-motion formalism relying on the approximate fourth-order coupled-cluster (CC) method, CC4. We demonstrate, using an extended set of more than 200 reference values based on CC including up to quadruples excitations (CCSDTQ), that CC4 is an excellent approximation to CCSDTQ for excited states with a dominant contribution from single excitations with an average deviation as small as 0.003 eV. We next assess the accuracy of several additive basis set correction schemes, in which vertical excitation energies obtained with a compact basis set and a high-order CC method are corrected with lower-order CC calculations performed in a larger basis set. Such strategies are found to be overall very beneficial, though their accuracy depends significantly on the actual scheme. Finally, CC4 is employed to improve several theoretical best estimates of the QUEST database for molecules containing between four and six (nonhydrogen) atoms, for which previous estimates were computed at the CCSDT level.

Cope rearrangements in shapeshifting molecules re-examined by means of high-level CCSDT(Q) composite ab initio methods

Benchmark reaction barrier heights for the degenerate Cope rearrangements in the highly fluxional bullvalene and semibullvalene hydrocarbon cages are obtained at the CCSDT(Q) level close to the one-particle basis set limit and include inner-shell, scalar-relativistic, and Born–Oppenheimer corrections. Our best theoretical CCSDT(Q) Gibbs free reaction barrier height for semibullvalene (ΔG298‡ = 27.9 kJ mol−1) is in good agreement with the most recent experimental value of 25.9 kJ mol−1. However, our CCSDT(Q) reaction barrier height for bullvalene (ΔG298‡ = 62.2 kJ mol−1) indicates that the most recent gas-phase experimental value of 54.8 ± 0.8 should be revised upward.

Selecting Quantum-Chemical Methods for Lanthanide-Containing Molecules: A Balance between Accuracy and Efficiency.

An analysis of how different density functionals, basis sets, and relativistic approximations affect the computed properties of lanthanide-containing molecules allows one to determine which method provides the highest accuracy. Historically, many different density functional methods have been employed to perform calculations on lanthanide complexes and so herein is a detailed analysis of how different methodological combinations change the computed properties of three different families of lanthanide-bearing species: lanthanide diatomic molecules (fluorides and oxides) and their dissociation energies; larger, molecular complexes and their geometries; and lanthanide bis(2-ethylhexyl)phosphate structures and their separation free energies among the lanthanide series. The B3LYP/Sapporo/Douglas-Kroll-Hess (DKH) method was shown to most accurately reproduce dissociation energies calculated at the CCSDT(Q) level of theory with a mean absolute deviation of 1.3 kcal/mol. For the calculations of larger, molecular complexes, the TPSSh/Sapporo/DKH method led to the smallest deviation from experimentally refined crystal structures. Finally, this same method led to calculated separation factors for lanthanide bis(2-ethylhexyl)phosphate structures that matched very closely with experimental values.

SPECTROSCOPIC AND THERMOCHEMICAL PROPERTIES OF ACTINIDE-CONTAINING SPECIES FROM FIRST PRINCIPLES: THORIUM AND AMERICIUM MONOXIDE MOLECULES

A relativistic version of a composite ab initio treatment of molecular spectroscopy and thermochemistry is developed, focusing on high-accuracy description of the properties of actinide (An) containing species. It is based on combining the calculation results at levels of theory with sufficiently full account of electron correlation, e.g., at the CCSDT(Q) level, but tackling only scalar relativity, with those obtained from more rigorous four-component relativistic calculations with the Dirac–Coulomb Hamiltonian. High accuracy achievable via this approach is revealed taking the examples of thorium and americium monoxide molecules. The errors in ab initio values for the bond length re, vibrational frequency ωe, and atomization energy D0 of the ThO molecule did not exceed 0.001 Å, 2.5 cm–1, and 0.5 kcal/mol, respectively. The composite numerical values for the first ionization potentials of the AmO molecule and the Am atom deviate from the experimental data just by 0.03 eV and 1 cm–1, respectively. For the first time, the proposed approach enabled high-accuracy evaluation of the molecular constants re, ωe and D0 for AmO and AmO+, as well as the second and third ionization potentials of the Am atom. The calculation results are indicative of a minor actinide contraction of the An–O bonds on going through the molecular series ThO → UO → AmO: the bond length in AmO is by 0.0073 Å shorter than that in ThO. The re(An–O) value is shown to be linearly dependent on the actinide atomic number in the periodic table. The results obtained may be used as benchmarks for parametrizing and calibrating the DFT functionals designed for treating An-containing molecules.

Spin States and Other Ligand-Field States of Aqua Complexes Revisited with Multireference ab Initio Calculations Including Solvation Effects.

High-level multireference (CASPT2, NEVPT2) calculations are reported for transition metal aqua complexes with electronic configurations from (3d)1 to (3d)8. We focus on the experimentally evidenced excitation energies to their various ligand-field states, including different spin states. By employing models accounting for both explicit and implicit solvation, we find that solvation effect may contribute up to 0.5 eV to the excitation energies depending on the charge of ion and character of the electronic transition. We further demonstrate that with an adequate choice of the active space and the energetics extrapolated to the complete basis set limit, the presently computed excitation energies are in a good agreement with the experimental data. This allows us to conclusively resolve significant discrepancies reported in earlier theory works [e.g., J. Phys. Chem. C 2014 , 118 , 29196 - 29208 ]. For the benchmark set of 19 spin-forbidden and 24 spin-allowed transitions (for which experimental data are unambiguous), we find the mean absolute error of 0.15 or 0.13 eV and the maximum error of 0.56 or 0.42 eV for CASPT2 or NEVPT2 calculations, respectively. For the particularly challenging sextet-quartet gap for [Fe(H2O)6]3+, we support our interpretation by additional calculations with multireference configuration interaction (MRCI) and coupled cluster theory up to the CCSDT(Q) level. By underlining a rather subtle interplay between the solvation and correlation effects, the findings of this Article are relevant not only for modeling and interpretation of optical spectra of transition metal complexes but also in further benchmarking of theoretical methods for the challenging problem of spin-state energetics.

Toward Chemical Accuracy in ab Initio Thermochemistry and Spectroscopy of Lanthanide Compounds: Assessing Core-Valence Correlation, Second-Order Spin-Orbit Coupling, and Higher Order Effects in Lanthanide Diatomics.

The higher order (HO) correlation beyond the coupled-cluster single double (triple) CCSD(T) level of theory, second-order spin-orbit coupling (SOC), and core-valence (CV) correlation effects on bond length, re, vibrational frequency, ωe, and dissociation energy, De, are studied for a set of 17 lanthanide containing diatomics, including lanthanum, europium, ytterbium, and lutetium oxides and halides. Convergence in the magnitudes of the SOC, CV, and HO corrections with respect to basis set size is examined using a sequence of double, triple, and quadruple-ζ basis sets, with the complete basis set (CBS) limit estimates provided in most cases. The CV effects on De, re, and ωe are calculated to amount up to 1.3 kcal·mol-1, 0.008 Å, and 5 cm-1, respectively. A detailed analysis of the origin of the CV effect with a particular accounting for various subvalence shells reveals that, generally, the Ln 4d correlation makes a major contribution, although in some instances the lower-lying 4sp shells contribute largely and even more substantially than 4d. The second-order SOC effect evaluated via two-component and four-component relativistic techniques proves to be non-negligible, especially for heavier species, e.g., LaI, in which it is as large as 0.8 kcal·mol-1 in De, 0.002 Å in re, and 1.3 cm-1 in ωe. Higher order correlation effects assessed through the CCSDT(Q) level are mostly less than 0.8 kcal·mol-1, 0.004 Å, and 5 cm-1; however, in species with prominence of nondynamical correlation, e.g., EuO, YbF, and LuO, the HO correction can amount to 1.2-1.6 kcal·mol-1, 0.005-0.008 Å, and 8-30 cm-1 in De, re, and ωe, respectively. In general, the [CCSD(T)+CV]/CBS + SOC + HO composite results are in good agreement with the available experimental data, exhibiting a mean absolute deviation of 1.8 kcal·mol-1 in De, 0.0023 Å in re, and 3.5 cm-1 in ωe. A significant experimental outlier, the bond length in YbI, is revealed, implying the need for re-examination of the experimental data.

Composite vibrational spectroscopy of the group 12 difluorides: ZnF2, CdF2, and HgF2.

The vibrational spectra of group 12 difluorides, MF2 (M = Zn, Cd, Hg), were investigated via coupled cluster singles, doubles, and perturbative triples, CCSD(T), including core correlation, with a series of correlation consistent basis sets ranging in size from triple-zeta through quintuple-zeta quality, which were then extrapolated to the complete basis set (CBS) limit using a variety of extrapolation procedures. The explicitly correlated coupled cluster method, CCSD(T)-F12b, was employed as well. Although exhibiting quite different convergence behavior, the F12b method yielded the CBS limit estimates closely matching more computationally expensive conventional CBS extrapolations. The convergence with respect to basis set size was examined for the contributions entering into composite vibrational spectroscopy, including those from higher-order correlation accounted for through the CCSDT(Q) level of theory, second-order spin-orbit coupling effects assessed within four-component and two-component relativistic formalisms, and vibrational anharmonicity evaluated via a perturbative treatment. Overall, the composite results are in excellent agreement with available experimental values, except for the CdF2 bond-stretching frequencies compared to spectral assignments proposed in a matrix isolation infrared and Raman study of cadmium difluoride vapor species [Loewenschuss et al., J. Chem. Phys. 50, 2502 (1969); Givan and Loewenschuss, J. Chem. Phys. 72, 3809 (1980)]. These assignments are called into question in the light of the composite results.

On a simple way to calculate electronic resonances for polyatomic molecules.

We propose a simple method for calculation of low-lying shape electronic resonances of polyatomic molecules. The method introduces a perturbation potential and requires only routine bound-state type calculations in the real domain of energies. Such a calculation is accessible by most of the free or commercial quantum chemistry software. The presented method is based on the analytical continuation in a coupling constant model, but unlike its previous variants, we experience a very stable and robust behavior for higher-order extrapolation functions. Moreover, the present approach is independent of the correlation treatment used in quantum many-electron computations and therefore we are able to apply Coupled Clusters (CCSD-T) level of the correlation model. We demonstrate these properties on determination of the resonance position and width of the (2)Πu temporary negative ion state of diacetylene using CCSD-T level of theory.

The electronic structure of vanadium monochloride cation (VCl(+)): tackling the complexities of transition metal species.

Six electronic states (X (4)Σ(-), A (4)Π, B (4)Δ, (2)Φ, (2)Δ, (2)Σ(+)) of the vanadium monochloride cation (VCl(+)) are described using large basis set coupled cluster theory. For the two lowest quartet states (X (4)Σ(-) and A (4)Π), a focal point analysis (FPA) approach was used that conjoined a correlation-consistent family of basis sets up to aug-cc-pwCV5Z-DK with high-order coupled cluster theory through pentuple (CCSDTQP) excitations. FPA adiabatic excitation energies (T0) and spectroscopic constants (re, r0, Be, B0, D¯e, He, ωe, v0, αe, ωexe) were extrapolated to the valence complete basis set Douglas-Kroll (DK) aug-cc-pV∞Z-DK CCSDT level of theory, and additional treatments accounted for higher-order valence electron correlation, core correlation, and spin-orbit coupling. Due to the delicate interplay between dynamical and static electronic correlation, single reference coupled cluster theory is able to provide the correct ground electronic state (X (4)Σ(-)), while multireference configuration interaction theory cannot. Perturbations from the first- and second-order spin orbit coupling of low-lying states with quartet spin multiplicity reveal an immensely complex rotational spectrum relative to the isovalent species VO, VS, and TiCl. Computational data on the doublet manifold suggest that the lowest-lying doublet state ((2)Γ) has a Te of ∼11 200 cm(-1). Overall, this study shows that laboratory and theoretical rotational spectroscopists must work more closely in tandem to better understand the bonding and structure of molecules containing transition metals.

Basis Set Convergence of the Post-CCSD(T) Contribution to Noncovalent Interaction Energies.

We investigated the basis set convergence of high-order coupled-cluster interaction energy contributions for 21 small weakly bound complexes. By performing CCSDT(Q) calculations in at least the aug-cc-pVTZ basis set, and CCSDT calculations in at least aug-cc-pVQZ (aug-cc-pVTZ for one system), we found the convergence to be quite slow. In particular, the 6-31G*(0.25) and 6-31G**(0.25,0.15) bases advocated by Hobza et al. (J. Chem. Theory Comput. 2013, 9, 2151; ibid. 2013, 9, 3420) are unsuitable for the post-CCSD(T) effects, with average errors for the CCSDT(Q)-CCSD(T) interaction energy contribution of about 80% for 6-31G**(0.25,0.15) and 110% for 6-31G*(0.25). Upgrading the basis set to aug-cc-pVDZ reduces the average error to about 35% and extremely demanding CCSDT(Q)/aug-cc-pVTZ calculations are necessary for further improvement in accuracy. An error cancellation between basis set incompleteness effects at the CCSDT-CCSD(T) and CCSDT(Q)-CCSDT levels occurs for most (but not all) complexes, making it unproductive to carry out CCSDT calculations in a larger basis set than the more demanding CCSDT(Q) calculations. We also found that the frozen natural orbital approximation at the CCSDT and CCSDT(Q) levels works well only if the thresholds for discarding least occupied natural orbitals are very tight (significantly tighter than the thresholds recommended for molecular correlation energies in the original work of Rolik and Kállay, J. Chem. Phys. 2011, 134, 124111), making the performance gains quite limited. The interaction energy contributions through CCSDT(Q) are both a necessity and a bottleneck in the construction of top-accuracy interaction potentials and further improvements in the efficiency of high-order coupled-cluster calculations will be of great help.

Relaxed active space: Fixing tailored-CC with high order coupled cluster. II

Due to the steep increase in computational cost with the inclusion of higher-connected cluster operators in coupled-cluster applications, it is usually not practical to use such methods for larger systems or basis sets without an active space partitioning. This study generates an active space subject to unambiguous statistical criteria to define a space whose size permits treatment at the CCSDT level. The automated scheme makes it unnecessary for the user to judge whether a chosen active space is sufficient to correctly solve the problem. Two demanding applications are presented: twisted ethylene and the transition states for the bicyclo[1,1,0]butane isomerization. As bi-radicals both systems require at least a CCSDT level of theory for quantitative results, for the geometries and energies.

W3X: A Cost-Effective Post-CCSD(T) Composite Procedure.

We have formulated the W3X procedure by incorporating cost-effective post-CCSD(T) components (up to the CCSDT(Q) level) into the W1X-1 protocol, the latter representing a recently reported economical yet accurate approximation to CCSD(T)/CBS. For medium-sized systems, W3X is moderately more computationally demanding than W1X-1, but it is significantly less costly than the W3.2lite and (especially) W3.2 procedures. Because of the use of the cost-effective W1X-1 method as the underlying CCSD(T) component, W3X is also less expensive than the W2.2 protocol, which does not incorporate post-CCSD(T) excitations. We find that, for single-reference systems (the G2/97 set and most of the W4-11 set), W3X is comparable in accuracy to the underlying W1X-1 protocol, as might have been expected. For the more challenging cases of the multireference systems within the W4-11 set, the dissociation of F2 and the automerization of cyclobutadiene, W3X provides improved performance compared with the CCSD(T)-based procedures (W1X-1 and W2.2). Highly multireference chromium oxides CrO, CrO2, and CrO3 are still somewhat challenging for W3X (and even for the higher-level W3.2lite and W3.2 procedures), but the inclusion of the economical post-CCSD(T) terms in W3X already leads to a significant improvement over W1X-1. Thus, W3X provides a cost-effective means for treating systems with significant (but perhaps not excessive) multireference character that are otherwise not well-described by CCSD(T)-based methods.

Convergence of the Interaction Energies in Noncovalent Complexes in the Coupled-Cluster Methods Up to Full Configuration Interaction.

The CCSD(T) method stands out among various coupled-cluster (CC) approximations as the "golden standard" in computational chemistry and is widely and successfully used in the realm of covalent and noncovalent interactions. The CCSD(T) method provides reliable interaction energies, but their surprising accuracy is believed to arise partially from an error compensation. The convergence of the CC expansion has been investigated up to fully iterative pentuple excitations (CCSDTQP); for the smallest eight electron complexes, the full CI calculations have also been performed. We conclude that the convergence of interaction energy at noncovalent accuracy (0.01 kcal/mol) for the complexes studied is reached already at CCSDTQ or CCSDT(Q) levels. When even higher accuracy (spectroscopic accuracy of 1 cm(-1), or 3 cal/mol) is required, then the noniterative CCSDTQ(P) method could be used.

Taming the low-lying electronic states of FeH

The low-lying electronic states (X (4)Δ, A (4)Π, a (6)Δ, b (6)Π) of the iron monohydride radical, which are especially troublesome for electronic structure theory, have been successfully described using a focal point analysis (FPA) approach that conjoined a correlation-consistent family of basis sets up to aug-cc-pwCV5Z-DK with high-order coupled cluster theory through hextuple (CCSDTQPH) excitations. Adiabatic excitation energies (T(0)) and spectroscopic constants (r(e), r(0), B(e), B(0), D(e), ω(e), v(0), α(e), ω(e)x(e)) were extrapolated to the valence complete basis set Douglas-Kroll (DK) aug-cc-pwCV∞Z-DK CCSDT level of theory, and additional treatments accounted for higher-order valence electron correlation, core correlation, spin-orbit coupling, and the diagonal Born-Oppenheimer correction. The purely ab initio FPA approach yields the following T(0) results (in eV) for the lowest spin-orbit components of each electronic state: 0 (X (4)Δ) < 0.132 (A (4)Π) < 0.190 (a (6)Δ) < 0.444 (b (6)Π). The computed anharmonic fundamental vibrational frequencies (v(0)) for the (4,6)Δ electronic states are within 3 cm(-1) of experiment and provide reliable predictions for the (4,6)Π states. With the cc-pVDZ basis set, even CCSDTQPH energies give an incorrect ground state of FeH, highlighting the importance of combining high-order electron correlation treatments with robust basis sets when studying transition-metal radicals. The FPA computations provide D(0) = 1.86 eV (42.9 kcal mol(-1)) for the 0 K dissociation energy of FeH and Δ(f)H(298) (∘) [FeH((g))] = 107.7 kcal mol(-1) for the enthalpy of formation at room temperature. Despite sizable multireference character in the quartet states, high-order single-reference coupled cluster computations improve the spectroscopic parameters over previous multireference theoretical studies; for example, the X (4)Δ → A (4)Π and a (6)Δ → b (6)Π transition energies are reproduced to 0.012 and 0.002 eV, respectively, while the error for the problematic X (4)Δ → a (6)Δ intercombination excitation is reduced from at least 0.17 eV to about 0.04 eV.

Multireference Fock space coupled cluster method in the effective and intermediate Hamiltonian formulation for the (2,0) sector

The effective and intermediate Hamiltonian (IH) multireference coupled cluster (CC) method with singles (S) and doubles (D) within the double electron attached (2,0) sector of the Fock space (FS) is formulated and implemented. The intermediate Hamiltonian realization of the (2,0) FS problem allows to replace the iterative scheme of the FS-CC equations based on the effective Hamiltonian with the diagonalization of the properly constructed matrix. The proposed method, IH-FS-CCSD (2,0), is rigorously size-extensive, easy to code, and numerically very efficient with the results comparable or slightly better than equation-of-motion ones at the CCSDT (T--triples) level. The performance of the method is discussed on the basis of test calculations for potential energy curves of the systems for which double positive ions dissociate into closed shell fragments (e.g., Na(2) dimer). The double electron attachment (DEA) scheme can be also useful in determination of the excitation spectra for difficult cases. The example is a carbon atom which has two electrons out of the closed shell structure. The newly implemented method is also analyzed by plotting potential energy curve for twisted ethylene case as a function of a dihedral angle between two methylene groups. Using DEA scheme one obtains a smooth, cusp free curve.

Theoretical investigation for spectroscopic constants of ground-state alkaline-earth dimers with high accuracy

In this work, we provide highly accurate theoretical estimates for spectroscopic constants of the ground-state alkaline-earth dimers (Ca2, Sr2, and Ba2). Electron correlation energies are calculated with coupled-cluster method at the single, double, and noniterative triple excitations [CCSD(T)] level, and the effects of full triples as well as quadruple excitations are also taken into account at the CCSDT and the CCSDT(Q) level. Our results demonstrate that high-order electron correlation is important to achieve results with high accuracy. We also find that results for Ca2 with counterpoise corrections, which are designed to eliminate the basis set superposition error, deviate further away from those at the complete basis set limit than the uncorrected ones. The calculated binding energies and equilibrium bond lengths for Ca2 and Sr2 are in excellent agreement with recent experimental data. On the other hand, our results for Ba2 are quite different from previous theoretical data, and there is no available experimental equilibrium bond length and binding energy for calibration. Based on the performance of the adopted approach for Ca2 and Sr2, our results should be more reliable and could be helpful for future investigations.

Ab initio virial equation of state for argon using a new nonadditive three-body potential

An ab initio nonadditive three-body potential for argon has been developed using quantum-chemical calculations at the CCSD(T) and CCSDT levels of theory. Applying this potential together with a recent ab initio pair potential from the literature, the third and fourth to seventh pressure virial coefficients of argon were computed by standard numerical integration and the Mayer-sampling Monte Carlo method, respectively, for a wide temperature range. All calculated virial coefficients were fitted separately as polynomials in temperature. The results for the third virial coefficient agree with values evaluated directly from experimental data and with those computed for other nonadditive three-body potentials. We also redetermined the second and third virial coefficients from the best experimental pρT data utilizing the computed higher virial coefficients as constraints. Thus, a significantly closer agreement of the calculated third virial coefficients with the experimental data was achieved. For different orders of the virial expansion, pρT data have been calculated and compared with results from high quality measurements in the gaseous and supercritical region. The theoretically predicted pressures are within the very small experimental errors of ±0.02% for p ≤ 12 MPa in the supercritical region near room temperature, whereas for subcritical temperatures the deviations increase up to +0.3%. The computed pressure at the critical density and temperature is about 1.3% below the experimental value. At pressures between 200 MPa and 1000 MPa and at 373 K, the calculated values deviate by 1% to 9% from the experimental results.

The Beryllium tetramer: Profiling an elusive molecule

The structure and energetics of Be(4) are investigated using state-of-the-art coupled-cluster methods. We compute the optimized bond length, dissociation energy, and anharmonic vibrational frequencies. A composite approach is employed, starting from coupled-cluster theory with single, double, and perturbative triple excitations extrapolated to the complete basis set (CBS) limit using Dunning's correlation consistent cc-pCVQZ and cc-pCV5Z basis sets. A correction for full triple and connected quadruple excitations in the smaller cc-pCVDZ basis set is then added, yielding an approximation to CCSDT(Q)/CBS denoted c∼CCSDT(Q). Corrections are included for relativistic and non-Born-Oppenheimer effects. We obtain D(e) = 89.7 kcal mol(-1), D(0) = 84.9 kcal mol(-1), and r(e) = 2.043 Å. Second-order vibrational perturbation theory (VPT2) is applied to a full quartic force field computed at the c∼CCSDT(Q) level of theory, yielding B(e) = 0.448 cm(-1) and fundamental frequencies of 666 (a(1)), 468 (e), and 571 (t(2)) cm(-1). Computations on the spectroscopically characterized Be(2) molecule are reported for the purpose of benchmarking our methods. Perturbative estimates of the effect of quadruple excitations are found to be essential to computing accurate parameters for Be(2); however, they seem to exert a much smaller influence on the structure and energetics of Be(4). Our extensive characterization of the Be(4) bonding potential energy surface should aid in the experimental identification of this thermodynamically viable but elusive molecule.

Convergence of the Møller-Plesset perturbation series for the fcc lattices of neon and argon

Complete basis set limit calculations are carried out for the fcc lattices of solid neon and argon, using second- to fourth-order Moller-Plesset theory, MP2–MP4, and coupled-cluster calculations, CCSDT ,t o describe electron correlation within a many-body expansion of the interaction potential up to third order. A correct description of the three-body Axilrod-Teller-Muto term for the solid state is only obtained from third order on in the many-body expansion of the correlation energy, correcting the severe underestimation of long-range three-body effects at the MP2 level of theory. MP4 shows good agreement with the CCSDT results, and the latter are in good agreement with experimental lattice constants, cohesive energies, and bulk moduli. However, with increasing pressures the convergence of the Moller-Plesset series deteriorates as the electronic band gap decreases, resulting in rather large deviations for the equation of state pressure-volume dependence. For neon, however, the errors in the MP2 two- and three-body terms almost cancel, i.e., at a volume of V =3 cm 3 / mol the MP2 pressure is underestimated by only 1 GPa compared to the pressure of P = 251 GPa calculated at the CCSDT level of theory. In contrast, for argon this is not the case, and at V = 5.5 cm 3 / mol the calculated MP2 pressure of 228 GPa deviates substantially from the CCSDT result of 252 GPa.