Interactions in Diatomic Dimers Involving Closed-Shell Metals

Ab initio study on the singlet states of Zn-RG (RG = He, Ne, Ar, Kr, Xe, Rn) molecules

The computations on the potential energy curves (PECs) oftheground state and low-lying singlet excited states for Zn-RG (RG = He, Ne, Ar, Kr, Xe, Rn) molecule have been carried out using coupled-cluster with single and double excitations (CCSD), coupled-cluster with single and double excitations and perturbative contribution of connected triple excitations (CCSD(T)) methods and the equation-of-motion coupled cluster method restricted to single and double excitations (EOM-CCSD). The spectroscopic constants of all the bound states of Zn-RG have been calculated, and comparisons with the available experimental and theoretical works have been made for the ground state and C¹Π state of the Zn-RG complexes, reasonable agreement is found. The transition dipole moments (TDMs) functions of C¹Π-X¹Σ⁺ and D¹Σ⁺-X¹Σ⁺ transitions, the vibrational band origins, rotational constants and Franck-Condon factors of C¹Π-X¹Σ⁺ transition have also been reported, which would be of value to understand the transition properties of Zn-RG. Our study is expected to be helpful for deep understanding on the electronic structure and spectroscopy of Zn-RG van der Waals molecules.

Dispersion Energy from the Time-Independent Coupled-Cluster Polarization Propagator

We present a new method of calculation of the dispersion energy in the second-order symmetry-adapted perturbation theory. Using the Longuet-Higgins integral and time-independent coupled-cluster response theory, one shows that the general expression for the dispersion energy can be written in terms of cluster amplitudes and the excitation operators σ, which can be obtained by solving a linear equation. We introduced an approximate scheme dubbed CCPP2(T) for the dispersion energy accurate to the second order of intramonomer correlation, which includes certain classes to be summed to infinity. Assessment of the accuracy of the CCPP2(T) dispersion energy against the FCI dispersion for He₂ demonstrates its high accuracy. For more complex systems, CCPP2(T) matches the accuracy of the best methods introduced for calculations of dispersion so far. The method can be extended to higher-order levels of excitations, providing a systematically improvable theory of dispersion interaction.

Explicitly Correlated Electronic Structure Calculations with Transcorrelated Matrix Product Operators

In this work, we present the first implementation of the transcorrelated electronic Hamiltonian in an optimization procedure for matrix product states by the density matrix renormalization group (DMRG) algorithm. In the transcorrelation ansatz, the electronic Hamiltonian is similarity-transformed with a Jastrow factor to describe the cusp in the wave function at electron-electron coalescence. As a result, the wave function is easier to approximate accurately with the conventional expansion in terms of one-particle basis functions and Slater determinants. The transcorrelated Hamiltonian in first quantization comprises up to three-body interactions, which we deal with in the standard way by applying robust density fitting to two- and three-body integrals entering the second-quantized representation of this Hamiltonian. The lack of hermiticity of the transcorrelated Hamiltonian is taken care of along the lines of the first work on transcorrelated DMRG [ J. Chem. Phys. 2020, 153, 164115] by encoding it as a matrix product operator and optimizing the corresponding ground state wave function with imaginary-time time-dependent DMRG. We demonstrate our quantum chemical transcorrelated DMRG approach at the example of several atoms and first-row diatomic molecules. We show that transcorrelation improves the convergence rate to the complete basis set limit in comparison to conventional DMRG. Moreover, we study extensions of our approach that aim at reducing the cost of handling the matrix product operator representation of the transcorrelated Hamiltonian.

Prediction of beryllium clusters (Ben; n = 3-25) from first principles

Evolutionary searches using the USPEX method (Universal Structure Predictor: Evolutionary Xtallography) combined with density functional theory (DFT) calculations were performed to obtain the global minimum structures of beryllium (Be_n, n = 3-25) clusters. The thermodynamic stability, optoelectronic and photocatalytic properties as well as the nature of bonding are considered for the most stable clusters. It is found that the cluster with n = 15 is the transition point at which the configurations change from 3D hollow cages to filled cage structures (with an interior atom appearing in the structure). All the ground state structures are energetically favorable with negative binding energies, suggesting good synthetic feasibility for these structures. The calculated relative stabilities and electronic structure show that the Be₄, Be₁₀ and, Be₁₇ clusters are the most stable structures and can be considered as superatoms. The electron configurations of Be₄, Be₁₀ and Be₁₇ clusters with 8, 20 and 34 electrons are identified as 1S² 1P⁶, 1S² 1P⁶ 1D¹⁰ 2S², 1S² 1P⁶ 1D¹⁰ 2S² 1F¹⁴, respectively. Theoretical simulations determined that all the ground state structures exhibit excellent thermal stability, where the upper-limit temperature that the structures can tolerate is 900 K. During AIMD simulation of O₂ adsorption onto the Be₁₇ cluster an interesting phenomenon was happening in which the pristine Be₁₇ cluster becomes a new stable Be₁₇O₁₆ cluster. Based on ELF (electron localization function) analysis, it can be concluded that the Be-Be bonds in the small clusters are primarily of van der Waals type, while for the larger clusters, the bonds are of metallic nature. The Be_n clusters show very strong absorption in the UV and visible regions with absorption coefficients larger than 10⁵ cm^-1, which suggests a wide range of potential advanced optoelectronics applications. The Be₁₇ cluster has a suitable band alignment in the visible-light excitation region which will produce enhanced photocatalytic activities (making it a promising material for water splitting).

Binding curve of the beryllium dimer using similarity-transformed FCIQMC: Spectroscopic accuracy with triple-zeta basis sets

We demonstrate how similarity-transformed full configuration interaction quantum Monte Carlo (FCIQMC) based on the transcorrelated Hamiltonian can be applied to make highly accurate predictions for the binding curve of the beryllium dimer, marking the first case study of a molecular system with this method. In this context, the non-Hermitian transcorrelated Hamiltonian, resulting from a similarity transformation with a Jastrow factor, serves the purpose to effectively address dynamic correlation beyond the used basis set and thus allows for obtaining energies close to the complete basis set limit from FCIQMC already with moderate basis sets and computational effort. Building on results from other explicitly correlated methods, we discuss the role of the Jastrow factor and its functional form, as well as potential sources for size consistency errors, and arrive at Jastrow forms that allow for high accuracy calculations of the vibrational spectrum of the beryllium dimer.

Quantum computation solves a half-century-old enigma: Elusive vibrational states of magnesium dimer found

The high-lying vibrational states of the magnesium dimer (Mg₂), which has been recognized as an important system in studies of ultracold and collisional phenomena, have eluded experimental characterization for half a century. Until now, only the first 14 vibrational states of Mg₂ have been experimentally resolved, although it has been suggested that the ground-state potential may support five additional levels. Here, we present highly accurate ab initio potential energy curves based on state-of-the-art coupled-cluster and full configuration interaction computations for the ground and excited electronic states involved in the experimental investigations of Mg₂. Our ground-state potential unambiguously confirms the existence of 19 vibrational levels, with ~1 cm^-1 root mean square deviation between the calculated rovibrational term values and the available experimental and experimentally derived data. Our computations reproduce the latest laser-induced fluorescence spectrum and provide guidance for the experimental detection of the previously unresolved vibrational levels.

Second-Order Exchange-Dispersion Energy Based on a Multireference Description of Monomers

We present a method for calculation of the second-order exchange-dispersion energy in the framework of the symmetry-adapted perturbation theory (SAPT) for weakly interacting monomers described with multiconfigurational wave functions. The proposed formalism is based on response properties obtained from extended random phase approximation (ERPA) equations and assumes the single-exchange (S²) approximation. The approach is applicable to closed shell systems where static correlation cannot be neglected or to systems in nondegenerate excited states. We examine the new method in combination with either generalized valence bond perfect pairing (GVB) or complete active space self-consistent field (CASSCF) description of the interacting monomers. For model multireference dimers in ground states (H₂···H₂, Be···Be, He···H₂), exchange-dispersion energies are reproduced accurately. For the interaction between the excited hydrogen molecule and the helium atom we found unacceptably large errors which is attributed to the neglect of diagonal double excitations in the employed approximation to the linear response function.

Polarizabilities, dispersion coefficients, and retardation functions at the complete basis set CCSD limit: From Be to Ba plus Yb

Static and dynamic polarizabilities of alkaline earth metal atoms Be-Ba and of the Yb atom, as well as dispersion coefficients and retardation functions for their long-range interactions, are used as a benchmark for the restricted coupled cluster method with singles and doubles (CCSD) and noniterative triples added [CCSD(T)] and related polarization propagator CCSD(3) methods at the complete basis set limit. The latter is attained through the sequence of the augmented correlation-consistent polarized weighted core valence n-zeta basis sets with the exact 2-component approximation for the scalar relativistic effects and with the small-core effective core potentials (for Ca, Sr, and Ba). At the converged level of core correlation treatment, the finite-field CCSD(T) method reproduces the best available data for the static dipole and quadrupole polarizabilities better than 1% and 4%, respectively. Systematic cancelation of the triple contribution in the CCSD(3) calculations of the dynamic polarizabilities of alkaline earth metal atoms makes their dispersion coefficients accurate within 3%. The retardation functions are computed and used for the analysis of the long-range interactions in the homonuclear dimers. Implications to accurate ab initio calculations of the global interaction potentials are discussed.

Assessing Electronic Structure Methods for Long-Range Three-Body Dispersion Interactions: Analysis and Calculations on Well-Separated Metal Atom Trimers

Three-body dispersion interactions are much weaker than their two-body counterpart. However, their importance grows quickly as the number of interacting monomers rises. To explore the numerical performance of correlation methods for long-range three-body dispersion, we performed calculations on eight very simple dispersion-dominated model metal trimers: Na₃, Mg₃, Zn₃, Cd₃, Hg₃, Cu₃, Ag₃, and Au₃. One encouraging aspect is that relatively small basis sets of augmented triple-ζ size appear to be adequate for three-body dispersion in the long-range. Coupled cluster calculations were performed at high levels to assess MP3, CCSD, CCSD(T), empirical density functional theory dispersion (D3), and the many-body dispersion (MBD) approach. We found that the accuracy of CCSD(T) was generally significantly lower than for two-body interactions, with errors sometimes reaching 20% in the investigated systems, while CCSD and particularly MP3 were generally more erratic. MBD is found to perform better than D3 at large distances, whereas the opposite is true at shorter distances. When computing reference numbers for three-body dispersion, care should be taken to appropriately represent the effect of the connected triple excitations, which are significant in most cases and incompletely approximated by CCSD(T).

Interactions of benzene, naphthalene, and azulene with alkali-metal and alkaline-earth-metal atoms for ultracold studies

We consider collisional properties of polyatomic aromatic hydrocarbon molecules immersed into ultracold atomic gases and investigate intermolecular interactions of exemplary benzene, naphthalene, and azulene with alkali-metal (Li, Na, K, Rb, and Cs) and alkaline-earth-metal (Mg, Ca, Sr, and Ba) atoms. We apply the state-of-the-art ab initio techniques to compute the potential energy surfaces (PESs). We use the coupled cluster method restricted to single, double, and noniterative triple excitations to reproduce the correlation energy and the small-core energy-consistent pseudopotentials to model the scalar relativistic effects in heavier metal atoms. We also report the leading long-range isotropic and anisotropic dispersion and induction interaction coefficients. The PESs are characterized in detail, and the nature of intermolecular interactions is analyzed and benchmarked using symmetry-adapted perturbation theory. The full three-dimensional PESs are provided for the selected systems within the atom-bond pairwise additive representation and can be employed in scattering calculations. The present study of the electronic structure is the first step toward the evaluation of prospects for sympathetic cooling of polyatomic aromatic molecules with ultracold atoms. We suggest azulene, an isomer of naphthalene which possesses a significant permanent electric dipole moment and optical transitions in the visible range, as a promising candidate for electric field manipulation and buffer-gas or sympathetic cooling.

Convergent energies and anharmonic vibrational spectra of Ca2H2 and Ca2H4 constitutional isomers

Three constitutional isomers of both Ca₂H₂ and Ca₂H₄ have been characterized with molecular electronic structure theory. Correlation methods as complete as CCSDT(Q) and basis sets as large as cc-pwCV5Z have been used to converge the relative energies within chemical accuracy (≤1 kcal mol^-1). Anharmonic vibrational frequencies were computed using second-order vibrational perturbation theory employing CCSD(T)/cc-pwCVTZ cubic and quartic force-fields and a CCSD(T)/cc-pwCVQZ quadratic force field. The monobridged [Ca(μ₂-H)CaH] and dibridged [Ca(μ₂-H)₂Ca] isomers of Ca₂H₂ were predicted to lie 6.5 and 12.9 kcal mol^-1 below the energy of the classical HCaCaH linear isomer, respectively. Despite the energetic favorability of the bridged Ca₂H₂ isomers, we conclude (surprisingly) that only the higher energy linear structure has been observed in the laboratory. At 0 K, the tribridged [Ca(μ₂-H)₃CaH] isomer of Ca₂H₄ is predicted to be enthalpically favored by 0.9 kcal mol^-1 in comparison to the enthalpy of the dibridged [HCa(μ₂-H)₂CaH] structure. Comparison of experiment with our computed frequencies suggests that the observed vibrational features arise from both the dibridged and the tribridged Ca₂H₄ structures.

Perspective: Found in translation: Quantum chemical tools for grasping non-covalent interactions

Today's quantum chemistry methods are extremely powerful but rely upon complex quantities such as the massively multidimensional wavefunction or even the simpler electron density. Consequently, chemical insight and a chemist's intuition are often lost in this complexity leaving the results obtained difficult to rationalize. To handle this overabundance of information, computational chemists have developed tools and methodologies that assist in composing a more intuitive picture that permits better understanding of the intricacies of chemical behavior. In particular, the fundamental comprehension of phenomena governed by non-covalent interactions is not easily achieved in terms of either the total wavefunction or the total electron density, but can be accomplished using more informative quantities. This perspective provides an overview of these tools and methods that have been specifically developed or used to analyze, identify, quantify, and visualize non-covalent interactions. These include the quantitative energy decomposition analysis schemes and the more qualitative class of approaches such as the Non-covalent Interaction index, the Density Overlap Region Indicator, or quantum theory of atoms in molecules. Aside from the enhanced knowledge gained from these schemes, their strengths, limitations, as well as a roadmap for expanding their capabilities are emphasized.

Can Popular DFT Approximations and Truncated Coupled Cluster Theory Describe the Potential Energy Surface of the Beryllium Dimer?

The potential energy surface (PES) of the ground state of the beryllium dimer poses a significant challenge for high-level ab initio electronic structure methods. Here, we present a systematic study of basis set effects over the entire PES of Be2 calculated at the full configuration interaction (FCI) level. The reference PES is calculated at the valence FCI/cc-pV{5,6}Z level of theory. We find that the FCI/cc-pV{T,Q}Z basis set extrapolation reproduces the shape of the FCI/cc-pV{5,6}Z PES as well as the binding energy and vibrational transition frequencies to within ~10 cm−1. We also use the FCI/cc-pV{5,6}Z PES to evaluate the performance of truncated coupled cluster methods (CCSD, CCSD(T), CCSDT, and CCSDT(Q)) and contemporary density functional theory methods (DFT) methods for the entire PES of Be2. Of the truncated coupled cluster methods, CCSDT(Q)/cc-pV{5,6}Z provides a good representation of the FCI/cc-pV{5,6}Z PES. The GGA functionals, as well as the HGGA and HMGGA functionals with low percentages of exact exchange tend to severely overbind the Be2 dimer, whereas BH&HLYP and M06-HF tend to underbind it. Range-separated DFT functionals tend to underbind the dimer. Double-hybrid DFT functionals show surprisingly good performance, with DSD-PBEP86 being the best performer. Møller–Plesset perturbation theory converges smoothly up to fourth order; however, fifth-order corrections have practically no effect on the PES.

Spooky correlations and unusual van der Waals forces between gapless and near-gapless molecules

We consider the zero-temperature van der Waals (vdW) interaction between two molecules, each of which has a zero or near-zero electronic gap between a ground state and the first excited state, using a toy model molecule (equilateral H₃) as an example. We show that the van der Waals energy between two ground state molecules falls off as D^-3 instead of the usual D^-6 dependence, when the molecules are separated by distance D. We show that this is caused by a perfect "spooky" correlation between the two fluctuating electric dipoles. The phenomenon is related to, but not the same as, the "resonant" interaction between an electronically excited and a ground state molecule introduced by Eisenschitz and London in 1930. It is also an example of "type C van der Waals non-additivity" recently introduced by one of us [J. F. Dobson, Int. J. Quantum Chem. 114, 1157 (2014)]. Our toy molecule H₃ is not stable, but symmetry considerations suggest that a similar vdW phenomenon may be observable, despite Jahn-Teller effects, in molecules with a discrete rotational symmetry and broken inversion symmetry, such as certain metal atom clusters. The motion of the nuclei will need to be included for a definitive analysis of such cases, however.

Quantum Monte Carlo calculation of the binding energy of the beryllium dimer

The accurate calculation of the binding energy of the beryllium dimer is a challenging theoretical problem. In this study, the binding energy of Be2 is calculated using the diffusion Monte Carlo (DMC) method, using single Slater determinant and multiconfigurational trial functions. DMC calculations using single-determinant trial wave functions of orbitals obtained from density functional theory calculations overestimate the binding energy, while DMC calculations using Hartree-Fock or CAS(4,8), complete active space trial functions significantly underestimate the binding energy. In order to obtain an accurate value of the binding energy of Be2 from DMC calculations, it is necessary to employ trial functions that include excitations outside the valence space. Our best estimate DMC result for the binding energy of Be2, obtained by using configuration interaction trial functions and extrapolating in the threshold for the configurations retained in the trial function, is 908 cm(-1), only slightly below the 935 cm(-1) value derived from experiment.

Accurate description of intermolecular interactions involving ions using symmetry-adapted perturbation theory

Three new data sets for intermolecular interactions, AHB21 for anion-neutral dimers, CHB6 for cation-neutral dimers, and IL16 for ion pairs, are assembled here, with complete-basis CCSD(T) results for each. These benchmarks are then used to evaluate the accuracy of the single-exchange approximation that is used for exchange energies in symmetry-adapted perturbation theory (SAPT), and the accuracy of SAPT based on wave function and density-functional descriptions of the monomers is evaluated. High-level SAPT calculations afford poor results for these data sets, and this includes the recently proposed "gold", "silver", and "bronze standards" of SAPT, namely, SAPT2+(3)-δMP2/aug-cc-pVTZ, SAPT2+/aug-cc-pVDZ, and sSAPT0/jun-cc-pVDZ, respectively [ Parker , T. M. , et al. , J. Chem. Phys. 2014 , 140 , 094106 ]. Especially poor results are obtained for symmetric shared-proton systems of the form X(-)···H(+)···X(-), for X = F, Cl, or OH. For the anionic data set, the SAPT2+(CCD)-δMP2/aug-cc-pVTZ method exhibits the best performance, with a mean absolute error (MAE) of 0.3 kcal/mol and a maximum error of 0.7 kcal/mol. For the cationic data set, the highest-level SAPT method, SAPT2+3-δMP2/aug-cc-pVQZ, outperforms the rest of the SAPT methods, with a MAE of 0.2 kcal/mol and a maximum error of 0.4 kcal/mol. For the ion-pair data set, the SAPT2+3-δMP2/aug-cc-pVTZ performs the best among all SAPT methods with a MAE of 0.3 kcal/mol and a maximum error of 0.9 kcal/mol. Overall, SAPT2+3-δMP2/aug-cc-pVTZ affords a small and balanced MAE (<0.5 kcal/mol) for all three data sets, with an overall MAE of 0.4 kcal/mol. Despite the breakdown of perturbation theory for ionic systems at short-range, SAPT can still be saved given two corrections: a "δHF" correction, which requires a supermolecular Hartree-Fock calculation to incorporate polarization effects beyond second order, and a "δMP2" correction, which requires a supermolecular MP2 calculation to account for higher-order induction-dispersion coupling. These corrections serve to remove artifacts introduced by the single exchange approximation in the exchange-induction and exchange-dispersion interactions, and obviate the need for ad hoc scaling of the first- and second-order exchange energies. Finally, some density-functional and MP2-based electronic structure methods are assessed as well, and we find that the best density-functional method for computing binding energies in these data sets is B97M-V/aug-cc-pVTZ, which affords a MAE of 0.4 kcal/mol, whereas complete-basis MP2 affords an MAE of 0.3 kcal/mol.

Corresponding states principle and van der Waals potentials of Zn2, Cd2, and Hg2

Based on the assumptions that the corresponding states principle is valid for the group 12 dimers and that the interaction potentials of these dimers can be described by the Tang-Toennies potential model, a set of correlation relations between the spectroscopic constants of these dimers are derived. Some recently measured spectroscopic constants satisfy these relations quite well, but older experimental data do not. These recent spectroscopic constants and the newly available dispersion coefficients are used to construct the entire van der Waals potentials of Zn2, Cd2, and Hg2. There are indications that the ground state Hg2 potential predicted by the present study is possibly the most accurate to date. No unequivocal conclusion can be made for Zn2 and Cd2 potentials. Compared with the recent experiments, the present Zn2 bond length is eight percent too small, and the present Cd2 bond length is eight percent too large. However, both Zn2 and Cd2 bond lengths predicted by the present study are in good agreement with the quantum Monte Carlo results.

Can the Counterpoise Correction for Basis Set Superposition Effect Be Justified?

The basis set superposition effect (BSSE) is a simple concept, and its validity is almost universally accepted. So is the counterpoise method to correct for it. The idea is that the basis set is biased toward the dimer because each monomer in the dimer can "use" the basis functions on the other monomer, which it cannot in a simple monomer calculation. This hypothesis can only be tested if basis set free benchmark numbers are available for monomers and dimer. We are testing the hypothesis on a few systems (in this paper Be2) that are small enough that sufficiently accurate benchmark numbers (basis set free, or close to basis set limit; full CI or close to full CI) are available or can be obtained. We find that the answer to the title question is negative: the standard basis sets of quantum chemistry appear to be biased toward the atom in the sense that basis set errors are larger for the dimer than the monomer. Applying the counterpoise correction increases the imbalance by reducing the already smaller basis set error of the monomer even further. Counterpoise corrected bond energies then deviate more from the basis set limit numbers than uncorrected bond energies. These conclusions hold both at the Hartree-Fock level and (much stronger) at the correlated (CCSD(T), full CI) levels. So the answer to the title question is No.

Symmetry-adapted perturbation theory based on unrestricted Kohn-Sham orbitals for high-spin open-shell van der Waals complexes

Two open-shell formulations of the symmetry-adapted perturbation theory are presented. They are based on the spin-unrestricted Kohn-Sham (SAPT(UKS)) and unrestricted Hartree-Fock (SAPT(UHF)) descriptions of the monomers, respectively. The key reason behind development of SAPT(UKS) is that it is more compatible with density functional theory (DFT) compared to the previous formulation of open-shell SAPT based on spin-restricted Kohn-Sham method of Żuchowski et al. [J. Chem. Phys. 129, 084101 (2008)]. The performance of SAPT(UKS) and SAPT(UHF) is tested for the following open-shell van der Waals complexes: He···NH, H(2)O···HO(2), He···OH, Ar···OH, Ar···NO. The results show an excellent agreement between SAPT(UKS) and SAPT(ROKS). Furthermore, for the first time SAPT based on DFT is shown to be suitable for the treatment of interactions involving Π-state radicals (He···OH, Ar···OH, Ar···NO). In the interactions of transition metal dimers ((3)Σ(u)(+))Au(2) and ((13)Σ(g)(+))Cr(2) we show that SAPT is incompatible with the use of effective core potentials. The interaction energies of both systems expressed instead as supermolecular UHF interaction plus dispersion from SAPT(UKS) result in reasonably accurate potential curves.

Short- and long-range binding of Be with Mg in the X1Σ+ ground state and in the A1Π excited state

We present results of configuration-interaction (CI) computations of wavefunctions and of properties of the first two singlet states, X(1)Σ(+) and A(1)Π, of the, as yet unobserved, BeMg polar molecule, for internuclear distances in the range [2.5-1000] Å. The X(1)Σ(+) state is very weakly bound, (D(e) = 469.4 cm(-1) at R(e) = 3.241 Å), whereas the A(1)Π state, which correlates with the excited dissociation channel [Mg KL3s3p(1)P(o) + Be 1s(2)2s(2) (1)S], is bound rather strongly (D(e) = 19 394 cm(-1) (55.5 kcal/mol) at R(e) = 2.385 Å). The X(1)Σ(+) state supports 12 vibrational levels, for which vibrationally averaged dipole moments, <μ>(υ), were obtained, while 71 vibrational levels were found for A(1)Π. For the level (X(1)Σ(+)), <μ>(0) = 0.213 D. The υ(") = 7 and 8 X(1)Σ(+) vibrational levels are found to have the highest probability to be reached via emission from the lowest lying vibrational levels of A(1)Π. The work had a dual outcome: First, it explored consequences of different choices of the state-specific reference "Fermi-sea" space ("active" space), which is required for the construction and execution of the multiconfigurational "complete active space self-consistent field" calculations and the subsequent multi-reference CI calculations. In this context, comparisons with results on the weakly bound ground states of the homonuclear Be(2) and Mg(2) molecules were made. Second, it produced reliable data for the short- as well as the long-range parts of the potential energy curve (PEC). Such information is relevant to analyses concerning cold and ultra-cold Physics and Chemistry. For example, accurate fits to the X(1)Σ(+) PEC, which was computed to nano-Hartree accuracy, with account for basis-set-superposition error, produced the C(6) and C(8) dispersion coefficients as 364.3 ± 1.1 a.u. and 28 000 ± 500 a.u., respectively. The result for C(6) is in excellent agreement with that of Derevianko et al. [At. Data Nucl. Data Tables 96, 323 (2010)], (364 ± 4 a.u.), that was obtained in the framework of the theory of long-range interactions and many-body calculations on the constituent atoms. On the other hand, our result for C(8) differs from that of Standard and Certain [J. Chem. Phys. 83, 3002 (1985)] by about 7000 a.u.

Computational study of Be2 using Piris natural orbital functionals

The third (PNOF3), fourth (PNOF4) and fifth (PNOF5) versions of the Piris natural orbital functional were used to characterize the beryllium dimer. The results obtained were compared to those gained afforded by CASSCF and CASPT2 as well as experimental data. The equilibrium distances (R e), dissociation energies (D e), effective bond orders (EBOs), and rovibrational levels were calculated. PNOF3, PNOF4, and CASPT2 predicted a bonded Be2 molecule, while PNOF5 and CASSCF did not, which demonstrates the importance of the dynamical electron correlation. We observed that PNOF3 yields the most accurate equilibrium distances, while PNOF4 most accurately calculates the rovibrational levels. However, both of these functionals overestimate dissociation energies. Both PNOF3 and PNOF4 predict EBOs that agree with that obtained using CASPT2.