ller-Plesset Perturbation Theory Research Articles

Third-Order Møller-Plesset Theory Made More Useful? The Role of Density Functional Theory Orbitals.

The practical utility of Møller-Plesset (MP) perturbation theory is severely constrained by the use of Hartree-Fock (HF) orbitals. It has recently been shown that the use of regularized orbital-optimized MP2 orbitals and scaling of MP3 energy could lead to a significant reduction in MP3 error [Bertels, L. W.; J. Phys. Chem. Lett. 2019, 10, 4170 4176]. In this work, we examine whether density functional theory (DFT)-optimized orbitals can be similarly employed to improve the performance of MP theory at both the MP2 and MP3 levels. We find that the use of DFT orbitals leads to significantly improved performance for prediction of thermochemistry, barrier heights, noncovalent interactions, and dipole moments relative to the standard HF-based MP theory. Indeed, MP3 (with or without scaling) with DFT orbitals is found to surpass the accuracy of coupled-cluster singles and doubles (CCSD) for several data sets. We also found that the results are not particularly functional sensitive in most cases (although range-separated hybrid functionals with low delocalization error perform the best). MP3 based on DFT orbitals thus appears to be an efficient, noniterative O(N6) scaling wave-function approach for single-reference electronic structure computations. Scaled MP2 with DFT orbitals is also found to be quite accurate in many cases, although modern double hybrid functionals are likely to be considerably more accurate.

Utilizing Essential Symmetry Breaking in Auxiliary-Field Quantum Monte Carlo: Application to the Spin Gaps of the C36 Fullerene and an Iron Porphyrin Model Complex.

We present three distinct examples where phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) can be reliably performed with a single-determinant trial wave function with essential symmetry breaking. Essential symmetry breaking was first introduced by Lee and Head-Gordon [ Phys. Chem. Chem. Phys. 2019, 21, 4763-4778, 10.1039/C8CP07613H]. We utilized essential complex and time-reversal symmetry breaking with ph-AFQMC to compute the triplet-singlet energy gap in the TS12 set. We found statistically better performance of ph-AFQMC with complex-restricted orbitals than with spin-unrestricted orbitals. We then showed the utilization of essential spin symmetry breaking when computing the singlet-triplet gap of a known biradicaloid, C36. ph-AFQMC with spin-unrestricted Hartree-Fock (ph-AFQMC+UHF) fails catastrophically even with spin-projection and predicts no biradicaloid character. With approximate Brueckner orbitals obtained from regularized orbital-optimized second-order Møller-Plesset perturbation theory (κ-OOMP2), ph-AFQMC quantitatively captures strong biradicaloid character of C36. Lastly, we applied ph-AFQMC to the computation of the quintet-triplet gap in a model iron porphyrin complex where brute-force methods with a small active space fail to capture the triplet ground state. We show unambiguously that neither triplet nor quintet is strongly correlated using UHF, κ-OOMP2, and coupled-cluster with singles and doubles (CCSD) performed on UHF and κ-OOMP2 orbitals. There is no essential symmetry breaking in this problem. By virtue of this, we were able to perform UHF+ph-AFQMC reliably with a cc-pVTZ basis set and predicted a triplet ground state for this model geometry. The largest ph-AFQMC in this work correlated 186 electrons in 956 orbitals. Our work highlights the utility, scalability, and accuracy of ph-AFQMC with a single-determinant trial wave function with essential symmetry breaking for systems mainly dominated by dynamical correlation with little static correlation.

Estimation of the decay rate of Be7 and Be27 encapsulated in C70

Electron capture ($\ensuremath{\beta}$-decay) rates of $^{7}\mathrm{Be}$ and $^{7}\mathrm{Be}_{2}$ encapsulated in ${\mathrm{C}}_{70}$ have been estimated by calculating the electron density $\ensuremath{\rho}(0)$ at the $^{7}\mathrm{Be}$ nucleus and comparing it with $\ensuremath{\rho}(0)$ and experimental $\ensuremath{\beta}$-decay rates of $^{7}\mathrm{Be}$ inside another fullerene---${\mathrm{C}}_{60}$. For that the endohedral fullerenes $^{7}\mathrm{Be}@{\mathrm{C}}_{70}$ and $^{7}\mathrm{Be}_{2}@{\mathrm{C}}_{70}$ have been examined by means of the ab initio approach using the Hartree-Fock method with the the second order M\o{}ller-Plesset perturbation theory accounting for the Van der Waals foces. Our calculations indicate that the $^{7}\mathrm{Be}_{2}@{\mathrm{C}}_{70}$ complex is stable with the binding energy of 1.3 eV and the $^{7}\mathrm{Be}$ dimer bond length 2.30 \AA{}. It has been found that $\ensuremath{\rho}(0)$ is practically the same in $^{7}\mathrm{Be}@{\mathrm{C}}_{70}$ and $^{7}\mathrm{Be}_{2}@{\mathrm{C}}_{70}$, but larger than in an isolated $^{7}\mathrm{Be}$ atom. The increase of $\ensuremath{\rho}(0)$ however is smaller than in $^{7}\mathrm{Be}@{\mathrm{C}}_{60}$. We also discuss in detail the mechanism underlying the increase of $\ensuremath{\rho}(0)$ and consequently the decrease of the decay rate in $^{7}\mathrm{Be}@{\mathrm{C}}_{70}$ in comparison with the isolated $^{7}\mathrm{Be}$ atom.

Theoretical assessment of the structure and stability of the λ phase of nitrogen

The $\ensuremath{\lambda}$ phase of nitrogen was reported in 2016 and is one of more than a dozen high-pressure solid nitrogen forms that have been discovered. However, its crystal structure could not be solved unambiguously from powder diffraction alone; rather the reported structure was determined by combining experimental monoclinic lattice parameters with atomic positions from an earlier, computationally predicted structure that had similar unit cell dimensions. Here, we revisit this structure using density functional theory and higher-level fragment-based second-order M\o{}ller-Plesset perturbation theory (MP2) and coupled cluster singles, doubles, and perturbative triples [CCSD(T)]. Crystal structure prediction is performed to demonstrate that the reported $P{2}_{1}/c$ structure is indeed the likeliest candidate for the $\ensuremath{\lambda}$ phase. Furthermore, we provide further evidence for the structural assignment by demonstrating reasonable agreement between its predicted and experimental structural parameters and Raman spectra. Finally, the thermodynamic stability of the $\ensuremath{\lambda}$ phase relative to other phases has been uncertain, but the calculations do suggest that it may be the thermodynamically most stable phase for at least part of the pressure range over which it has been observed.

Third-Order Nonlinear Optical Properties of a Carboxylic Acid Derivative

We report a study of the structural and electrical properties of a carboxylic acid derivative (CAD) with structural formula C5H8O2 ((E)-pent-2-enoic acid). Using the M∆ller-Plesset Perturbation Theory (MP2) and the Density Functional Theory (DFT/CAM-B3LYP) with the 6-311++G(d,p) basis set the dipole moment, the linear polarizability and the first and second hyperpolarizabilities are calculated in presence of static and dynamic electric field. Through the supermolecule approach the crystalline phase of the carboxylic acid derivative is simulated and the environment polarization effects on the electrical parameters are studied. Static and dynamic estimation of the linear refractive index and the third-order nonlinear susceptibility of the crystal are obtained and compared with available experimental results. The characteristic vibrational modes and functional groups present in CAD were analyzed by Fourier Transform Infrared Spectrum (FTIR) in the region of 400-4000 cm-1. Through the Hirshfeld surface analysis the molecular structure and the vibrational modes properties of the CAD crystal are explored. The effects of solvent medium on the molecular properties are taken into account through the Polarizable Continuum Model (PCM). Also, the frontiers molecular orbitals, the band gap energy, and the global chemical reactivity descriptors are discussed. All the properties studied suggest that the present material may be considered for nonlinear optical material.

Regularized Orbital-Optimized Second-Order Møller-Plesset Perturbation Theory: A Reliable Fifth-Order-Scaling Electron Correlation Model with Orbital Energy Dependent Regularizers.

We derive and assess two new classes of regularizers that cope with offending denominators in the single-reference second-order Møller-Plesset perturbation theory (MP2). In particular, we discuss the use of two types of orbital energy dependent regularizers, κ and σ, in conjunction with orbital-optimized MP2 (OOMP2). The resulting fifth-order-scaling methods, κ-OOMP2 and σ-OOMP2, have been examined for bond-breaking, thermochemistry, nonbonded interactions, and biradical problems. Both methods with strong enough regularization restore restricted to unrestricted instability (i.e., Coulson-Fischer points) that unregularized OOMP2 lacks when breaking bonds in H2, C2H6, C2H4, and C2H2. The training of the κ and σ regularization parameters was performed with the W4-11 set. We further developed scaled correlation energy variants, κ-S-OOMP2 and σ-S-OOMP2, by training on the TAE140 subset of the W4-11 set. Those new OOMP2 methods were tested on the RSE43 set and the TA13 set where unmodified OOMP2 itself performs very well. The modifications we made were found insignificant in these data sets. Furthermore, we tested the new OOMP2 methods on singlet biradicaloids using Yamaguchi's approximate spin-projection. Unlike the unregularized OOMP2, which fails to converge these systems due to the singularity, we show that regularized OOMP2 methods successfully capture strong biradicaloid characters. While further assessment on larger data sets is desirable, κ-OOMP2 with κ = 1.45 E h-1 appears to combine favorable recovery of Coulson-Fischer points with good numerical performance.

Laplace transformed MP2 for three dimensional periodic materials using stochastic orbitals in the plane wave basis and correlated sampling.

We present an implementation and analysis of a stochastic high performance algorithm to calculate the correlation energy of three-dimensional periodic systems in second-order Møller-Plesset perturbation theory (MP2). In particular we measure the scaling behavior of the sample variance and probe whether this stochastic approach is competitive if accuracies well below 1 meV per valence orbital are required, as it is necessary for calculations of adsorption, binding, or surface energies. The algorithm is based on the Laplace transformed MP2 (LTMP2) formulation in the plane wave basis. The time-dependent Hartree-Fock orbitals, appearing in the LTMP2 formulation, are stochastically rotated in the occupied and unoccupied Hilbert space. This avoids a full summation over all combinations of occupied and unoccupied orbitals, as inspired by the work of Neuhauser, Rabani, and Baer [J. Chem. Theory Comput. 9, 24 (2013)]. Additionally, correlated sampling is introduced, accelerating the statistical convergence significantly.

Laplace-transformed multi-reference second-order perturbation theories in the atomic and active molecular orbital basis.

In the present article, we show how to formulate the partially contracted n-electron valence second-order perturbation theory (NEVPT2) energies in the atomic and active molecular orbital basis by employing the Laplace transformation of orbital-energy denominators (OEDs). As atomic-orbital (AO) basis functions are inherently localized and the number of active orbitals is comparatively small, our formulation is particularly suited for a linearly scaling NEVPT2 implementation. In our formulation, there are two kinds of NEVPT2 energy contributions, which differ in the number of active orbitals in the two-electron integrals involved. Those involving integrals with either no or a single active orbital can be formulated completely in the AO basis as single-reference second-order Møller-Plesset perturbation theory and benefit from sparse active pseudo-density matrices-particularly if the active molecular orbitals are localized only in parts of a molecule. Conversely, energy contributions involving integrals with either two or three active orbitals can be obtained from Coulomb and exchange matrices generalized for pairs of active orbitals. Moreover, we demonstrate that Laplace-transformed partially contracted NEVPT2 is nothing less than time-dependent NEVPT2 [A. Y. Sokolov and G. K.-L. Chan, J. Chem. Phys. 144, 064102 (2016)] iff the all-active intermediates are computed with the internal-contraction approximation. Furthermore, we show that for multi-reference perturbation theories it is particularly challenging to find optimal parameters of the numerical Laplace transformation as the fit range may vary among the 8 different OEDs by many orders of magnitude. Selecting the number of quadrature points for each OED separately according to an accuracy-based criterion allows us to control the errors in the NEVPT2 energies reliably.

Construction of explicitly correlated geminal-projected particle-hole creation operators for many-electron systems using the diagrammatic factorization approach

The computational cost of performing a configuration interaction (CI) calculation for treating electron-electron correlation is directly proportional to the number of terms in the CI expansion. In this work, we present a diagrammatic projection approach for a priori identification of noncontributing terms in a CI expansion. This method known as the geminal-projected configuration interaction (GP-CI) method is based on using a two-body R12 geminal operator for describing electron-electron correlation in a reference many-electron wave function. The diagrammatic projection procedure was performed by first deriving the Hugenholtz diagrams of the energy expression of the R12 reference wave function and then performing diagrammatic factorization of effective particle-hole creation operators. The projection operation, which is a functional of the geminal function, was defined and used for the construction of the geminal-projected particle-hole creation operators. The form of the two-body R12 geminal operator was derived analytically by imposing an approximate Kato cusp condition. A linear combination of the geminal-projected one-particle one-hole and two-particle two-hole operators were used for the construction of the GP-CI wave function. The applicability and implementation of the diagrammatic projection method was demonstrated by performing proof-of-concept calculations on an isoelectronic series of 10 electron systems: ${\mathrm{CH}}_{4},\phantom{\rule{0.16em}{0ex}}{\mathrm{NH}}_{3},\phantom{\rule{0.16em}{0ex}}{\mathrm{H}}_{2}\mathrm{O},\phantom{\rule{0.16em}{0ex}}\mathrm{HF}$, and $\mathrm{Ne}$. The results from the calculations show that compared to conventional CI calculations, the GP-CI method was able to substantially reduce the size of the CI space (by a factor of 6--9) while maintaining an accuracy of ${10}^{\ensuremath{-}5}$ Hartrees for the ground-state energies. These results demonstrate the ability of the diagrammatic projection procedure to identify noncontributing states using an analytical form of the R12 geminal correlator operator. The geminal-projection method was also applied to second-order M\o{}ller-Plesset perturbation theory (GP-MP2) giving similar results to the GP-CI method in terms of reduction of the double excitation space and accuracy to the ground-state energy. This work also extends the analytical derivation of the geminal-projected particle-hole creation operators that were used for the construction of the CI wave function to coupled-cluster theory (GP-CCSD). This general derivation can also be applied to other many-electron theories and multideterminant quantum Monte Carlo calculations.

Correlation energy for the homogeneous electron gas: Exact Bethe-Salpeter solution and an approximate evaluation

The correlation energy of the homogeneous electron gas is evaluated by solving the Bethe-Salpeter equation (BSE) beyond the Tamm-Dancoff approximation for the electronic polarisation propagator. The BSE is expected to improve upon the random phase approximation, owing to the inclusion of exchange diagrams. For instance, since the BSE reduces in second order to M{\o}ller-Plesset perturbation theory, it is self-interaction free in second order. Results for the correlatione energy are compared with Quantum Monte Carlo benchmarks and excellent agreement is observed. For low densities, however, we find imaginary eigenmodes in the polarisation propagator. To avoid the occurence of imaginary eigenmodes, an approximation to the BSE kernel is proposed, which allows to completely remove this issue in the low electron density region. We refer to this approximation as the random phase approximation with screened exchange (RPAsX). We show that this approximation even slightly improves upon the standard BSE kernel.

Theoretical study on the mechanism of the cycloaddition reaction between ketenimine and hydrogen cyanide

The cycloaddition reaction mechanism between interstellar molecules ketenimine and HCN has been investigated employing the second-order M?ller-Plesset perturbation theory (MP2) method in order to better understand the reactivity of nitrogenous cumulene ketenimine with carbon-nitrogen triple bond compound HCN. Geometry optimizations and vibrational analyses have been performed for the stationary points on the potential energy surfaces of the system. The calculated results show that it can be produced the five-membered cyclic carbene intermediates through pericyclic reaction processes between ketenimine and HCN. Through the following H-transfer processes, carbene intermediates can isomerize to the pyrazole and imidazole compounds, respectively. The present study is helpful to understand the formation of prebiotic species in interstellar space.

Comparative study of pure and Co-dopedBaFe2As2

We present a comparative calculation of the electronic structure of the high critical temperature superconductor Co-doped ${\text{BaFe}}_{2}{\text{As}}_{2}$ and its parent compound at the electron correlation level by the embedded cluster method; the electron correlation is calculated through the second-order M\o{}ller-Plesset perturbation theory. The superconducting doped material is represented by the ${\text{Ba}}_{4}{\text{CoFe}}_{4}{\text{As}}_{8}$ cluster. The analysis of the orbital populations in this cluster reveals the formation of an antiferromagnetic order in the Fe plane with a spin-density increase on the central Co atom with respect to the spin density of the central Fe atom of the undoped case. This increase is associated with an increase of the ${d}_{{z}^{2}}$ orbital population of the central atom. However, the formation mechanism of the local magnetic moment implies also a spin transfer from the nearest-neighbor Fe atoms and from the next-nearest-neighbor As atoms to the central Co atom, and it corresponds to a ${J}_{1}\ensuremath{-}{J}_{2}$ antiferromagnetic Heisenberg model. Some particular features of ${d}_{yz}$ and ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ orbitals in the triplet and in the singlet cluster states are interpreted to correspond to a spinless fermion. This result, as well as the result relative to the formation mechanism of the magnetic moments, can be connected with a model of resonating-valence-bond (RVB) superconductors suggested recently by Poilblanc et al. [Phys. Rev. B 89, 241106 (2014)] and based on the Anderson RVB theory.

Extended Møller-Plesset perturbation theory for dynamical and static correlations

We present a novel method that appropriately handles both dynamical and static electron correlations in a balanced manner, using a perturbation theory on a spin-extended Hartree-Fock (EHF) wave function reference. While EHF is a suitable candidate for degenerate systems where static correlation is ubiquitous, it is known that most of dynamical correlation is neglected in EHF. In this work, we derive a perturbative correction to a fully spin-projected self-consistent wave function based on second-order Møller-Plesset perturbation theory (MP2). The proposed method efficiently captures the ability of EHF to describe static correlation in degeneracy, combined with MP2's ability to treat dynamical correlation effects. We demonstrate drastic improvements on molecular ground state and excited state potential energy curves and singlet-triplet splitting energies over both EHF and MP2 with similar computational effort to the latter.

Theoretical Study on the Reaction Mechanism of Azacyclopropenylidene with Epoxypropane: An Insertion Process

The reaction mechanism between azacyclopropenylidene and epoxypropane has been systematically investigated employing the second-order M<TEX>${\o}$</TEX>ller-Plesset perturbation theory (MP2) method to better understand the reactivity of azacyclopropenylidene with four-membered ring compound epoxypropane. Geometry optimization, vibrational analysis, and energy property for the involved stationary points on the potential energy surface have been calculated. It was found that for the first step of this reaction, azacyclopropenylidene can insert into epoxypropane at its C-O or C-C bond to form spiro intermediate IM. It is easier for the azacyclopropenylidene to insert into the C-O bond than the C-C bond. Through the ring-opened step at the C-C bond of azacyclopropenylidene fragment, IM can transfer to product P1, which is named as pathway (1). On the other hand, through the H-transferred step and subsequent ring-opened step at the C-N bond of azacyclopropenylidene fragment, IM can convert to product P2, which is named as pathway (2). From the thermodynamics viewpoint, the P2 characterized by an allene is the dominating product. From the kinetic viewpoint, the pathway (1) of formation to P1 is primary.

Double-hybrid density-functional theory applied to molecular crystals.

We test the performance of a number of two- and one-parameter double-hybrid approximations, combining semilocal exchange-correlation density functionals with periodic local second-order Møller-Plesset (LMP2) perturbation theory, for calculating lattice energies of a set of molecular crystals: urea, formamide, ammonia, and carbon dioxide. All double-hybrid methods perform better on average than the corresponding Kohn-Sham calculations with the same functionals, but generally not better than standard LMP2. The one-parameter double-hybrid approximations based on the PBEsol density functional give lattice energies per molecule with an accuracy of about 6 kJ/mol, which is similar to the accuracy of LMP2. This conclusion is further verified on molecular dimers and on the hydrogen cyanide crystal.

Cubic-scaling algorithm and self-consistent field for the random-phase approximation with second-order screened exchange

The random-phase approximation with second-order screened exchange (RPA+SOSEX) is a model of electron correlation energy with two caveats: its accuracy depends on an arbitrary choice of mean field, and it scales as O(n(5)) operations and O(n(3)) memory for n electrons. We derive a new algorithm that reduces its scaling to O(n(3)) operations and O(n(2)) memory using controlled approximations and a new self-consistent field that approximates Brueckner coupled-cluster doubles theory with RPA+SOSEX, referred to as Brueckner RPA theory. The algorithm comparably reduces the scaling of second-order Mo̸ller-Plesset perturbation theory with smaller cost prefactors than RPA+SOSEX. Within a semiempirical model, we study H2 dissociation to test accuracy and Hn rings to verify scaling.

Explicitly correlated plane waves: Accelerating convergence in periodic wavefunction expansions

We present an investigation into the use of an explicitly correlated plane wave basis for periodic wavefunction expansions at the level of second-order Møller-Plesset (MP2) perturbation theory. The convergence of the electronic correlation energy with respect to the one-electron basis set is investigated and compared to conventional MP2 theory in a finite homogeneous electron gas model. In addition to the widely used Slater-type geminal correlation factor, we also derive and investigate a novel correlation factor that we term Yukawa-Coulomb. The Yukawa-Coulomb correlation factor is motivated by analytic results for two electrons in a box and allows for a further improved convergence of the correlation energies with respect to the employed basis set. We find the combination of the infinitely delocalized plane waves and local short-ranged geminals provides a complementary, and rapidly convergent basis for the description of periodic wavefunctions. We hope that this approach will expand the scope of discrete wavefunction expansions in periodic systems.

Ab initiostudies of electron correlation effects in heavier closed-shell atoms: Structure of the all-electron correlation energies of Zn2+and Zn

To provide reliable reference results for various components of the electron correlation energies of Zn${}^{2+}$ and Zn, which play a similar role for $3d$-electron systems as Ne and Mg do for lighter atoms, we have performed extensive calculations of the all-electron correlation energy and of its various components with several state-of-the-art ab initio techniques. Two pairs of basis-set sequences that systematically converge to the complete basis set (CBS) limit have been employed in the calculations. One pair [cc-pV$n$Z and aug-cc-pV$n$Z (correlation consistent polarized valence $n$-zeta and augmented cc-pV$n$Z with $n=$ D, T, Q, 5, $6(\ensuremath{-}k)$)] is oriented towards the description of valence electron correlation. The second pair of sequences [cc-pCCV$n$Z and aug-cc-pCCV$n$Z (core core-valence $n$-zeta, with $n$ = D, T, Q, 5, $6(\ensuremath{-}k)$)] is developed for the description of all-electron correlation effects. The correlation energies have been determined with second-order M\o{}ller-Plesset perturbation theory (MP2) and several single-reference coupled-cluster (CC) methods. The present correlation energies represent accurate post-MP2 correlation energies for closed-shell atoms including 3$d$ electrons both at the all-electron and subshell levels and should be useful benchmark results for various transitions. We have also employed the present results for assessments of the focal-point approximation (FPA), broadly used in approximations of difference correlation effects for molecular interaction problems, in applications aiming at estimating correlation effects in heavier atoms. Our results indicate that for the systems considered, the magnitudes of the MP2 correlation energies overestimate the magnitudes of the CC values for all electrons correlated as well as of their various subsets. For the all-electron correlation energies of the Zn atom, our result confirms the finding of S. P. McCarthy and A. J. Thakkar [J. Chem. Phys. 134, 044102 (2011)] obtained by means of non--ab initio approaches for all heavy closed-shell atoms from Zn to Rn. We have shown that for both Zn${}^{2+}$ and Zn this overestimation is directly caused by the presence of the $3{d}^{10}$ electron configuration.

Theoretical study of properties of Cs&lt;sub&gt;2&lt;/sub&gt;Cl&lt;sup&gt;+&lt;/sup&gt;, CsCl&lt;sub&gt;2&lt;/sub&gt;&lt;sup&gt;−&lt;/sup&gt;, Cs&lt;sub&gt;3&lt;/sub&gt;Cl&lt;sub&gt;2&lt;/sub&gt;&lt;sup&gt;+&lt;/sup&gt;, and Cs&lt;sub&gt;2&lt;/sub&gt;Cl&lt;sub&gt;3&lt;/sub&gt;&lt;sup&gt;−&lt;/sup&gt; ions: Effect of Basis set and Computation Method

Theoretical study of properties of Cs2Cl+, CsCl2&#8722;, Cs3Cl2+ and Cs2Cl3&#8722; ions has been performed using the density functional theory (DFT/B3LYP) and the second order M&#248;ller-Plesset perturbation theory (MP2). Two triple-zeta basis sets, the midsized B1 and the extended one B2, have been used. Equilibrium structure, vibrational spectra, energies and enthalpies of dissociation reactions of the ions have been found. The effect of the basis set size and the computation method on the results has been analyzed. The MP2 method with the extended basis B2 set was accepted as the more accurate among the others. For the triatomic ions Cs2Cl+ and CsCl2&#8722;, the equilibrium structure has been found to be linear. For the pentaatomic ions, three isomeric forms were considered. The most abundant isomer in saturated vapor was found to be the angular V-shaped of C2v symmetry for Cs3Cl2+ and the linear of D&#8734;h symmetry for Cs2Cl3&#8722;. Thermodynamic functions of the ions were computed and applied to the treatment of experimental mass spectrometric data. Enthalpies of formation &#916;fH&#186;(0 K) were determined (in kJ/mol): 51 &#177; 4 (Cs2Cl+), &#8722;622 &#177; 3 (CsCl2&#8722;), &#8722;301 &#177; 8 (Cs3Cl2+), &#8722;975 &#177; 6(Cs2Cl3&#8722;).

Dispersion-corrected density functional theory comparison of hydrogen adsorption on boron-nitride and carbon nanotubes

One of the main challenges for the future hydrogen economy is finding a safe and efficient way to store hydrogen. Materials with large surface areas, like carbon nanotubes and their analogues boron-nitride nanotubes, are being studied as potential candidates for this purpose. We perform density functional theory (DFT) and dispersion-corrected DFT (DFT-D) calculations of the adsorption of molecular hydrogen on graphene and boron-nitride sheets and compare the results against M\o{}ller-Plesset perturbation theory (MP2 and MP2.5). Our results indicate that DFT underestimates the binding energies, while DFT-D gives a very good agreement with the higher-order theory. Within DFT-D, we show that the binding energy of molecular hydrogen to the outer walls of carbon nanotubes is more than 40% larger than that of boron-nitride nanotubes.