Online complete basis set limit extrapolation calculator

Decomposition and Growth Pathways for Ammonium Nitrate Clusters and Nanoparticles

Understanding the formation and decomposition mechanisms of aerosolized ammonium nitrate species will lead to improvements in modeling the thermodynamics and kinetics of aerosol haze formation. Studying the sputtered mass spectra of cation and anion ammonium nitrate clusters can provide insights as to which growth and evaporation pathways are favored in the earliest stages of nucleation and thereby guide the development and use of accurate models for intermolecular forces for these systems. Simulated annealing Monte Carlo optimization followed by density functional theory optimizations can be used reliably to predict minimum-energy structures and interaction energies for the cation and anion clusters observed in mass spectra as well as for neutral nanoparticles. A combination of translational and rotational mag-walking and sawtooth simulated annealing methods was used to find optimum structures of the various heterogeneous clusters identifiable in the mass spectra. Following these optimizations with ωB97X-D3 density functional theory calculations made it possible to rationalize the pattern of peaks in the mass spectra through computation of the binding energies of clusters involved in various growth and dissociation pathways. Testing these calculations against CCSD(T) and MP2 predictions of the structures and binding energies for small clusters demonstrates the accuracy of the chosen model chemistry. For the first time, the peaks corresponding with all detectable species in both the positive and negative ion mass spectra of ammonium nitrate are identified with their corresponding structures. Thermodynamic control of particle growth and decomposition of ions due to loss of ammonia or nitric acid molecules is indicated. Structures and interaction energies for larger (NH4NO3)n nanoparticles are also presented, including the prediction of new particle morphologies with trigonal pyramidal character.

Computational Studies of Nucleophilic Substitution at Nitrogen Center: Reactions of NH2Cl with HO-, CH3O- and C2H5O. Chemphyschem 2024:e202400365. [PMID: 38923666 DOI: 10.1002/cphc.202400365] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

The atomic-level mechanisms of the nucleophilic substitution reactions at the nitrogen center (SN2@N) were investigated for the reactions of chloramine (NH2Cl) with the alkoxide ions (RO-, where R=H, CH3, and C2H5) using DFT and MP2 methods. The computed potential energy profiles for the SN2@N pathways involving the back-side attack of the nucleophiles show the typical double-well potential with submerged barriers similar to the SN2 reactions at the carbon center (SN2@C). However, the pre-reaction and post-reaction complexes are, respectively, the N-H⋅⋅⋅O and N-H⋅⋅⋅Cl hydrogen-bonded intermediates, which are different from those generally seen in SN2@C reactions. The SN2@N pathways involving front-side attack of the nucleophiles have high-energy barriers. The potential energy surfaces (PESs) along the proton-transfer pathways were flat. In addition to the proton-transfer and SN2 pathways, we also observed a new path for the methoxide and ethoxide nucleophiles where a hydride-transfer from the nucleophile to chloramine resulted in the products Cl-+R'CHO+NH3, (R'=H, CH3), and was the most exoergic. A comparison of the energetics obtained used different DFT and MP2 methods with that of the benchmark coupled-cluster methods reveals that CAM-B3LYP best describes the PESs.

Quantum Tunneling Instability in Pericyclic Reactions

Several cycloreversion reactions of the retro-Diels-Alder type were computationally assessed to understand their quantum tunneling (QT) reactivity. N2, CO, and other leaving groups were considered based on their strong exothermicity, as it reduces their thermodynamic and kinetic stabilities. Our results indicate that for many of these reactions, it is essential to take into account their QT decomposition rate, which can massively weaken their molecular stability and shorten their half-lives even at deep cryogenic temperatures. In practical terms, this indicates that many supposedly stable molecules will actually be unsynthesizable or unisolable, and therefore trying to prepare or detect them would be a futile attempt. In addition, we discuss the importance of tunneling to correctly understand the enthalpy of activation and the collective atomic effect on the tunneling kinetic isotope effects to test if third-row atoms can tunnel in a chemical reaction. This project raises the question of the importance of in silico chemistry to guide in vitro chemistry, especially in cases where the latter cannot solve its own uncertainties.

When, Where and Why Boron Prefers Boron to Nitrogen

Boron is the archetypal Lewis acid, and therefore it is only natural that it prefers to bind nitrogen, its usual Lewis base counterpart. To challenge this assumption, we present a computationally designed bicyclopentane molecule akin to [1.1.1]propellane, but with pyramidal B and N inner atoms bonded by an "inverted" dative bond. Unexpectedly, the dimer of this system prefers to interact via an atypical boron-boron bond over the supposedly obvious boron-nitrogen bond. A molecular orbital analysis shows that the boron in this peculiar entity acts both as an electron donor and an electron acceptor, making the dimerization an amphoteric-amphoteric interaction process.

The inert pair effect on heavy noble gases: insights from radon tetroxide

A quantum chemical survey of radon and xenon tetroxides (NgO₄, Ng = Xe, Rn) is reported herein. The intermediate species, which are formed in their explosive decomposition back to their elemental states (Ng and O₂), were also studied and their energetics were compared. While T_d symmetric RnO₄ has a minimum energy structure, its standard enthalpy of formation is 88.6 kJ mol^-1 higher than for XeO₄. The reason for this higher instability lies in what is known as the inert pair effect. This work establishes that the high-valent chemical trends of the sixth period of groups 13-15 are indeed extended to group 18.

Influence of the complete basis set approximation, tight weighted-core, and diffuse functions on the DLPNO-CCSD(T1) atomization energies of neutral H,C,O-compounds

The impact of complete basis set extrapolation schemes (CBS), diffuse functions, and tight weighted-core functions on enthalpies of formation predicted via the DLPNO-CCSD(T1) reduced Feller-Peterson-Dixon approach has been examined for neutral H,C,O-compounds. All tested three-point (TZ/QZ/5Z) extrapolation schemes result in mean unsigned deviation (MUD) below 2 kJ mol^-1 relative to the experiment. The two-point QZ/5Z and TZ/QZ CBS 1 / l max 3 extrapolation schemes are inferior to their inverse power counterpart ( 1 / l max + 1 / 2 4 ) by 1.3 and 4.3 kJ mol^-1 . The CBS extrapolated frozen core atomization energies are insensitive (within 1 kJ mol^-1 ) to augmentation of the basis set with tight weighted core functions. The core-valence correlation effects converge already at triple-ζ, although double-ζ/triple-ζ CBS extrapolation performs better and is recommended. The effect of diffuse function augmentation converges slowly, and cannot be reproduced with double- ζ or triple- ζ calculations as these are plagued with basis set superposition and incompleteness errors.

Molecules of life: studying the interaction between water and phosphine in argon matrices

The interaction between water and phosphine isolated in solid argon matrices has been investigated. Infrared spectra of matrices containing water and phosphine, as well as their deuterium and ¹⁸O isotopologues, revealed that a weak hydrogen bonded complex is formed, with an O-H⋯P bonding motif. This was supported by high level ab initio calculations, which predict a binding energy of only 5.1 kJ mol^-1 (430 cm^-1).

A theoretical investigation of the hydrolysis of uranium hexafluoride: the initiation mechanism and vibrational spectroscopy

Depleted uranium hexafluoride (UF₆), a stockpiled byproduct of the nuclear fuel cycle, reacts readily with atmospheric humidity, but the mechanism is poorly understood. We compare several potential initiation steps at a consistent level of theory, generating underlying structures and vibrational modes using hybrid density functional theory (DFT) and computing relative energies of stationary points with double-hybrid (DH) DFT. A benchmark comparison is performed to assess the quality of DH-DFT data using reference energy differences obtained using a complete-basis-limit coupled-cluster (CC) composite method. The associated large-basis CC computations were enabled by a new general-purpose pseudopotential capability implemented as part of this work. Dispersion-corrected parameter-free DH-DFT methods, namely PBE0-DH-D3(BJ) and PBE-QIDH-D3(BJ), provided mean unsigned errors within chemical accuracy (1 kcal mol^-1) for a set of barrier heights corresponding to the most energetically favorable initiation steps. The hydrolysis mechanism is found to proceed via intermolecular hydrogen transfer within van der Waals complexes involving UF₆, UF₅OH, and UOF₄, in agreement with previous studies, followed by the formation of a previously unappreciated dihydroxide intermediate, UF₄(OH)₂. The dihydroxide is predicted to form under both kinetic and thermodynamic control, and, unlike the alternate pathway leading to the UO₂F₂ monomer, its reaction energy is exothermic, in agreement with observation. Finally, harmonic and anharmonic vibrational simulations are performed to reinterpret literature infrared spectroscopy in light of this newly identified species.

Theoretical study of water-assisted reaction between methane and nitrosonium cation

The water-assisted reaction between CH4 and NO+ has been studied employing post Hartree–Fock and density functional theory methods. Two reaction pathways were considered: (i) a frontside NO+ attack on the C–H bond of methane with retention of configuration and (ii) a backside attack with inversion of configuration. The first pathway leads to a thermodynamically more favorable hydrate of N-protonated nitrosomethane, and the second one leads to its O-protonated isomer. The catalytic effect of a single water molecule is expressed in decreasing the activation energy for the elementary step by about a factor of two for the frontside mechanism and by a factor of four to five for the backside one when compared with the calculated literature data on water-free methane nitrosation. The combination of the activation strain model of reactivity and the energy decomposition analysis reveals that the activation barriers are largely determined by the relative stability of the termolecular reactant complexes. The crucial factor that stabilizes these complexes comes from the electrostatic attraction. The catalytic effect of the key water molecule is decreased with introduction of additional one or two explicit water molecules, which form a coordinate O→N bonding with NO+. On the contrary, an additional water molecule hydrogen bonded to the key catalytic water molecule enhances the catalytic effect.

Polarizable Water Potential Derived from a Model Electron Density

A new empirical potential for efficient, large scale molecular dynamics simulation of water is presented. The HIPPO (Hydrogen-like Intermolecular Polarizable POtential) force field is based upon the model electron density of a hydrogen-like atom. This framework is used to derive and parametrize individual terms describing charge penetration damped permanent electrostatics, damped polarization, charge transfer, anisotropic Pauli repulsion, and damped dispersion interactions. Initial parameter values were fit to Symmetry Adapted Perturbation Theory (SAPT) energy components for ten water dimer configurations, as well as the radial and angular dependence of the canonical dimer. The SAPT-based parameters were then systematically refined to extend the treatment to water bulk phases. The final HIPPO water model provides a balanced representation of a wide variety of properties of gas phase clusters, liquid water, and ice polymorphs, across a range of temperatures and pressures. This water potential yields a rationalization of water structure, dynamics, and thermodynamics explicitly correlated with an ab initio energy decomposition, while providing a level of accuracy comparable or superior to previous polarizable atomic multipole force fields. The HIPPO water model serves as a cornerstone around which similarly detailed physics-based models can be developed for additional molecular species.

Correlation consistent basis sets for explicitly correlated wavefunctions: Pseudopotential-based basis sets for the group 11 (Cu, Ag, Au) and 12 (Zn, Cd, Hg) elements

New correlation consistent basis sets for the group 11 (Cu, Ag, Au) and 12 (Zn, Cd, Hg) elements have been developed specifically for use in explicitly correlated F12 calculations. This includes orbital basis sets for valence only (cc-pVnZ-PP-F12, n = D, T, Q) and outer core-valence (cc-pCVnZ-PP-F12) correlation, along with both of these augmented with additional high angular momentum diffuse functions. Matching auxiliary basis sets required for density fitting and resolution-of-the-identity approaches to conventional and F12 integrals have also been optimized. All of the basis sets are to be used in conjunction with small-core relativistic pseudopotentials [Figgen et al., Chem. Phys. 311, 227 (2005)]. The accuracy of the basis sets is determined through benchmark calculation at the explicitly correlated coupled-cluster level of theory for various properties of atoms and diatomic molecules. The convergence of the properties with respect to the basis set is dramatically improved compared to conventional coupled-cluster calculations, with cc-pVTZ-PP-F12 results close to conventional estimates of the complete basis set limit. The patterns of convergence are also greatly improved compared to those observed from the use of conventional correlation consistent basis sets in F12 calculations.

Local energy decomposition analysis and molecular properties of encapsulated methane in fullerene (CH4@C60)

Methane has been successfully encapsulated within cages of C₆₀ fullerene, which is an appropriate model system to study confinement effects. Its chemistry and physics are also relevant for theoretical model descriptions. Here we provide insights into intermolecular interactions and predicted spectroscopic responses of the CH₄@C₆₀ complex and compared them with results from other methods and with data from the literature. Local energy decomposition analysis (LED) within the domain-based local pair natural orbital coupled cluster singles, doubles, and perturbative triples (DLPNO-CCSD(T)) framework was used, and an efficient protocol for studies of endohedral complexes of fullerenes is proposed. This approach allowed us to assess energies in relation to electronic and geometric preparation, electrostatics, exchange, and London dispersion for the CH₄@C₆₀ endohedral complex. The calculated stabilization energy of CH₄ inside the C₆₀ fullerene was -13.5 kcal mol^-1 and its magnitude was significantly larger than the latent heat of evaporation of CH₄. Evaluation of vibrational frequencies and polarizabilities of the CH₄@C₆₀ complex revealed that the infrared (IR) and Raman bands of the endohedral CH₄ were essentially "silent" due to the dielectric screening effect of C₆₀, which acted as a molecular Faraday cage. Absorption spectra in the UV-vis domain and ionization potentials of C₆₀ and CH₄@C₆₀ were predicted. They were almost identical. The calculated ¹H/¹³C NMR shifts and spin-spin coupling constants were in very good agreement with experimental data. In addition, reference DLPNO-CCSD(T) interaction energies for complexes with noble gases (Ng@C₆₀; Ng = He, Ne, Ar, Kr) were calculated. The values were compared with those derived from supramolecular MP2/SCS-MP2 calculations and estimates with London-type formulas by Pyykkö and coworkers [Phys. Chem. Chem. Phys., 2010, 12, 6187-6203], and with values derived from DFT-based symmetry-adapted perturbation theory (DFT-SAPT) by Hesselmann & Korona [Phys. Chem. Chem. Phys., 2011, 13, 732-743]. Selected points at the potential energy surface of the endohedral He₂@C₆₀ trimer were considered. In contrast to previous theoretical attempts with the DFT/MP2/SCS-MP2/DFT-SAPT methods, our calculations at the DLPNO-CCSD(T) level of theory predicted the He₂@C₆₀ trimer to be thermodynamically stable, which is in agreement with experimental observations.

Switch chemistry at cryogenic conditions: quantum tunnelling under electric fields

While the influence of intramolecular electric fields is a known feature in enzymes, the use of oriented external electric fields (EEF) to enhance or inhibit molecular reactivity is a promising topic still in its infancy. Herein we will explore computationally the effects that EEF can provoke in simple molecules close to the absolute zero, where quantum tunnelling (QT) is the sole mechanistic option. We studied three exemplary systems, each one with different reactivity features and known QT kinetics: π bond-shifting in pentalene, Cope rearrangement in semibullvalene, and cycloreversion of diazabicyclohexadiene. The kinetics of these cases depend both on the field strength and its direction, usually giving subtle but remarkable changes. However, for the cycloreversion, which suffers large changes on the dipole through the reaction, we also observed striking results. Between the effects caused by the EEF on the QT we observed an inversion of the Arrhenius equation, deactivation of the molecular fluxionality, and stabilization or instantaneous decomposition of the system. All these effects may well be achieved, literally, at the flick of a switch.

Extrapolation in quantum chemistry: Insights on energetics and reaction dynamics

Since there is no exact solution for problems in physics and chemistry, extrapolation methods may assume a key role in quantitative quantum chemistry. Two topics where it bears considerable impact are addressed, both at the heart of computational quantum chemistry: electronic structure and reaction dynamics. In the first, the problem of extrapolating the energy obtained by solving the electronic Schrödinger equation to the limit of the complete one-electron basis set is addressed. With the uniform-singlet-and-triplet-extrapolation (USTE) scheme at the focal point, the emphasis is on recent updates covering from the energy itself to other molecular properties. The second topic refers to extrapolation of quantum mechanical reactive scattering probabilities from zero total angular momentum to any of the values that it may assume when running quasiclassical trajectories, QCT/QM-[Formula: see text]J. With the extrapolation guided in both cases by physically motivated asymptotic theories, realism is seeked by avoiding unsecure jumps into the unknown. Although, mostly review oriented, a few issues are addressed for the first time here and there. Prospects for future work conclude the overview.

Is There a Single Ideal Parameter for Halogen-Bonding-Based Lewis Acidity?

Halogen-bond donors (halogen-based Lewis acids) have now found various applications in diverse fields of chemistry. The goal of this study was to identify a parameter obtainable from a single DFT calculation that reliably describes halogen-bonding strength (Lewis acidity). First, several DFT methods were benchmarked against the CCSD(T) CBS binding data of complexes of 17 carbon-based halogen-bond donors with chloride and ammonia as representative Lewis bases, which revealed M05-2X with a partially augmented def2-TZVP(D) basis set as the best model chemistry. The best single parameter to predict halogen-bonding strengths was the static σ-hole depth, but it still provided inaccurate predictions for a series of compounds. Thus, a more reliable parameter, Ωσ* , has been developed through the linear combination of the σ-hole depth and the σ*(C-I) energy, which was further validated against neutral, cationic, halogen- and nitrogen-based halogen-bond donors with very good performance.

Spin state and reactivity of iron(iv)oxido complexes with tetradentate bispidine ligands

The iron(iv)oxido complex [(bispidine)Fe^IVO(Cl)]⁺is shown by experiment and high-level DLPNO-CCSD(T) quantum-chemical calculations to be an extremely short-lived and very reactive intermediate-spin (S= 1) species.

On the Prediction of Standard Enthalpy of Formation of C2-C4 Oxygenated Species

In this study, to determine an efficient and accurate method for predicting standard enthalpy of formation (Δ_fH^o) of oxygenated species, we calculated Δ_fH^o for several typical C2-C4 oxygenated species using atomization and isodesmic reactions in combination with various quantum chemical methods, including six density functional theory methods, three compound methods, and CCSD(T)/CBS. Compared with experimental values, at the same quantum chemical level, Δ_fH^o values predicted by using isodesmic reactions are more accurate than those using atomization reactions. Comparing various quantum chemical methods when isodesmic reactions are used, the performance of G4 is the best with a mean unsigned deviation (MUE) of 0.3 kcal/mol and a standard deviation (SD) of 0.3 kcal/mol, while M06-2X can predict Δ_fH^o efficiently and accurately with an MUE of 0.6 kcal/mol and SD of 0.5 kcal/mol. Using the best methods we have found, we calculated the enthalpies of formation and other thermodynamic properties for dimethyl carbonate (DMC) and its associated species and then applied them in a DMC combustion model for predicting ignition delay times. Better agreement with the experiments is achieved when the newly computed thermodynamic properties are adopted.

Computational Study of 3d Metals and Their Influence on the Acidity of Methane C-H Bonds

CCSD(T) methods in conjunction with correlation consistent basis sets are used to predict the pK _a for the deprotonation of methane in a 3d metal ion adduct, [M···CH₄]⁺ (M = Sc-Cu), in dimethyl sulfoxide solvent, which is modeled by the SMD continuum solvent model. Results show that the coordination of methane to different M⁺ ions has a substantial difference of ∼27 pK _a units, from most to least acidic, and increases the acidity of the methane C-H bond from ∼8 to 36 pK _a units. Furthermore, even with the omission of the more expensive quadruple and quintuple zeta basis sets in the prediction process, similar trends in pK _a(C-H) as a function of 3d metal ions are exhibited. This research serves to illustrate the substantial effect that metal ion identity has on the acidity of a coordinated hydrocarbon and the utility that correlation consistent basis sets have in lowering the computational cost of modeling larger systems.

Performance of polarization-consistent vs. correlation-consistent basis sets for CCSD(T) prediction of water dimer interaction energy

Detailed study of Jensen’s polarization-consistent vs. Dunning’s correlation-consistent basis set families performance on the extrapolation of raw and counterpoise-corrected interaction energies of water dimer using coupled cluster with single, double, and perturbative correction for connected triple excitations (CCSD(T)) in the complete basis set (CBS) limit are reported. Both 3-parameter exponential and 2-parameter inverse-power fits vs. the cardinal number of basis set, as well as the number of basis functions were analyzed and compared with one of the most extensive CCSD(T) results reported recently. The obtained results for both Jensen- and Dunning-type basis sets underestimate raw interaction energy by less than 0.136 kcal/mol with respect to the reference value of − 4.98065 kcal/mol. The use of counterpoise correction further improves (closer to the reference value) interaction energy. Asymptotic convergence of 3-parameter fitted interaction energy with respect to both cardinal number of basis set and the number of basis functions are closer to the reference value at the CBS limit than other fitting approaches considered here. Separate fits of Hartree-Fock and correlation interaction energy with 3-parameter formula additionally improved the results, and the smallest CBS deviation from the reference value is about 0.001 kcal/mol (underestimated) for CCSD(T)/aug-cc-pVXZ calculations. However, Jensen’s basis set underestimates such value to 0.012 kcal/mol. No improvement was observed for using the number of basis functions instead of cardinal number for fitting.

Reassessment of the Mechanisms of Thermal C-H Bond Activation of Methane by Cationic Magnesium Oxides: A Critical Evaluation of the Suitability of Different Density Functionals

The mechanisms of the thermal reactions of the two iconic magnesium oxide cations MgO^.+ and Mg₂ O₂ ^.+ with methane have been re-evaluated at the CCSD(T)/CBS//CCSD/def2-TZVP level of theory. For the reaction of MgO^.+ with CH₄ , only the classical hydrogen-atom transfer (HAT) was found; in contrast, for the Mg₂ O₂ ^.+ /CH₄ couple, both HAT and proton-coupled electron-transfer (PCET) exist as mechanistic variants. In order to evaluate the suitability of density functional theory (DFT) methods, the reactions were computed by using 27 density functionals. The results obtained demonstrate that the various DFT methods often deliver rather different results for both geometric and energetic features. As to the prediction of the apparent barriers, pure functionals give the largest mean absolute errors. BMK, ωB97XD, and the double-hybrid functional mPW2PLYP were confirmed to come closest to the results provided by CCSD(T)/CBS. Thus, mechanistic conclusions based on a single DFT method should be viewed with great caution. In summary, this study may assist in the selection of a suitable quantum chemical method to unravel the mechanistic details of C-H bond activation by charged metal oxides.

Electron Propagator Theory Approach to the Electron Binding Energies of a Prototypical Photo-Switch Molecular System: Azobenzene

The electron binding energies for the trans and cis conformers of azobenzene (AB), a prototypical photoswitch, were investigated by electron propagator theory (EPT). The EPT results are compared with data from photoelectron and electron transmission spectroscopies and complemented by the calculation of the differences between vertical and adiabatic ionization energies and electron affinities of the AB conformers. These differences are discussed in terms of the geometry changes associated with the processes of ionization and electron attachment. The results pointed out a major difference between these processes when we compare trans-AB and cis-AB. For trans-AB, electron attachment leads to a small geometry change, whereas for cis-AB, it is the ionized structure that keeps some similarity with the neutral species. We emphasize the interest of the present results for a better understanding of recent experiments on the dark cis-trans isomerization in different environments, specifically for azobenzenes in interaction with gold nanoparticles, where the proposed cis-trans isomerization mechanism relies on electron transfer induced isomerization.

Gaussian basis sets for use in correlated molecular calculations. XI. Pseudopotential-based and all-electron relativistic basis sets for alkali metal (K-Fr) and alkaline earth (Ca-Ra) elements

New correlation consistent basis sets based on pseudopotential (PP) Hamiltonians have been developed from double- to quintuple-zeta quality for the late alkali (K-Fr) and alkaline earth (Ca-Ra) metals. These are accompanied by new all-electron basis sets of double- to quadruple-zeta quality that have been contracted for use with both Douglas-Kroll-Hess (DKH) and eXact 2-Component (X2C) scalar relativistic Hamiltonians. Sets for valence correlation (ms), cc-pVnZ-PP and cc-pVnZ-(DK,DK3/X2C), in addition to outer-core correlation [valence + (m-1)sp], cc-p(w)CVnZ-PP and cc-pwCVnZ-(DK,DK3/X2C), are reported. The -PP sets have been developed for use with small-core PPs [I. S. Lim et al., J. Chem. Phys. 122, 104103 (2005) and I. S. Lim et al., J. Chem. Phys. 124, 034107 (2006)], while the all-electron sets utilized second-order DKH Hamiltonians for 4s and 5s elements and third-order DKH for 6s and 7s. The accuracy of the basis sets is assessed through benchmark calculations at the coupled-cluster level of theory for both atomic and molecular properties. Not surprisingly, it is found that outer-core correlation is vital for accurate calculation of the thermodynamic and spectroscopic properties of diatomic molecules containing these elements.

Straightening the Hierarchical Staircase for Basis Set Extrapolations: A Low-Cost Approach to High-Accuracy Computational Chemistry

Because the one-electron basis set limit is difficult to reach in correlated post-Hartree-Fock ab initio calculations, the low-cost route of using methods that extrapolate to the estimated basis set limit attracts immediate interest. The situation is somewhat more satisfactory at the Hartree-Fock level because numerical calculation of the energy is often affordable at nearly converged basis set levels. Still, extrapolation schemes for the Hartree-Fock energy are addressed here, although the focus is on the more slowly convergent and computationally demanding correlation energy. Because they are frequently based on the gold-standard coupled-cluster theory with single, double, and perturbative triple excitations [CCSD(T)], correlated calculations are often affordable only with the smallest basis sets, and hence single-level extrapolations from one raw energy could attain maximum usefulness. This possibility is examined. Whenever possible, this review uses raw data from second-order Møller-Plesset perturbation theory, as well as CCSD, CCSD(T), and multireference configuration interaction methods. Inescapably, the emphasis is on work done by the author's research group. Certain issues in need of further research or review are pinpointed.