A general efficient implementation of the BSSE-free SCF and MP2 methods based on the chemical Hamiltonian approach

We describe some details related to a new, general, and efficient implementation of the BSSE‐free SCF and second‐order Møller–Plesset perturbation theories of intermolecular interactions, based on the “Chemical Hamiltonian Approach” (CHA). The program is applicable for both open‐shell and closed‐shell systems and for an arbitrary number of interacting subsystems. With the new program the CHA method is faster than the usual “counterpoise correction” scheme for single point calculations, especially for clusters consisting of several molecules. The numerical results provided by these conceptually different schemes, however, have again found to be very close to each other. The CHA scheme is particularly good for providing truly BSSE‐free MP2 data for intermolecular potentials. © 2006 Wiley Periodicals, Inc. J Comput Chem 27: 1505–1516, 2006     

BSSE‐corrected geometry and harmonic and anharmonic vibrational frequencies of formamide–water and formamide–formamide dimers

The basis set superposition error (BSSE) influence in the geometry structure, interaction energies, and intermolecular harmonic and anharmonic vibrational frequencies of cyclic formamide–formamide and formamide–water dimers have been studied using different basis sets (6‐31G, 6‐31G**, 6‐31++G**, D95V, D95V**, and D95V++**). The a posteriori “counterpoise” (CP) correction scheme has been compared with the a priori “chemical Hamiltonian approach” (CHA) both at the Hartree–Fock (HF) and second‐order Møller–Plesset many‐body perturbation (MP2) levels of theory. The effect of BSSE on geometrical parameters, interaction energies, and intermolecular harmonic vibrational frequencies are discussed and compared with the existing experimental data. As expected, the BSSE‐free CP and CHA interaction energies usually show less deep minima than those obtained from the uncorrected methods at both the HF and MP2 levels. Focusing on the correlated level, the amount of BSSE in the intermolecular interaction energies is much larger than that at the HF level, and this effect is also conserved in the values of the force constants and harmonic vibrational frequencies. All these results clearly indicate the importance of the proper BSSE‐free correlation treatment with the well‐defined basis functions. At the same time, the results show a good agreement between the a priori CHA and a posteriori CP correction scheme; this agreement is remarkable in the case of large and well‐balanced basis sets. The anharmonic frequency correction values also show an important BSSE dependence, especially for hydrogen bond stretching and for low frequencies belonging to the intermolecular normal modes. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

A BSSE-free SCF algorithm for intermolecular interactions

A very simple modification of the usual (～N⁴) SCF procedure is proposed, permitting the exclusion of basis set superposition errors (BSSE ) in problems of intermolecular interactions. No a posteriori corrections are required. The results of this “CHA /F method” are numerically close to those of the Boys–Bernardi correction scheme but are free from the “overcompensation” characteristic of the latter at smaller distances.     

On the effect of the BSSE on intermolecular potential energy surfaces. Comparison of a priori and a posteriori BSSE correction schemes

A comparative study of geometrical parameters is performed on the complexes HF–HF, H₂O–H₂O, and HF–H₂O using 12 different basis sets at the RHF, MP2, and DFT (BLYP and B3LYP) levels of theory. The equilibrium geometries were obtained from uncorrected, a posteriori (counterpoise, CP) and a priori (Chemical Hamiltonian Approach, CHA) BSSE‐corrected potential energy surfaces. The calculation of equilibrium geometries using the CP and CHA schemes is described in details. The effect of the BSSE on various intermolecular parameters is discussed and the performance of the applied theoretical models is critically evaluated from the BSSE point of view. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 765–786, 2001     

On the non-additivity of the basis set superposition error and how to prevent its appearance

An analytical consideration is made for the simplest possible model in which the BSSE problem may appear. The results demonstrate that BSSE cannot be corrected in any consistent manner by readjusting the monomer energies to the enlarged basis, because the energy effects caused by BSSE and by the true interactions are not additive. The way out is to correct BSSE, or prevent its appearance by an appropriate analysis and special treatment at the supermolecule level, permitting to keep the supermolecule problem consistent with the monomer calculations, as provided by the chemical Hamiltonian approach recently introduced.     

Comparison of basis set superposition error corrected perturbation theories for calculating intermolecular interaction energies

Recently, two different but conceptually similar basis set superposition error (BSSE) free second‐order perturbation theoretical schemes were developed by us that are being based on the chemical Hamiltonian approach (CHA). Using these CHA‐MP2 and CHA‐PT2 methods, a comparison is made between the a posteriori and a priori BSSE correction schemes at the correlated level. Sample calculations are presented for four hydrogen bonded complexes (HFH₃N, HFH₂O, H₂SHF, and H₂OHCl) in nine different basis sets (from 6–31G to TZV**++). The results show that the BSSE content is very significant in the interaction energy if electron correlation is accounted for, so removing the BSSE is very important. The differences of the two perturbational theories discussed are connected solely with the different one electron orbital sets used for building up the unperturbed single determinant wave function. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 274–283, 1999     

Comparison of a posteriori and a priori BSSE correction schemes for SCF intermolecular energies

A systematic SCF study has been undertaken to compare the conventional a posteriori Boys–Bernardi BSSE correction scheme with our recent CHA/F method in which BSSE is excluded in a priori manner. Potential curves have been obtained for nine simple hydrogen-bonded systems by using nine different basis sets for each. It is concluded that the difference between the a posteriori BB and the a priori CHA schemes diminishes much faster when the basis set improves than BSSE disappears from the uncorrected SCF results. This fact gives an additional confidence in the CHA results, permitting one to draw the explicit conclusion that, at the SCF level of theory, the a priori CHA/F scheme can be considered the ultimate solution of the BSSE problem for weakly bonded systems. © 1993 John Wiley & Sons, Inc.     

Improved intermolecular SCF theory and the BSSE problem

Analytical and numerical studies are performed concerning the exclusion of the basis set superposition error (BSSE ) from the SCF calculations of intermolecular interactions. Based on these studies a new procedure is proposed, which consists of the following steps: (1) determine the orbitals by the SCF scheme based on the recent “chemical Hamiltonian approach” (CHA-SCF method), i.e., excluding the delocalization effects caused by BSSE , and then (2) calculate the usual energy expectation value. (This gives results superior to those obtained by the previous nonsymmetric CHA energy formula.) The actual numerical calculations performed for different simple systems (He₂, water dimer) by using various basis sets indicate that the CHA/CE (CHA with “conventional energy” formula) potential curves are well-balanced and are close to those obtained by the Boys–Bernardi (BB ) method and usually (but not necessarily) go slightly beyond the latter. So our method gives results better than (or close to) those given by the BB method by performing only a single ～N⁴ calculation at each geometrical arrangement of the system.     

Intermolecular bond lengths: extrapolation to the basis set limit on uncorrected and BSSE‐corrected potential energy hypersurfaces

Geometry optimizations were carried out for the (HF)₂, (H₂O)₂, and HF–H₂O intermolecular complexes using the MP2/aug‐cc‐pVXZ {X=2, 3, 4, and 5} theoretical models on both the uncorrected and counterpoise (CP) corrected potential energy hypersurfaces (PES). Our results and the available literature data clearly show that extrapolation of intermolecular distances to the complete basis set (CBS) limit is satisfactory on PESs corrected for BSSE. On the other hand, one should avoid such extrapolations using data obtained from uncorrected PESs. Also, fixing intramolecular parameters at their experimental values could cause difficulties during the extrapolation. As the available literature data and our results clearly show, the MP2/aug‐cc‐pVXZ {X=2, 3, 4} data series of intermolecular distances obtained from the CP‐corrected surfaces can be safely used for the purpose of CBS extrapolations. © 2000 John Wiley & Sons, Inc. J Comput Chem 22: 196–207, 2001     

Implementation of gradient-optimization algorithms and force constant computations in BSSE-free direct and conventional SCF approaches

A modification of the Roothaan equations was described in a previous work, which aimed to avoid the BSSE at the Hartree–Fock level of theory. The resulting scheme was called the self-consistent field for molecular interactions (SCF-MI) to underline its special usefulness in the computation of intermolecular interactions. The method provides a complete a priori elimination of the BSSE, while taking into account the natural nonorthogonality of the MOs of the two interacting fragments. Compatibility with the usual formulation of the analytic derivatives of the SCF energy is also guaranteed. This allowed the implementation of gradient-optimization algorithms and force constant matrix computations in both the direct and conventional SCF approaches. The SCF-MI method has been incorporated into the GAMESS-US package. Tests have been performed at the Department of Chemistry of the Iowa State University. Increases in the complication and computation time are minimal if compared to standard SCF codes and the method shows much less basis-set dependence in the predicted molecular properties. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 151–158, 1998     

A BSSE-free SCF algorithm for intermolecular interactions. II. Sample calculations on hydrogen-bonded complexes

The usefulness and reliability of the recent BSSE -free SCF algorithm based on the “chemical Hamiltonian approach” (CHA /F ) is demonstrated by calculating potential curves for several hydrogen-bonded complexes with 4-31G , 6-31G , and 6-31G ** basis sets. It is concluded that the CHA /F scheme gives results that are numerically close to those of the Boys–Bernardi a posteriori correction scheme but are free from the “overcompensation” characteristic of the latter at smaller distances and given basis sets. © 1992 John Wiley & Sons, Inc.     

Ab initio investigation on stability and properties of XYCO... HZ complexes. II: Post hartree-fock studies on H2CO... HF

Ab initio MP2 level of theory in conjunction with three basis sets of a triple-zeta quality was applied to study the molecular geometry and stability of the H₂CO... HF complex. An interaction energy predicted for this system at the highest, MP4(SDTQ)/6-311 + +G(2df, 2pd)//MP2/6-311 + +G(2df, 2pd), level corrected for the BSSE and ZPE contributions amounts to -4.85 kcal/ mol. BSSE contributes significantly to the interaction energies at all applied levels. Reliable MP2/ 6-311 + +G(2df, 2pd) level harmonic vibrational frequencies, IR intensities, and the predicted isotopic shifts upon deuteration and¹⁸O substitution are presented in order to facilitate experimental studies on the IR spectrum of the title complex.     

Counterpoise estimates of the BSSE in the evaluation of protonation energies

Counterpoise estimates of the BSSE in the evaluation of protonation energies have been calculated for basis sets ranging from minimal to split-valence plus polarization quality. Three-, five- and six-membered-ring heterocycles have been chosen as suitable model compounds for this study. Counterpoise corrections are significant, at the minimal basis set and 3–21G levels, when considering both, absolute and relative protonation energies and depend on the nature of the centre which undergoes protonation. In general, second- and third-order counterpoise corrections to the protonation energies are comparable to the corresponding SCF values. BSSE depend not only on the size of the basis sets but also on their quality. The presence in the basis of quite diffuse functions (either sp or d) leads to lower protonation energies and greater BSSE. Relative protonation energies are not substantially affected by BSSE or correlation effects.     

Comment on "aromatic-backbone interactions in model alpha-helical peptides" [Palermo et al., J Comput Chem 2007, 28, 1208

Palermo et al. have recently published a method to correct for intramolecular basis set superposition errors (J Comput Chem 2007, 28, 1208) in intramolecular interactions occurring in peptides. By considering the intermolecular equivalent of this method, it is shown that the method presented by Palermo et al. underestimates the magnitude of the intramolecular BSSE.     

Combined bond-polarization basis sets for accurate determination of dissociation energies

Summary The effect of bond functions on the basis set superposition error (BSSE) is investigated at both SCF (self consistent field) and correlated levels for a number of basis sets using the pairwise additive function counterpoise (PAFC), the site-site function counterpoise (SSFC), and the newly proposed successive reaction counterpoise method (SRCP). BSSEs using bond functions are shown to be roughly twice those without bond functions, whereas the latter may still be quite sizeable. The addition of f functions dramatically decreases the bond function BSSE. The results obtained support the empirical decision in our earlier papers to neglect BSSE altogether.     

Atom transfer radical polymerization of acrylates in an ionic liquid: Synthesis of block copolymers

Atom transfer radical polymerization (ATRP) of acrylates in ionic liquid, 1‐butyl‐3‐methylimidazolium hexaflurophospate, with the CuBr/CuBr₂/amine catalytic system was investigated. Sequential polymerization was performed by synthesizing AB block copolymers. Polymerization of butyl acrylate (monomer that is only partly soluble in an ionic liquid forming a two‐phase system) proceeded to practically quantitative conversion. If the second monomer (methyl acrylate) is added at this stage, polymerization proceeds, and block copolymer formed is essentially free of homopolymer according to size exclusion chromatographic analysis. The number‐average molecular weight of the copolymer is slightly higher than calculated, but the molecular weight distribution is low (M_w/M_n = 1.12). If, however, methyl acrylate (monomer that is soluble in an ionic liquid) is polymerized at the first stage, then butyl acrylate in the second‐stage situation is different. Block copolymer free of homopolymer of the first block (with M_w/M_n = 1.13) may be obtained only if the conversion of methyl acrylate at the stage when second monomer is added is not higher than 70%. Matrix‐assisted laser desorption/ionization time‐of‐flight analysis confirmed that irreversible deactivation of growing macromolecules is significant for methyl acrylate polymerization at a monomer conversion above 70%, whereas it is still not significant for butyl acrylate even at practically quantitative conversion. These results show that ATRP of butyl acrylate in ionic liquid followed by addition of a second acrylate monomer allows the clean synthesis of block copolymers by one‐pot sequential polymerization even if the first stage is carried out to complete conversion of butyl acrylate. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 2799–2809, 2002     

Chiral Triazolium Salts and Ionic Liquids: From the Molecular Design Vectors to Their Physical Properties through Specific Supramolecular Interactions

An exhaustive experimental study based on X‐ray diffraction analysis, NMR, FTIR‐ATR (attenuated total reflection), and Raman spectroscopy as well as theoretical calculations is reported in order to understand how the non‐covalent intermolecular contacts are fundamental to explain structure–property relationships and allowing us to correlate a basic macroscopic property (i.e., the melting point, T_m) with the structural variables of a family of enantiopure 1,4‐dialkyl‐1,2,4‐triazolium salts. The effect of different structural vectors such as the ring size, the spatial disposition of the substituent, the substitution on the oxygen atom, the nature of the anion, or the N4 alkylation of the triazole on the intermolecular interactions of these chiral salts of a well‐defined 3D structure is reported. The non‐covalent intermolecular contacts mainly implicating the triazolium H3 proton are fundamental to explain structure–property relationships and, therefore, the physical properties of these new chiral salts, rather than simple anion–cation interactions. Overall, our findings highlight the importance of the specific supramolecular interactions for the understanding of the physical properties of triazolium salts and ionic liquids.     

Density Functional Theory Studies on Intermolecular Interactions of 4‐Amino‐3,5‐dinitropyrazole with NH3 and H2O

Density functional theory (DFT) method with 6‐311++G** basis set was applied to study intermolecular interactions of 4‐amino‐3,5‐dinitropyrazole (LLM‐116)/NH₃ and LLM‐116/H₂O supermolecules. Four optimized stable supermolecules were found on the potential energy surface. The intermolecular interaction energy was calculated with basis set superposition error (BSSE) correction and zero point energy (ZPE) correction. The greatest corrected intermolecular interaction energies of LLM‐116/NH₃ and LLM‐116/H₂O supermolecules are –42.75 and –19.09 kJ×mol^‐1 respectively, indicating that the intensity of interaction between LLM‐116 and NH₃ is stronger than that of LLM‐116/H₂O. The intermolecular interaction is an exothermic process accompanied by a decrease in the probability of supermolecules formation, and the interactions become weak as temperature increase. Natural bond orbital (NBO) analysis was performed to reveal the origin of interaction. The IR spectra were obtained and assigned by vibrational analysis. Based on vibrational analysis, the changes of thermodynamic properties from LLM‐116 to supermolecules with temperature ranging from 200.0 to 400.0 K were obtained using statistical thermodynamic method.     

Intramolecular Cyclization of Carbonate and Thiocarbonate Derivatives of myo‐Inositol in the Solid State: Implications for Acyl Group Transfer Reactions in Molecular Crystals

Racemic 4‐O‐phenoxycarbonyl and 4‐O‐phenoxythiocarbonyl derivatives of myo‐inositol orthoformate undergo thermal intramolecular cyclization in the solid state to yield the corresponding 4,6‐bridged carbonates and thiocarbonates, respectively. The thermal cyclization also occurs in the solution and molten states, but less efficiently, suggesting that these cyclization reactions are aided by molecular pre‐organization, although not strictly topochemically controlled. Crystal structures of two carbonates and a thiocarbonate clearly revealed that the relative orientation of the electrophile and the nucleophile in the crystal lattice facilitates the intramolecular cyclization reaction and forbids the intermolecular reaction. The correlation observed between the chemical reactivity and the non‐covalent interactions in the crystal of the reactants provides a way to estimate the chemical stability of analogous molecules in the solid state.