Dimerization Energies Research Articles

Evaluating Binding Affinities of Dimerization of Bar Proteins in Solution and on Membrane Surface

Membrane remodeling is a crucial process for various cellular pathways like signaling, viral assembly and clathrin-mediated endocytosis. This process is governed by a network of protein-protein interactions that perform specific tasks with high spatial and temporal accuracy. An important type of these proteins is the BAR domain family, proteins of which, self-assemble on the membrane surface and induce curvature. The localization of proteins to the 2D membrane surface from 3D solution reduces their search space, and our lab has shown how proteins can exploit this dimensionality reduction to trigger self-assembly. Further, the dimerization of BAR proteins, which is crucial in mediating protein-protein and protein-lipid interactions, is poorly understood from a quantitative perspective. We address this gap by applying Molecular Dynamics simulations to investigate the thermodynamics of binding in solution and on membrane surface. We employ metadynamics to evaluate the free energy of protein dimerization and obtain the binding affinity (KD). In addition, we aim to deconvolute the energetic and entropic contributions to the binding process and characterize the intermediate pathways of dimerization. Our results would quantify the role of dimensionality reduction on the binding affinity and also contribute to the theoretical framework of our reaction-diffusion software, NERDSS, that enables self-assembly simulations of a broad range of biological systems.

A Quadratic Pair Atomic Resolution of the Identity Based SOS-AO-MP2 Algorithm Using Slater Type Orbitals

We report a production level implementation of pair atomic resolution of the identity (PARI) based second-order Møller–Plesset perturbation theory (MP2) in the Slater type orbital (STO) based Amsterdam Density Functional (ADF) code. As demonstrated by systematic benchmarks, dimerization and isomerization energies obtained with our code using STO basis sets of triple-ζ-quality show mean absolute deviations from Gaussian type orbital, canonical, basis set limit extrapolated, global density fitting (DF)-MP2 results of less than 1 kcal/mol. Furthermore, we introduce a quadratic scaling atomic orbital based spin-opposite-scaled (SOS)-MP2 approach with a very small prefactor. Due to a worst-case scaling of , our implementation is very fast already for small systems and shows an exceptionally early crossover to canonical SOS-PARI-MP2. We report computational wall time results for linear as well as for realistic three-dimensional molecules and show that triple-ζ quality calculations on molecules of several hundreds of atoms are only a matter of a few hours on a single compute node, the bottleneck of the computations being the SCF rather than the post-SCF energy correction.

Magnetic anisotropy of iridium dimers on two-dimensional materials.

Magnetic dimers with very large magnetic anisotropy have great potential in information storage applications. By using density functional theory calculations (DFT), we systematically investigated the magnetic anisotropy energy (MAE) of bi-iridium (Ir2) dimers on four types of graphene-like two-dimensional (2D) material substrates. We considered four possible adsorption sites for Ir2 on each substrate. The Ir2 dimer prefers to remain at the single vacancy site with the largest binding energy for all the 2D materials considered. The spin moment and MAE of Ir2 can be largely affected by the substrate. On the substrate of germanene, the MAE of Ir2 can be enlarged to approximately 100 meV, even with the higher Ir2 areal density of 1.804 nm-2. Moreover, the direction of the easy magnetization axis is determined by the d states in the vicinity of the Fermi level. The present DFT results can be understood with the help of perturbation theory analysis.

DFT study of formation and properties of dinuclear zirconocene cations: Effects of ligand structure, solvent, and metal on the dimerization process

Density functional theory calculations were performed to determine the stability and properties of the formation of dinuclear zirconocene cation [(Cp2ZrMe)2(μ-Me)]+, a species formed during metallocene/cocatalyst (e.g., B(C6F5)3 or MAO) activated polymerization. To improve the catalytic system by minimizing catalyst dimerization, knowledge on the geometric and electronic properties of the process is required. Here, a series of metallocene catalysts were analyzed as a function of their ligand structures, solvent and metal. Two different isomers (cis and trans) of the dimer were considered. The results show that in general the dimer structure in trans form is more stable than in the cis form. Changing ligand structures tend to destabilize the dimerization process, which is influenced by the steric hindrance on the ligand. The stability of the dimer structure is greatly affected by the choice of solvent polarity, i.e., the more polar solvent the less stability of the dimer. Substitution of Zr into Hf also shows the same trend with a more stable dimer. Vibrational frequencies were calculated for the dimers and the changes in frequencies of the Zr-(μ-Me) stretching vibration were found to correlate well with the dimerization energies (R2 = 0.88). Our study might facilitate future catalyst design in metallocene-mediated cationic polymerization.

New approaches to assessing the stability of carbenes

Carbenes are known to be highly reactive compounds, which can, in turn, spontaneously transform to dimers and products of rearrangements. Therefore, the question about the estimation of stability of carbenes is fundamental in the design of compounds for their subsequent synthesis and application.Aim. To consider the known methods for assessing the stability and stabilization of carbenes, first of all, created by the authors of the article, and show their possibilities in predicting the properties of carbenes.Materials and methods. The study was performed using the DFT method (B3LYP5, 6-311G**, RHF) to estimate the stabilization energies, and the DFT (B3LYP5, 6-31G, RHF) to obtain dimerization energies.Results and discussion. The ways of solving the problem of stability of carbenes by the methods of quantum chemistry are discussed, in particular the application of new criteria for the stabilization of cyclic compounds – energies of the general and cyclic stabilization, energies of non-aromatic conjugations. To assess the possibility of isolating compounds the study of standard dimerization enthalpies (according to the ESP electronic and steric parameter proposed) for different classes of heterocyclic carbenes has been performed taking into account conformational factors. The scale of substituent effects on the stability of carbenes has been developed. It has been shown that sterically shielding substituents cause not only the kinetic stabilization, but also the thermodynamic one. The skeletons of the molecules have been estimated for their degree of influence on the stability of the compounds.Conclusions. The parameters proposed for assessing the energies of the total and cyclic stabilization of carbenes, the dimerization energies of complex carbenes (electronic and steric parameter) allow identifying the most stable structures in the design of compounds for their subsequent synthesis and application.

Molecular structure of β-oxy-bis-acrylamides on the pathway of the dimers formation. DFT and FTIR study

Abstract Conformational isomers of β-oxy-bis-acrylamides O(CH=CHCONR1R2)2 and their dimers were calculated with DFT methods using NBO and QTAIM analysis. The low rotational barriers about the =С–С= and =C–O– bonds in monomers provide ease of their transitions and simultaneous participation in the formation of dimers. The calculated dissociation energies of dimers depend on the structural features of the conformers and PA values of the carbonyl oxygen. The cyclic dimers with three and two intermolecular N–H⋯O C bonds are the most stable. The influence of the orbital interaction of lone pair of nitrogen with carbonyl group on the proton affinity of the conformers was analyzed. The structures of compounds and their dimers were analyzed in solid state and in solutions at comparing of FTIR spectroscopy and calculated data. X-ray analysis of β-oxy-bis-N,N′-dimethylacrylamide was carry out.

New Insight into an Old Problem: Analysis, Interpretation, and Theoretical Modeling of the Absorption and Magnetic Circular Dichroism Spectra of Monomeric and Dimeric Zinc Phthalocyanine Cation Radical.

The chemically or spectroelectrochemically generated formation and aggregation of zinc(II) tetra-tert-butylphthalocyanine cation radical [ZnPctBu]+•, which was highly soluble in common organic solvents, were investigated using UV-vis and magnetic circular dichroism (MCD) spectroscopies with an emphasis on the influence of the axial ligand on the fingerprint (∼500 nm) and NIR (720∼1000 nm) spectral envelopes. MCD spectroscopy is suggestive that the NIR band at ∼1000 nm observed for the antiferromagnetically coupled cation radical dimer, [ZnPctBu]22+, has no degeneracy, the monomer-dimeric equilibrium is temperature dependent, and higher degree aggregates can be formed at specific conditions. Sixteen different exchange-correlation functionals were tested to accurately predict the energies, intensities, and profiles of the UV-vis and MCD spectra of the phthalocyanine cation radical monomer and dimer. It was found that the M05 exchange-correlation functional (along with several other functionals that include 27-42% of Hartree-Fock exchange) provided an excellent agreement (∼0.1 eV for the degenerate excited states observed by MCD spectroscopy) between theory and experiment for the phthalocyanine cation-radical monomer and dimer. Not only did time-dependent density functional theory (TDDFT) calculations with M05 exchange-correlation functional correctly predict the nondegenerate NIR charge-transfer band at ∼1000 nm, all degenerate excited states, monomer and dimer energies, and oscillator strengths, but also they correctly described the nature of the experimentally observed at ∼500 nm MCD B-term (fingerprint band) detected for both the monomeric and dimeric phthalocyanine cation radicals. The TDDFT data explain the similarities in the UV-vis and MCD spectra of the monomeric and dimeric species observed between the UV and fingerprint spectral envelopes as well as correctly predicted the antiferromagnetic coupling between the two singly oxidized phthalocyanine macrocycles in the dimer.

Pathogenicity of new BEST1 variants identified in Italian patients with best vitelliform macular dystrophy assessed by computational structural biology

BackgroundBest vitelliform macular dystrophy (BVMD) is an autosomal dominant macular degeneration. The typical central yellowish yolk-like lesion usually appears in childhood and gradually worsens. Most cases are caused by variants in the BEST1 gene which encodes bestrophin-1, an integral membrane protein found primarily in the retinal pigment epithelium.MethodsHere we describe the spectrum of BEST1 variants identified in a cohort of 57 Italian patients analyzed by Sanger sequencing. In 13 cases, the study also included segregation analysis in affected and unaffected relatives. We used molecular mechanics to calculate two quantitative parameters related to calcium-activated chloride channel (CaCC composed of 5 BEST1 subunits) stability and calcium-dependent activation and related them to the potential pathogenicity of individual missense variants detected in the probands.ResultsThirty-six out of 57 probands (63% positivity) and 16 out of 18 relatives proved positive to genetic testing. Family study confirmed the variable penetrance and expressivity of the disease. Six of the 27 genetic variants discovered were novel: p.(Val9Gly), p.(Ser108Arg), p.(Asn179Asp), p.(Trp182Arg), p.(Glu292Gln) and p.(Asn296Lys). All BEST1 variants were assessed in silico for potential pathogenicity. Our computational structural biology approach based on 3D model structure of the CaCC showed that individual amino acid replacements may affect channel shape, stability, activation, gating, selectivity and throughput, and possibly also other features, depending on where the individual mutated amino acid residues are located in the tertiary structure of BEST1. Statistically significant correlations between mean logMAR best-corrected visual acuity (BCVA), age and modulus of computed BEST1 dimerization energies, which reflect variations in the in CaCC stability due to amino acid changes, permitted us to assess the pathogenicity of individual BEST1 variants.ConclusionsUsing this computational approach, we designed a method for estimating BCVA progression in patients with BEST1 variants.

Revisiting the Potential Energy Surface of the Stacked Cytosine Dimer: FNO-CCSD(T) Interaction Energies, SAPT Decompositions, and Benchmarking

Nucleobase stacking interactions are crucial for the stability of nucleic acids. This study investigates base stacking energies of the cytosine homodimer in different configurations, including intermolecular separation plots, detailed twist dependence, and displaced structures. Highly accurate ab initio quantum chemical single point energies using an energy function based on MP2 complete basis set extrapolation ([6 → 7]ZaPa-NR) and a CCSD(T)/cc-pVTZ-F12 high-level correction are presented as new reference data, providing the most accurate stacking energies of nucleobase dimers currently available. Accurate SAPT2+(3)δMP2 energy decomposition is used to obtain detailed insights into the nature of base stacking interactions at varying vertical distances and twist values. The ab initio symmetry adapted perturbation theory (SAPT) energy decomposition suggests that the base stacking originates from an intricate interplay between dispersion attraction, short-range exchange-repulsion, and Coulomb interaction. The interpretation of the SAPT data is a complex issue as key energy terms vary substantially in the region of optimal (low energy) base stacking geometries. Thus, attempts to highlight one leading stabilizing SAPT base stacking term may be misleading and the outcome strongly depends on the used geometries within the range of geometries sampled in nucleic acids upon thermal fluctuations. Modern dispersion-corrected density functional theory (among them DSD-BLYP-D3, ωB97M-V, and ωB97M-D3BJ) is benchmarked and often reaches up to spectroscopic accuracy (below 1 kJ/mol). The classical AMBER force field is benchmarked with multiple different sets of point-charges (e.g. HF, DFT, and MP2-based) and is found to produce reasonable agreement with the benchmark data.

New mild amphoteric sulfohydroxybetaine-type surfactants containing different labile spacers: Synthesis, surface properties and performance

HypothesisThe excellent performance of zwitterionic alkylamide-type surfactants may be tuned by slight modifications of their structures, especially concerning linking groups between hydrophilic and hydrophobic moieties and the moderation of strong NH hydrogen bonds via the introduction of a methyl group attached to the nitrogen. ExperimentsThe influence of the structure of alkylamidehydroxysulfobetaine-type surfactants on their adsorption and micellization, lime soap dispersing ability, wettability, as well as antimicrobial and hemolytic activities was studied in this work. We synthesized a series of novel surfactants with labile CON(Me)CH2 or CH2N(Me) CO spacers that were adjacent to the hydrophobic tail CnH2n+1 and separated from the zwitterionic hydroxysulfobetaine headgroup by C3H6 or C2H4 linkers, i.e., [(3-alkanoyilomethyoamine)propyl] dimethylammonium 2-hydroxypropanesulfonates (CnTMDAS) and [3-(alkylmetyloamino)-3-oxopropyl] dimethylammonium 2-hydroxypropanesulfonates (CnDMPAS), respectively. FindingsThe CnTMDAS surfactants showed slightly higher surface activity and lower CMC than the respective CnDMPAS with the same number of carbon atoms. Moreover, the CnTMDAS series exhibited significantly higher lime soap dispersing abilities and softer interactions with biological systems than CnDMPAS. The molecular modeling computations revealed that the difference in surface activity originated from lower dipole moment of CnTMDAS, hence, lower polarity, whereas higher free energy of dimerization of those surfactants with oleic acid may account for the favorable formation of mixed micelles.

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.Graphical

Theoretical study on wetting behavior of B-SWNT: Effects of doping concentration

Wettability is a key property of single-walled carbon nanotubes (SWNTs), governed both by the chemical composition and geometrical microstructure of the contact surface. Wettability of SWNTs can be enhanced via doping with heteroatoms such as boron or nitrogen to tune the electronic properties of SWNTs. We investigated the adsorption of the water monomer and dimer on pristine and B-doped (5,5) SWNTs by first-principles calculations. The calculated adsorption energy of the water monomer and dimer on pristine (5,5) SWNTs was low. The water dimer can form BO dative bonds with B-doped (5,5) SWNTs, enhancing interactions among each other. A higher adsorption energy of the water dimer was obtained with higher B-doping concentration. Additionally, electronic property analysis showed electron transfer from the water dimer to the boron of the SWNT, forming a BO dative bond, then from the SWNT to the water dimer through an OH⋯π interaction. The interactions between water dimer and SWNT are strongly cooperative. We further compared the adsorption energies of the water dimer and trimer on B-doped SWNTs with their cohesive energies. The adsorption energies increase due to cooperative effects, thereby enhancing wettability. We can expect that B-doped SWNTs can efficiently improve the wettability of carbon nanotubes.

Effect of Structure on the Spin Switching and Magnetic Bistability of Solid-State Aryl Dicyanomethyl Monoradicals and Diradicals.

Stable organic radicals with switchable spin states have applications in medicine, biology, and material science. An emerging class of such spin-switchable radicals is based on dicyanomethyl radicals, which are typically thermally and air-stable species that form weakly bonded (closed-shell singlet) dimers at a lower temperature that rupture into electron paramagnetic resonance-active diradicals at a higher temperature. However, thus far, the study of these dicyanomethyl radicals has focused on their solution-phase behavior. An understanding of how chemical structure affects the solid-state spin switching behavior for these radicals is unknown. Here, we examine the solid-state spin crossover behavior of 6 monoradicals and 10 tethered diradicals and demonstrate that these species also undergo spin switching in the solid state. We find that the susceptibility for solid-state spin switching for the intermolecular dimers is weakly correlated to the solution-phase Gibbs free energies of dimerization, but no apparent correlations are seen between the solution-state free energies for the intramolecular dimerization and the solid-state behavior. Furthermore, intramolecular diradical dimers have greatly enhanced temperature-responsive behavior compared to their intermolecular counterparts. Crystalline and amorphous powders of the same radicals feature similar spin switching behavior, but the crystalline materials have slower bond-rupture kinetics at higher temperatures, suggesting that solid-state packing effects are an important kinetic consideration. An interesting feature of these systems is that, upon cooling down to room temperature after heating, some radicals remain trapped in the solids, indicating magnetic bistability, while others partially or fully return to the diamagnetic dimers. This work provides insights into how chemical structure affects spin crossover in the solid state for this new class of air-stable radicals, the knowledge of importance for the construction of dynamically responsive solid-state materials, and organic spin crossover polymers.

Method for Fast Estimation of Lattice Distortion Energy in Organic Semiconductors

The efficient operation of organic electronic devices requires a high mobility of charge carriers in their active layers. According to modern concepts, the charge mobility in the best organic semiconductors is limited by dynamic disorder, i.e., fluctuations of intermolecular charge transfer integrals caused by the nonlocal electron–phonon coupling and thermal motion of molecules. However, the estimate of nonlocal electron–phonon coupling currently requires time- and resource-consuming methods, which complicates the search for high-mobility organic semiconductors among numerous candidates. In this work, a method has been proposed to rapidly estimate the lattice distortion energy, which is the main characteristic of the nonlocal electron–phonon coupling, by comparing the reorganization energies of molecules and molecular dimers. The determined lattice distortion energies are in good agreement with the values previously obtained by other methods. Furthermore, the proposed method has allowed addressing the effect of intermolecular delocalization on the nonlocal electron–phonon coupling. The results obtained indicate that the proposed approach is promising for the efficient search for organic semiconductors with a weak nonlocal electron–phonon coupling and a high charge mobility.

BSSE-correction scheme for consistent gaussian basis sets of double- and triple-zeta valence with polarization quality for solid-state calculations.

Revised versions of our published pob-TZVP [Peintinger, M. F.; Oliveira, D. V. and Bredow, T., J. Comput. Chem., 2013, 34 (6), 451-459.] and unpublished pob-DZVP basis sets, denoted as pob-TZVP-rev2 and pob-DZVP-rev2, have been derived for the elements HBr. It was observed that the pob basis sets suffer from the basis set superposition error (BSSE). In order to reduce this effect, we took into account the counterpoise energy of hydride dimers as an additional parameter in the basis set optimization. The overall performance, portability, and SCF stability of the resulting rev2 basis sets are significantly improved compared to the original pob basis sets. © 2019 Wiley Periodicals, Inc.

A Quantum Chemistry Approach Based on the Analogy with π-System in Polymers for a Rapid Estimation of the Resonance Wavelength of Nanoparticle Systems.

In this paper, the Variational Method based on the Hückel Theory is applied to NPs chain and aggregate systems in order to estimate the energy of the plasmon and, in turn, the resonance wavelength shift, which is caused by the interaction of adjacent NPs. This method is based on the analogies of NPs dipole interactions and the π-system in molecules. Differently from the Hartree-Fock method that is a self-consistent model, in this approach, the input data that this method requires is the dimer energy shift with respect to single NPs. This enables us to acquire a simultaneous estimation of the wavefunctions of the NPs system as well as the expectation energy value of every kind of NPs system. The main advantage of this approach is the rapid response and ease of application to every kind of geometries and spacing from the linear chain to clusters, without the necessity of a time-consuming calculation. The results obtained with this model are closely aligned to related literature and open the way to further development of this methodology for investigating other properties of NPs systems.

The four-helix bundle in cholinesterase dimers: Structural and energetic determinants of stability

The crystal structures of truncated forms of cholinesterases provide good models for assessing the role of non-covalent interactions in dimer assembly in the absence of cross-linking disulfide bonds. These structures identify the four-helix bundle that serves as the interface for formation of acetylcholinesterase and butyrylcholinesterase dimers. Here we performed a theoretical comparison of the structural and energetic factors governing dimerization. This included identification of inter-subunit and intra-subunit hydrogen bonds and hydrophobic interactions, evaluation of solvent-accessible surfaces, and estimation of electrostatic contributions to dimerization. To reveal the contribution to dimerization of individual amino acids within the contact area, free energy perturbation alanine screening was performed. Markov state modelling shows that the loop between the α13 and α14 helices in BChE is unstable, and occupies 4 macro-states. The order of magnitude of mean first passage times between these macrostates is ~10−8 s. Replica exchange molecular dynamics umbrella sampling calculations revealed that the free energy of human BChE dimerization is −15.5 kcal/mol, while that for human AChE is −26.4 kcal/mol. Thus, the C-terminally truncated human butyrylcholinesterase dimer is substantially less stable than that of human acetylcholinesterase. An animated Interactive 3D Complement (I3DC) is available in Proteopedia at http://proteopedia.org/w/Journal:CHEMBIOINT:1.

Apolipoprotein A1 Forms 5/5 and 5/4 Antiparallel Dimers in Human High-density Lipoprotein

Apolipoprotein A1 (APOA1), the major protein of high-density lipoprotein (HDL), contains 10 helical repeats that play key roles in protein-protein and protein-lipid interactions. The current structural model for HDL proposes that APOA1 forms an antiparallel dimer in which helix 5 in monomer 1 associates with helix 5 in monomer 2 along a left-left (LL5/5) interface, forming a protein complex with a 2-fold axis of symmetry centered on helix 5. However, computational studies suggest that other orientations are possible. To test this idea, we used a zero-length chemical cross-linking reagent that forms covalent bonds between closely apposed basic and acidic residues. Using proteolytic digestion and tandem mass spectrometry, we identified amino acids in the central region of the antiparallel APOA1 dimer of HDL that were in close contact. As predicted by the current model, we found six intermolecular cross-links that were consistent with the antiparallel LL5/5 registry. However, we also identified three intermolecular cross-links that were consistent with the antiparallel LL5/4 registry. The LL5/5 is the major structural conformation of the two complexes in both reconstituted discoidal HDL particles and in spherical HDL from human plasma. Molecular dynamic simulations suggest that that LL5/5 and LL5/4 APOA1 dimers possess similar free energies of dimerization, with LL5/5 having the lowest free energy. Our observations indicate that phospholipidated APOA1 in HDL forms different antiparallel dimers that could play distinct roles in enzyme regulation, assembly of specific protein complexes, and the functional properties of HDL in humans.

Discovering new M-quinolate materials: theoretical insight into understanding the charge transport, electronic, self-aggregation properties in M-quinolate materials (M = Li, Na, K, Rb, Cs, Cu, Ag, and Au)

A series of M-quinolate complexes were theoretically investigated to understand the effect of metal ions on electronic and charge transport properties by employing density functional theory simulation. It was found that both electronic and carrier transport properties in M-quinolate materials significantly depend on singly oxidized metal ions. In particular, Csq apparently showed an excellent advantage over other M-quinolate materials (M = Li, Na, K, Rb, Cs, Cu, Ag, and Au) in terms of electron mobility and injection. In addition, the dimerization and vertical detachment energies of all M-quinolate materials were compared to understand self-aggregation effect on carrier transport. As a result, it is expected that Csq is not only likely to be present in dimer form, but also reduce the density of electron traps in electron transporting materials.

Size consistency and counterpoise correction in explicitly correlated calculations of interaction energies and interaction-induced properties

Explicitly correlated calculations of interaction energies with wave functions that include all interparticle distances have suffered so far from the lack of size-consistency resulting from the difficulty to define monomer energies corresponding to the applied dimer basis. As a consequence it has not been possible to obtain interaction energies vanishing at infinite intermonomer distance $R$. This has dramatically reduced the accuracy of calculations at distances where the error in the dimer energy was comparable with the interaction energy itself. The same problem occurs in calculations of interaction-induced properties. In this communication we show how to circumvent this difficulty and obtain interaction energies or interaction-induced properties that vanish at large $R$. This is achieved by relaxing the Pauli principle in the diagonalization of the Hamiltonian of noninteracting monomers. The basis functions used for this diagonalization belong to the representation of the permutation group of the dimer induced by the product of representations appropriate for the monomer spin states. Nonlinear parameters of the basis set are optimized only for the dimer in the Pauli-allowed sector of the Hilbert space. In this way, one obtains $R$-dependent energy of noninteracting monomers and the corresponding interaction energy includes a counterpoise correction for the basis set superposition error. The efficiency of this procedure is demonstrated for the interaction of two hydrogen atoms where accurate reference data are known.