Counterpoise Corrected Binding Energies Research Articles

A DFT study of inclusion complexes of substituted calix[n]arenes with dasatinib and lapatinib

Herein, we have presented the results of Density Functional Theory (DFT) based calculations of inclusion complexes of lapatinib and dasatinib with calix[n]arene macrocycles. A total of 48 calix [n]arene complexes were modeled via considering varied ring sizes (n = 4,5,6,8) and upper-rim functionalization viz. SO3H, tert-Butyl, iso-Propyl, COOH, C2H5OH, and C2H5NH2. From the results of multilevel molecular docking, DFT energetics, and reactivity descriptors; it has been demonstrated that dasatinib form optimal complexes with calix 4f, 3f (−35 to −40 kcal/mol). Moreover, for lapatinib, hosts 3f, 4a, 1f, 3d have the capability to generate promising complexes (>35 kcal/mol). Based on counterpoise corrected binding energies (Ebind) and global reactivity descriptors, we anticipate that the proposed complexes can vitally be used as analogous to carrier-mediated-drug-delivery.

Adsorption of quaternary amine surfactants and their penetration into the intracrystalline cavities of sepiolite

Organoclays are very important composite materials used in many diverse industries including plastics and paint. In this study, an organoclay was formed using sepiolite and homologs of quaternary amine surfactants of tetradecyl dimethyl ethylbenzyl ammonium chloride (TDEBAC), hexadecyl dimethyl ethylbenzyl ammonium chloride (HDEBAC) and octadecyl dimethyl ethylbenzyl ammonium chloride (ODEBAC). Adsorption isotherms of sepiolite/quaternary amine surfactants show that the surfactant with the longest chain, ODEBAC, is adsorbed at most onto the surface of sepiolite. FTIR spectroscopy of organosepiolite indicated that spectroscopic features related to the surface and tunnel of sepiolite are notably modified in the presence of surfactants. In addition to these experiments, high level ab initio counter-poise corrected binding energy computations at MP2, SCS-MP2, B97-D and B2PLYP-D levels of theory employing the TZVP basis set were also performed. At all levels, basal interaction of the surfactant at the surface of sepiolite was found to exhibit the most favourable configuration. Furthermore, penetration of the surfactant into the intra-crystalline cavities of sepiolite was also found to be plausible.

On the incremental evaluation of BSSE-free interaction energies

A recently proposed approximate procedure to calculate directly the BSSE-free binding energy of a H 2S–benzene complex within the incremental scheme for the evaluation of correlation contributions is tested for the dimers of helium, methane, water and hydrogen sulfide at the coupled cluster level. The counterpoise corrected binding energy as well as the basis set extrapolated binding energy are evaluated in conventional manner and compared to results obtained with the recently proposed scheme. Furthermore the basis set dependence of the results is monitored. It is demonstrated that the new proposal is not generally applicable and in particular that larger basis sets do not improve the accuracy of the results.

Calculating interaction energies in transition metal complexes with local electron correlation methods

The results of density fitting and local approximations applied to the calculation of transition metal-ligand binding energies using second order Møller-Plesset perturbation theory are reported. This procedure accurately reproduces counterpoise corrected binding energies from the canonical method for a range of test complexes. While counterpoise corrections for basis set superposition error are generally small, this procedure can be time consuming, and in some cases gives rise to unphysical dissociation of complexes. In circumventing this correction, a local treatment of electron correlation offers major efficiency savings with little loss of accuracy. The use of density fitting for the underlying Hartree-Fock calculations is also tested for sample Ru complexes, leading to further efficiency gains but essentially no loss in accuracy.

Theoretical investigation of equilibrium and transition state structures, binding energies and barrier heights of water-encapsulated open-cage [59]fullerenone complexes

The encapsulation of a water molecule within two open-cage [59]fullerenones with 18-membered-ring ( 1) or 19-membered-ring orifices ( 2) is studied by DFT with empirical dispersion terms. The equilibrium structure of each H 2O@[59]fullerenone and the transition-state structure for the water molecule leaving the cage are optimised and the counterpoise-corrected binding energy and barrier height are calculated. While the H 2O binding energies in H 2O@ 1 and H 2O@ 2 are almost equal, the barrier for H 2O leaving the cage is much higher for 1 (108 kJ mol −1) than for 2 (46 kJ mol −1). A water molecule can enter the cage-opened fullerenone 2 almost barrierless, whereas this barrier is 63 kJ mol −1 in 1.

The rotational spectrum and structure for the argon-cyclopentadienyl thallium van der Waals complex: Experimental and computational studies of noncovalent bonding in an organometallic π-complex

The rotational spectrum of a noble gas-organometallic complex was measured using a pulse molecular beam Fourier transform microwave spectrometer. Rotational transitions for the neutral argon-cyclopentadienyl thallium weakly bound complex were measured in the 4-9 GHz range. Analysis of the spectrum showed that the complex is a prolate symmetric-top rotor with C(5V) symmetry. The experimentally determined molecular parameters for Ar-C(5)H(5) (205)Tl are B=372.4479(3) MHz, D(J)=0.123(2) kHz, and D(JK)=0.45(2) kHz. For Ar-C(5)H(5) (203)Tl, B=373.3478(5) MHz, D(J)=0.113(3) kHz, and D(JK)=0.37(3) kHz. Using a pseudodiatomic model with Lennard-Jones potential yields an approximate binding energy of 339 cm(-1). The argon atom is located on the a-axis of the C(5)H(5)Tl monomer, directly opposite from the thallium metal atom. The measured separation distance between argon and the cyclopentadienyl ring is R=3.56 A. The overall size of the cluster is about 6 A, measuring from argon to thallium. Relatively small D(J) and D(JK) centrifugal distortion constants were observed for the complex, indicating that the structure of Ar-C(5)H(5)Tl is somewhat rigid. MP2 calculations were used to investigate the possible structures and binding energies of the argon-cyclopentadienyl thallium complex. Calculated, counterpoise corrected binding energies are evaluated at R=3.56 A for Ar-C(5)H(5)Tl range from 334 to 418 cm(-1). The experimental binding energy epsilon=339 cm(-1) for Ar-C(5)H(5)Tl falls within this range. The higher-level MP2/aug-cc-pVTZ-PP (thallium)/aug-cc-pVTZ(Ar, C, H) calculation with variable R yielded R(e)=3.46 A and binding energy of 535 cm(-1). Our estimated binding energy for argon-cyclopentadienyl thallium is very similar to the binding energy of argon-benzene. Calculations for the new van der Waals complexes, Ar(C(5)H(5)Tl)(2) and (C(5)H(5)Tl)(2), have been obtained, providing further information on the structures and bonding properties of previously observed cyclopentadienyl thallium polymer chains. The calculated intermolecular distance R(Tl-Cp)=3.05 A for the (CpTl)(2) chain subunit (Cp is cyclopentadienyl, C(5)H(5)) is slightly longer than the measured x-ray value R(M-Cp)(M=Tl)=2.75 A. The x-ray distance R(Tl-Tl)=5.5 A for the chain structure is almost identical to the calculated R(Tl-Tl)=5.51 A for the (C(5)H(5)Tl)(2) dimer.

MP2 and QCISD(T) study on the convergence of interaction energies of weak O–H⋯F–C, C–H⋯O, and C–H⋯F–C hydrogen bridges

The equilibrium structures and the hydrogen bond strengths of the weakly bonded systems: H 2O · CH 3F ( 1), CH 4 · H 2O ( 2), CH 4 · CH 3F ( 3), C 2H 4 · CH 3F ( 4), C 2H 2 · CH 3F ( 5), and cyclo-C 3H 5F · cyclo-C 3H 5F ( 6) were investigated by quantum chemical computations employing a series of correlation-consistent basis sets, cc-pVXZ and aug-cc-pVXZ [X = 2(D), 3(T), 4(Q)], and the MP2 and QCISD(T) methods. The binding energies (BE) and the counterpoise corrected binding energies (CPBE) were extrapolated to the one-particle basis set limit by two-point (3, 4) procedures giving the BE(lim) and CPBE(lim) values. It is shown that the simple average of the total energies BE(lim) and CPBE(lim) [Δ E AV(lim)] calculated at the MP2 level with non-augmented basis set differs by less than 3% ( 1a, 1b, 2, 3), and 3–6% ( 4– 6) from the corresponding values obtained with the aug-cc-pVXZ sets. The same is valid for the Δ E AV(lim) values calculated with the QCISD(T) method for which the analogous differences are less than 2%. The MP2 interaction energies are very close to the QCISD(T) ones. With respect to the MP2 data the QCISD(T) BE(lim) and CPBE(lim) values are systematically shifted to a more negative values [by 0.09–0.35 kJ mol −1 (cc-pVXZ) and 0.03–0.43 kJ mol −1 (aug-cc-pVXZ)]. For the majority of the cases studied the counterpoise corrected CPBE values are only useful as an upper limit estimate of the interaction energies. With respect to the extrapolated, limiting values, the use of the 1/2 CP correction for given X provides considerably improved interaction energies. The best compromise between accuracy and computational costs provide the cc-pVTZ and aug-cc-pVDZ basis sets, for which the interaction energies with 1/2 CP corrections (Δ E AV) differ mostly less than 10% (cc-pVTZ) and 15% (aug-cc-pVDZ) from the extrapolated limiting values. The addition of diffuse functions to the cc-pVXZ basis set for X ⩾ 3 improves the Δ E AV only marginally. It is also shown that the C–H⋯F and C–H⋯O bridges of 2– 4 and 6 share structural features with the so-called blue shifted hydrogen bonds, while the C–H⋯F interaction of 5 and the O–H⋯F interaction of 1 display similarities with conventional red shifted systems.

Efficiency of numerical basis sets for predicting the binding energies of hydrogen bonded complexes: Evidence of small basis set superposition error compared to Gaussian basis sets

Binding energies of selected hydrogen bonded complexes have been calculated within the framework of density functional theory (DFT) method to discuss the efficiency of numerical basis sets implemented in the DFT code DMol3 in comparison with Gaussian basis sets. The corrections of basis set superposition error (BSSE) are evaluated by means of counterpoise method. Two kinds of different numerical basis sets in size are examined; the size of the one is comparable to Gaussian double zeta plus polarization function basis set (DNP), and that of the other is comparable to triple zeta plus double polarization functions basis set (TNDP). We have confirmed that the magnitudes of BSSE in these numerical basis sets are comparative to or smaller than those in Gaussian basis sets whose sizes are much larger than the corresponding numerical basis sets; the BSSE corrections in DNP are less than those in the Gaussian 6-311+G(3df,2pd) basis set, and those in TNDP are comparable to those in the substantially large scale Gaussian basis set aug-cc-pVTZ. The differences in counterpoise corrected binding energies between calculated using DNP and calculated using aug-cc-pVTZ are less than 9 kJ/mol for all of the complexes studied in the present work. The present results have shown that the cost effectiveness in the numerical basis sets in DMol3 is superior to that in Gaussian basis sets in terms of accuracy per computational cost.

DFT study of hydrogen bond bridging mode of pyridine and diazenes in water environment

Optimized geometries and vibrational spectra of pyridine (Py), pyridazine (Py 1,2), pyrimidine (Py 1,3), pyrazine (Py 1,4) and their complexes with water molecules have been calculated with a view to look into the strength of hydrogen bonds, binding energies and vibrational wavenumbers of hydrogen bond bridging modes. The counterpoise corrected binding energies for different complexes are also calculated. The results of DFT calculations have been used to draw the potential energy curve and to calculate the amplitude of stretching vibration of hydrogen bond bridging modes. The three types of hydrogen bonds: N…H O, O…H O, and O…H C have been studied. The relative hydrogen bond strengths and vibrational wavenumbers of these bridging modes have been explained in terms of redistribution of electronic charges on individual atoms.

The single excitation perturbation expansion theory based on the locally projected molecular orbitals for molecular interaction: Comparison with the counterpoise corrected energy

The single excitation second order perturbation expansion (SPT) based on the locally projected self-consistent field molecular orbitals for molecular interaction is numerically tested for isomers of uracil–water and for 24 water clusters. For the extensive basis sets, the calculated binding energy BE SPT becomes close to the counterpoise corrected binding energy BE SCF CP . The required cpu time is less than that for a single supermolecule calculation. For smaller basis sets, by restricting the excited orbitals to the strictly monomer basis set (SMBS), BE SPT becomes approximate to BE SCF CP . The use of the SMBS for the excited orbitals has a clear advantage over the orthogonal but delocalized excited orbitals.

Endogenous neurotransmitters as anti-amigdaloidic agents: a density functional investigation of the interaction between melatonin and histidine

Recent insight has implicated the formation of β-amyloid fibril formation as a culpable process for the progression of Alzheimer's disease. Amyloid-β (Aβ) is a peptide naturally secreted by neurons in a random coil structure. It has been deduced that a conformational transition from a random coil to a β-pleated sheet is responsible for Aβ's neurotoxicity. The disruption of a His-Asp salt bridge has been found to inhibit this conformational change to the β-pleated sheet—a phenomenon observed in vitro when the peptides are incubated with melatonin. To further investigate this interaction between melatonin and histidine, the binding was investigated at the B3LYP/6-31g(d) level of theory for the two lowest energy conformers of melatonin: χ 2= g+, χ 3= anti, χ 4= g+, and χ 2= g−, χ 3= anti, χ 4= g−, and imidazolium. The most favorable interaction was found to be an intersecting one; the respective counterpoise corrected binding energies were found to be −17.8 and −19.8 kcal/mol.

Basis set limit binding energies of hydrogen bonded clusters

The utility of the recently developed extrapolation method to estimate the binding energies of weakly bound clusters at the basis set limit exploiting the similar basis set convergence behaviour of correlation energies of the monomer and cluster in correlated calculations (J. chem. Phys., 116, 5389 (2002)) was tested for small to medium (HF)n and (H2O)n (n = 2–5) clusters using various correlation consistent cc-pVXZ (X= D,T,Q,5) basis sets containing different numbers of diffuse functions and 6–31G type basis sets at the MP2 and CCSD(T) level for which accurate basis set limits are available for comparison. It is shown that the basis set limit binding energies estimated by this extrapolation method with modest size of basis sets (cc-pVDZ/cc-pVTZ or 6–3 1 G(d,p)/6-3 IG(2df,2pd)) are much closer to the exact basis set limits than the estimates by commonly used X −3 extrapolation or counterpoise corrected binding energies, signifying the importance of this extrapolation method for the study of large weakly bound clusters. It is also shown that the inclusion of appropriate diffuse functions in the basis sets can significantly improve the accuracy of the estimated basis set limits by this extrapolation method. For (HF)n clusters the MP2 and CCSD(T) basis set limits estimated by this extrapolation method with aug-cc-pVDZ and aug-cc-pVTZ basis sets are 18.4 (18.5) and 18.9 (18.9) for the dimer, 61.8 (62) and 63.2 (63) for the trimer, 113.5 and 114.7 (116) for the tetramer, and 155.2 and 156.3 (158) for the pentamer, respectively, with the values in parentheses representing the apparent basis set limits, with the numbers in units of kJ mol−1. The corresponding results for (H2O)n clusters are 20.5 (20.5) and 20.6 (20.7) for (H2O)2, and 60.5 (61) and 60.1 (60) for (H2O)3, respectively.

Accurate Structures and Binding Energies for Stacked Uracil Dimers

The face-to-face and face-to-back stacked uracil dimers have been investigated by second-order Moller−Plesset (MP2) perturbation theory and by the coupled-cluster singles and doubles method augmented with a perturbative contribution from connected triple substitutions [CCSD(T)]. Full MP2 geometry optimizations were performed with a TZ2P(f,d)++ basis and with the 6-31G* basis for which harmonic vibrational frequencies were computed as well. Complete basis set MP2 binding energies were obtained from basis set extrapolations using the correlation-consistent basis sets cc-pVXZ (X = D−5) and aug-cc-pVXZ (X = D−Q). Higher-order correlation effects were gauged by computing the MP2 → CCSD(T) shift in the counterpoise-corrected binding energy using a modified 6-31G* basis set. By adding this correction to the infinite basis set limit MP2 binding energies, final estimates of 9.7 and 8.8 kcal mol-1 are obtained for the binding energies of the face-to-face and face-to-back structures, respectively.

A Comparative Study of Hydrogen Bonding Using Density Functional Theory

AbstractThe hydrogen‐bond energies of water dimer and water‐formaldehyde complexes have been studied using density functional theory (DFT). Basis sets up to aug‐cc‐pVXZ (X=D, T, Q) were used. It was found that counterpoise corrected binding energies using the aug‐cc‐pVDZ basis set are very close to those predicted with the aug‐cc‐pVQZ set. Comparative studies using various DFT functionals on these two systems show that results from B3LYP, mPW1PW91 and PW91PW91 functionals are in better agreements with those predicted using high‐level ab initio methods. These functionals were applied to the study of hydrogen bonding between guanine (G) and cytosine (C), and between adenine (A) and thy mine (T) base pairs. With the aug‐cc‐pVDZ basis set, the predicted binding energies of base pairs are in good agreement with the most elaborate ab initio results.

Predicting the binding energies of H-bonded complexes: A comparative DFT study

Comparisons with the results of coupled cluster calculations were made to assess the quality of density functionals in predicting the electronic binding energies of H-bonded complexes. A variety of different density functionals, namely B3LYP, B97-1, PBE0, HCTH, BLYP, PBE, LDA and a recently derived improvement of the HCTH functional (HCTH38), as well as the standard abinitio Hartree–Fock and second-order Moller–Plesset perturbation theory methods were applied using a triple-ζ plus double polarisation basis set. Equilibrium structures, counterpoise corrected binding energies and harmonic frequencies were calculated for the (HF)2, (HCl)2, (H2O)2, (CO)(HF), (OC)(HF), (FH)(NH3), (ClH)(NH3), (H2O)(NH3) and (H3O+)(H2O) complexes. Although the hybrid methods performed well in general, the new HCTH38 functional as a pure GGA predicted binding energies of better quality than the B3LYP functional. Bond length changes and frequency shifts were compared to MP2 results.

The ab initio neon–water potential-energy surface and its relationship with the hydrophobic hydration shell

The neon–water system has been investigated by abinitio quantum-chemical calculations. The potential-energy surface (PES) for the 1:1 Ne–H2O interaction has been scanned at the MP2(full) level, with the 6-311++G(3df,2pd) basis set augmented with bond functions located midway between Ne and O. The most stable neon–water arrangement has r = 320 pm, θ = 120°, with a counterpoise-corrected binding energy of −0.54 kJ mol−1. The PES is otherwise quite flat (with binding energies of ca. −0.4 kJ mol−1) for all θ values if r > ca. 310 pm. The off-plane, perpendicular approach is unfavourable. NMR shielding and the electric field gradient at all nuclei show only very small changes with respect to the isolated components.