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     

Some investigations of the MP2-R12 method

Summary The MP2-R12 method was introduced by Kutzelnigg and Klopper to overcome the problem caused by truncation of the one electron basis set in correlation energy calculations at the Møller-Plesset second order level of approximation. Here, we have evaluated the integrals required by their simplest scheme using the Rys-quadrature procedure. Results are presented for Ne, H₂O, and HF using largespdf gaussian basis sets.     

Study on Pair Correlation Energies of Isoelectronic Systems F^－, HF and H2F^＋

The intrapair and interpair correlation energies of F-, HF and H2F^ systems are calculated and analyzed using MP2-OPT2 method of MELD program with cc-PVSZ^* basis set. From the analysis of pair correlation energies of these isoelectronlc sysoterns, it is found that the 1sF^2 pair correlation energy is trans-ferable in these three isociectronic systems. According to the definition of pair correlation contribution of one electron pair to a system, the pair correlation contribution values of these three systems are calculated. The correlation contribution values of inner electron pairs and H—F bonding electron pair in HF molecule with those in H2F^ system are compared. The results indicate that the bonding effect of a molecule is one of the im-portant factors to influence electron correlation energy of the system. The comparison of correlation energy contributions in-cluding triple and quadruple excitations with those only includ-ing singles and doubles calculated with 6-311 G(d) basis set shows that the higher.excitation correlation energy contribution gives more than 2 % of the total correlation energy for these sys-tems.     

Møller-plesset calculations taking care of the correlation CUSP

Møller-Plesset calculations to second order have been carried out on the ten-electron systems Ne, HF and H₂O with a new functional, including r₁₂-dependent pair correlation functions, which takes care of the correlation cusp. The calculated second-order pair energies are accurate to within a few millihartree in comparison with the estimated exact values. In particular, second-order energies of 384.2, 380.1 and 362.9 mE_h, have been obtained for Ne, HF and H₂O respectively.     

Application of multiconfigurational many-body perturbation theory to the calculation of ionization potentials,electron affinities and excitation energ

Multiconfigurational many-body perturbation theory is applied to the problem of calculating ionization potentials, electron affinities, and excitation energies. H₂O, C₂H₄, and H₂ are studied, with correlation corrections through third order and inclusive of certain higher-order terms. Results are compared with those by other many-body theoretical methods.     

Skin Bond Electron Relaxation Dynamics of Germanium Manipulated by Interactions with H2, O2, H2O,H2O2, HF,and Au

Although germanium performs amazingly well at sites surrounding hetero‐coordinated impurities and under‐coordinated defects or skins with unusual properties, having important impact on electronic and optical devices, understanding the behavior of the local bonds and electrons at such sites remains a great challenge. Here we show that a combination of density functional theory calculations, zone‐resolved X‐ray photoelectron spectroscopy, and bond order length strength correlation mechanism has enabled us to clarify the physical origin of the Ge 3d core‐level shift for the under‐coordinated (111) and (100) skin with and without hetero‐coordinated H₂, O₂, H₂O, H₂O₂, HF impurities. The Ge 3d level shifts from 27.579 (for an isolated atom) by 1.381 to 28.960 eV upon bulk formation. Atomic under‐coordination shifts the binding energy further to 29.823 eV for the (001) and to 29.713 eV for the (111) monolayer skin. Addition of O₂, HF, H₂O, H₂O₂ and Au impurities results in quantum entrapment by different amounts, but H adsorption leads to polarization.     

A Novel Method for Fixed‐node Quantum Monte Carlo

In this paper, a novel method for fixed‐node quantum Monte Carlo is given. By comparing this method with the traditional fixed‐node one, this novel method can be applied to calculate molecular energy more exactly. An expansion of the eigenvalue of the energy for a system has been derived. It is proved that the value of the energy calculated using the traditional fixed‐node method is only the zeroth order approximation of the eigenvalue of the energy. But when using this novel method, in the case of only increasing less computing amounts ( < 1%), the first order approximation, the second order approximation, and so on can be obtained conveniently with the detailed equations and steps in the practical calculation to calculate the values of the zeroth, first and second approximation of the energies of 1 ¹A, state of CH₂, ¹A₂(C_4h, acet) state of C₈ and the ground‐states of H₂, LiH, Li₂, and H₂O The results indicate that for these states it needs only the second order approximation to obtain over 97% of electronic correlation energy, which demonstrates that this novel method is very excellent in both the computing accuracy and the amount of calculation required.     

Simple and Highly Efficient Catalytic Thiocyanation of Aromatic Compounds in Aqueous Media

Two simple, mild, and efficient procedures for the thiocyanation of N‐heterocycles, substituted anilines (electron‐rich and electron‐deficient), and N‐substituted aromatic amines at room temperature are reported (Table 3). The first uses H₂O₂ as pollution‐free oxidant and the second H₅IO₆; both with the reagent potassium thiocyanate in H₂O as solvent. These procedures provided the target thiocyanates after a short reaction time in good to excellent yields and high regioselectivity.     

Correlated and gauge origin independent calculations of magnetic properties

Summary We have applied a gauge origin invariant method for calculations of nuclear magnetic shielding constants to the singly bonded molecules BF, F₂, BH₃, CH₄, NH₃, H₂O, and HF as well as to the¹H shielding constants of HCN and C₂H₂. The calculations were performed at the RPA and second order polarization propagator (SOPPA) level of theory. For most molecules the correlation contribution in SOPPA is less diamagnetic than in the comparable MP2 calculations. For F₂, SOPPA gives a large paramagnetic correlation correction whereas the MP2 method gives a very small correlation contribution. For all molecules agreement with experimental results is generally improved at the SOPPA level compared to RPA. We have also demonstrated that second order gauge origin invariant, common and local origin (SOLO) methods do not necessarily give the same shielding even in the limit of a converged basis set.     

Ab initio pseudopotential study of M2As− and M2Br+ (M = Cu,Ag, Au)

The equilibrium geometries and the vibration frequencies of M₂As⁻ and M₂Br⁺ (M = Cu, Ag, Au) are calculated at the Hartree–Fock (HF) and the second‐order Møller–Plesset (MP2) levels with pseudopotentials. The calculated results indicate that the species have a bent structure (C_2v). The electron correlation corrections on the geometrical structure are investigated at the MP2 level, the bond angles are reduced by 10°–20° for considered species. The electron correlation effects on the geometry of the Au₂As⁻ are studied particularly at MP2, MP3, MP4, CCSD and CCSD(T) levels. Comparing the species containing Ag and Au, the relativistic effects slightly short the bond lengths of the species. The bonding possibility of the Au₂As⁻ is predicted. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 80: 38–43, 2000     

Encapsulation of the interstellar abundant H3+ in a C60 fullerene

The possible encapsulation of the interstellar abundant H₃⁺ ion inside a C₆₀ fullerene cage has been examined by using the Hartree‐Fock (HF) and the second order Møller‐Plesset perturbation (MP2) methods both with the 6‐31G** basis set. It was found that H₃⁺ forms various stable endohedral complexes inside the cage. Six configurations have been examined among which four were stable compared with the separated initial species, the dissociated H₂ + H⁺ inside the cage being the most stable. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

An application of the method of conjugate gradients to the calculation of minimal basis set localized orbitals

Using an STO -3G basis set, energy localized molecular orbitals (LMO ) were determined for the ten electron series HF, H₂O, NH₃, and CH₄ as well as for CH₃OH and C₂H₂F₂. The method of conjugate gradients is shown to be a viable alternative to other non-eigenvalue methods. The characterization of the LMO in terms of first and second moment measures indicates that the STO -3G basis set LMO may be accurately correlated to larger sp basis set LMO . Also, it is shown that the first and second moment measures display a good linear correlation with the classical concept of electronegativity.     

Method/basis set dependence of the traceless quadrupole moment calculation for N2, CO2, SO2, HCl,CO, NH3, PH3, HF,and H2O

Dipole moments and traceless quadrupole moments for a training set of nine molecules—N₂, CO₂, SO₂, HCl, CO, NH₃, PH₃, HF, and H₂O—were deduced from the final optimized density matrices of a series of ab initio calculations, thereby employing different levels of theory with varying basis set quality. All the results were obtained in a true ab initio sense, meaning that at a certain combination of method/basis set, the configurations of the molecules were first subjected to a geometry optimization and only afterwards the dipole and traceless quadrupole moments were derived for the final relaxed structures. All results could be compared to experimental data, thus the quality of the different models with respect to applicability and reliability of calculating molecular moments without any knowledge of structural details of the equilibrium geometries could be evaluated. Generally, a combination of methods that take into account correlation effects, together with a high‐level basis set, was found to yield molecular moments close to the experimental values. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Interstitial and lattice substituted models of an expanded ice-I hlattice

An ice-I _hlattice (O?O=0.286 nm) with small molecules placed interstitially and with some placed at lattice positions was investigated by the CNDO/2-MO technique. The interstitial molecules included H₂, N₂, O₂, HF, CO₂, H₂O, NH₃, CH₄ and CH₂O, whereas those involved in lattice substitution included HF, NH₃ and H₂O. From the calculations it is found that all interstitial and lattice substituted systems are stabler than the sum of the components, the enhanced stability depending on the system. Generally, lattice substituted systems are stabler than the corresponding interstitial models. Charges residing on the atomic positions reflect the amount of interaction with the matrix as well as indicating how the change in charge would facilitate other interactions with the solvent.     

Synthesis,kinetics and mechanism of the reaction of a quasi‐aromatic copper(II) complex, [Cu(PnAO)‐6H]0, with aromatic aldehydes

The quasi‐aromatic metal complex (1,1,2,8,9,9‐hexamethyl‐4,6‐dioxa‐5‐hydro‐3,7,10,14‐tetraazacyclotetradecane‐2,7,10,12‐tetraene)copper(II), [Cu(PnAO)‐6H]⁰ (AH), was synthesized. Reactions of AH were studied spectrophotometrically in acidic media (pH = 1 ∼ 2, EtOH:H₂O = 1:4 v/v) with para‐substituted benzaldehydes (ald). The Cu,2N,3C quasi‐aromatic heterocyclic ring in AH is highly reactive at the central‐aromatic‐carbon atom, C12, to most aldehydes. A novel parallel, competitive and consecutive second‐order reaction mechanism is proposed. To obtain the rate constants following this mechanism, the Gauss‐Newton‐Marquardt and Runge‐Kutta methods were employed. Consistent results were obtained. Effects of acidity, solvent, temperature and substituent R (RH, CH₃, OCH₃, Cl) of the aromatic aldehydes on the reaction rate constants were studied. The results support the proposed SN2 mechanism. A linear free energy relationship between the rate constant k₁ and the Hammett parameters for the substituted benzaldehydes as well the activation parameters are presented. © 2000 John Wiley & Sons, Inc. Int J Chem Kinet 33: 1–8, 2001     

Longitudinal NLO properties of C2H2, HCCF,and C2F2: Electron correlation and vibration effects

Electron correlation and vibration effects on longitudinal nonlinear optical properties of acetylene (C₂H₂), fluoroacetylene (HCCF), and difluoroacetylene (C₂F₂) have been studied using various quantum chemistry methods, including the second‐order perturbation theory (MP2); coupled cluster approach with singles, doubles (CCSD), and noniterative triples (CCSD(T)); and density functional methods (B3LYP and B98). Evaluation of the static and dynamic vibration (nuclear relaxation) contributions was based on the finite field relaxation method. Particular attention has been devoted to the assessment of the electron correlation effects on the nuclear relaxation contributions to the molecular properties. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Ab initio study,including electron correlation,of the electronic structures,the dipole moments,the static polarizabilities and of the harmonic force fields of H2CO,H2CS and H2SiO

Ab initio calculations including electron correlation (on the PNO-CI and CEPA-PNO levels) are carried out for the isovalence electronic molecules H₂CO, H₂CS and H₂SiO, and for comparison also for H₂O and CO. The CEPA equilibrium distances are accurate to within 0.003 Å, while SCF results show significantly larger errors. The harmonic force constants on CEPA level are satisfactory as well, but for stretching of double or triple bonds inclusion of singly substituted configurations is imperative. Dipole moments were obtained with an error of 0.1 Debye from CEPA calculations with sufficiently large basis sets and inclusion of singly substituted configurations. The dipole polarizabilities are less sensitive to correlation effects but require larger basis sets.The population analysis reveals that the SiO bond in H₂SiO is highly polar and thatd-AO's cannot be regarded as valence AO's in any of the molecules of this study. The binding energy of H₂SiO (with respect to H₂Si(¹ A ₁) + O(³ P)) is predicted as 140 ± 5 kcal/mol. The contributions of different pairs in terms of localized orbitals to the correlation energy of the molecules of this study are analyzed.     

Electron correlation in the interacting quantum atoms partition via coupled‐cluster lagrangian densities

The electronic energy partition established by the Interacting Quantum Atoms (IQA) approach is an important method of wavefunction analyses which has yielded valuable insights about different phenomena in physical chemistry. Most of the IQA applications have relied upon approximations, which do not include either dynamical correlation (DC) such as Hartree‐Fock (HF) or external DC like CASSCF theory. Recently, DC was included in the IQA method by means of HF/Coupled‐Cluster (CC) transition densities (Chávez‐Calvillo et al., Comput. Theory Chem. 2015, 1053, 90). Despite the potential utility of this approach, it has a few drawbacks, for example, it is not consistent with the calculation of CC properties different from the total electronic energy. To improve this situation, we have implemented the IQA energy partition based on CC Lagrangian one‐ and two‐electron orbital density matrices. The development presented in this article is tested and illustrated with the H₂, LiH, H₂O, H₂S, N₂, and CO molecules for which the IQA results obtained under the consideration of (i) the CC Lagrangian, (ii) HF/CC transition densities, and (iii) HF are critically analyzed and compared. Additionally, the effect of the DC in the different components of the electronic energy in the formation of the T‐shaped (H₂)₂ van der Waals cluster and the bimolecular nucleophilic substitution between F^– and CH₃F is examined. We anticipate that the approach put forward in this article will provide new understandings on subjects in physical chemistry wherein DC plays a crucial role like molecular interactions along with chemical bonding and reactivity. © 2016 Wiley Periodicals, Inc.     

Physicochemical Characterization of Four Gadolinium(III) DTPA‐like Complexes

The analysis of ¹⁷O NMR transverse relaxation rates and EPR transverse electronic relaxation rates for aqueous solutions of the four DTPA‐like (DTPA = diethylenetriamine‐N,N,N′,N″,N″‐pentaacetic acid) complexes, [Gd(DTPA‐PY)(H₂O)]^? (DTPA‐PY = N′‐(2‐pyridylmethyl)), [Gd(DTPA‐HP)(H₂O)₂]^? (DTPA‐HP = N′‐(2‐hydroxypropyl)), [Gd(DTPA‐H1P)(H₂O)₂]^? (DTPA‐H1P = N′‐(2‐hydroxy‐1‐phenylethyl)) and [Gd(DTPA‐H2P)(H₂O)₂] (DTPA‐H2P = N′‐(2‐hydroxy‐2‐phenylethyl)), at various temperatures allows us to understand the water exchange dynamics of these four complexes. The water‐exchange lifetime (τM) parameters for [Gd(DTPA‐PY)(H₂O)]^?, [Gd(DTPA‐HP)(H₂O)₂]^?, [Gd(DTPA‐H1P)(H₂O)₂]^? and [Gd(DTPA‐H2P)(H₂O)₂] are of 585, 98, 163, and 69 ns, respectively. Compared with [Gd(DTPA)(H₂O)]^2? (τM = 303 ns), the τM value of [Gd(DTPA‐PY)(H₂O)]^? is slightly higher, but the other three complexes values are significantly lower than those of [Gd(DTPA)(H₂O)]^2?. This difference is explained by the fact that the gadolinium(III) complexes of DTPA‐HP, DTPA‐H1P, and DTPA‐H2P have two inner‐sphere waters. The ²H longitudinal relaxation rates of the labeled diamagnetic lanthanum complex allow the calculation of its rotational correlation time (τR). The τR values calculated for DTPA‐PY, DTPA‐HP, DTPA‐H1P, and DTPA‐H2P are of 127, 110, 142 and 147 ps, respectively. These four values are higher than the value of [La(DTPA)]^2? (τR = 103 ps), because the rotational correlation time is related to the magnitude of its molecular weight.