The relative energies of polypeptide conformers predicted by linear scaling second-order Møller-Plesset perturbation theory

We describe an implementation of the cluster-in-molecule(CIM) resolution of the identity(RI) approximation second-order M?ller–Plesset perturbation theory(CIM-RI-MP2), with the purpose of extending RI-MP2 calculations to very large systems. For typical conformers of several large polypeptides, we calculated their conformational energy differences with the CIM-RI-MP2 and the generalized energy-based fragmentation MP2(GEBF-MP2) methods, and compared these results with the density functional theory(DFT) results obtained with several popular functionals. Our calculations show that the conformational energy differences obtained with CIM-RI-MP2 and GEBF-MP2 are very close to each other. In comparison with the GEBF-MP2 and CIM-RI-MP2 relative energies, we found that the DFT functionals(CAM-B3LYP-D3, LC-?PBE-D3, M05-2X, M06-2X and ?B97XD) can give quite accurate conformational energy differences for structurally similar conformers, but provide less-accurate results for structurally very different conformers.     

Performance of theoretical methods and basis sets on the molecular structure, atomisation and ionisation energies, electron affinity, and vibrational spectrum of silylene

This work compares the performance of theoretical methods and basis sets on the molecular structure, atomisation and ionisation energies, electron affinity, and vibrational spectrum of silylene. Silylene, its cation and anion have been studied in ¹ A ₁, ² A ₁ and ² B ₁ states, respectively, in the gas phase and C_2v symmetry. The methods considered are second-order Møller-Plesset perturbation theory (MP2), the density functional theory (DFT), Gaussian-2 (G2) and complete basis set methods (CBS-4M and CBS-Q). The basis sets used are 6-31G(d,p), 6-311G(d,p), 6-31++G(d,p) and 6-311++G(d,p). The functional used for the DFT method is B3LYP. Silylene and its cation and anion have been optimised using the MP2 and DFT methods and the named basis sets. Single-point energy calculations (G2, CBS-4M and CBS-Q) were performed using MP2/6-311++G(d,p) structures and these energies have been used to calculate atomisation energy, ionisation energy and adiabatic electron affinity. Frequency calculations were also done and the raw vibrational frequencies were assigned. It is interesting to note the close similarity between the predicted parameters and some of the available literature values. The results obtained are consistent and converge with different basis sets with improved size and quality. However, the parameters obtained are very much method dependent.     

Theoretical study on the molecular structures of toluene,para‐fluorotoluene,para‐chlorotoluene,and 4‐methylpyridine and their sixfold internal rotational barriers

Two kinds of sixfold internal rotational configurations of toluene, para‐fluorotoluene, para‐chlorotoluene, and 4‐methylpyridine were calculated using Hartree–Fock (HF), second‐order Møller–Plesset (MP2), and Beck's three parameter hybrid functional using the LYP correlation functional (B3LYP) theory methods with various high‐level basis sets. Structures and energies were compared for different configurations. Calculations indicate that the orthogonal configuration has a local minimum while the planar configuration is a transition structure. Furthermore, geometries of the orthogonal and the planar configurations are quite similar, except for a methyl CH bond. Sixfold internal rotational barriers were calculated from the energy difference of two different configurations. For the calculated results, HF methods underestimated the rotational barriers, but MP2 calculations overestimated them. However, the density functional theory (DFT) method is a reliable method since the calculated internal rotational barriers are similar to the experimental ones. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 772–778, 2000     

The vibrational frequencies of CaO2, ScO2, and TiO2: a comparison of theoretical methods

The vibrational frequencies of several states of␣CaO₂, ScO₂, and TiO₂ are computed using density functional theory (DFT), the Hartree-Fock approach, second-order M?ller-Plesset perturbation theory (MP2), and the complete-active-space self-consistent-field theory. Three different functionals are used in the DFT calculations, including two hybrid functionals. The coupled cluster singles and doubles approach including the effect of connected triples, determined using perturbation theory, is applied to selected states. The Becke-Perdew 86 functional appears to be the most cost-effective method of choice, although even this functional does not perform well for one state of CaO₂. The MP2 approach is significantly inferior to the DFT approaches. Received: 3 September 1997 / Accepted: 8 December 1997     

The use of the hybrid density functional theory (DFT) approach for calculation of vibrational spectra: nitromethane

The molecular geometry of nitromethane was optimized and its force field and vibrational spectrum were calculated by the BECKE3LYP method. The accuracy of optimization of the geometry of MeNO₂ obtained by this method using the 6–311G(d,p) and 6–311++G(d,p) basis sets is not poorer than that obtained at the second-order Møller-Plesset level of perturbation theory (MP2). The vibrational frequencies of nitromethane and its d₁, d₂, and d₃ isotopomers obtained by the BECKE3LYP method are in much better agreement with the experimental data than those calculated at the MP2 level using the same basis set. The average absolute error of calculations performed without the use of any scaling factors is ～2% for frequencies; the maximum deviation is ～4%.     

The inclusion of correlation in the calculation of phosphorus NMR chemical shieldings

The effects of including correlation in the calculation of phosphorus nuclear magnetic resonance (NMR) chemical shielding has been investigated for a variety of molecules in the Hartree-Fock, second-order Møller-Plesset (MP2), and estimated infinite-order Møller-Plesset theory ab initio approaches in the gauge including atomic orbital (GIAO) scheme. The inclusion of correlation in the shielding calculations often leads to significant changes from the Hartree-Fock theory and provides results that are in improved agreement with experiment. © 1996 John Wiley & Sons, Inc.     

Structure, force fields, and vibrational spectra of cerium tetrahalides

The geometrical structure, force fields, and vibrational spectra of CeX₄ (X = F, Cl, Br, I) were investigated by second, third, and fourth order Möller-Plesset perturbation theory, CISD+Q configuration interaction method, and the CCSD(T) coupled cluster method. Calculations on CeF₄ were also performed by multiconfiguration second order perturbation theory MCQDPT2/CASSCF. The wave function of the ground state of CeX₄ molecules was found to be appreciably non-one-configurational; this property increases from cerium fluorides to iodides and leads to the divergence of the series of Möller-Plesset perturbation theory. The calculated data point to a tetrahedral equilibrium nuclear configuration in CeX₄ molecules. The energy barriers to the inversion of the tetrahedral CeX₄ molecules via the square configurations are high enough, 74–89 kJ/mol. The calculated vibration frequencies, effective internuclear distances, and mean amplitudes of nuclear vibrations in CeF₄ agree with IR and Raman spectroscopic and high-temperature gas-phase electron diffraction data.     

Tuning the physisorption of molecular hydrogen: binding to aromatic,hetero-aromatic and metal-organic framework materials

We present a study on the binding properties of molecular hydrogen to several polar aromatic molecules and to a model for the metal-oxide corner of the metal organic framework materials recently investigated as promising supports for hydrogen storage. Density functional theory employing the Perdew Wang exchange-correlation functional and second order Møller-Plesset calculations are used to determine the equilibrium structures of complexes with molecular hydrogen and their stability. It is found that for most hetero-aromatics the edge sites for molecular hydrogen physisorption have stabilities comparable to the top sites. The DFT predicted binding energies compare favorably with those estimated at MP2 level, and get closer to the MP2 results for increased electrostatic contributions (induced by the polar aromatics) to the intermolecular interaction. Vibrational frequencies are also computed at the DFT level, and infrared activities of the H₂ stretching frequency are compared for the various complexes. Pyrrole, pyridine and n-oxide pyridine are predicted to form the more stable complexes among one-ring aromatics. The computed binding energies to metal-organic framework materials are in good agreement with experimental observations. It is suggested that replacement of the organic linker in MOF materials with some of the more efficient aromatics investigated here might contribute to enhance the H₂ storage properties of mixed inorganic–organic materials.     

Internal rotation study of some sixfold barrier molecules

Molecular orbital calculations of sixfold barriers in nitromethane, methyl boron difluoride, and trifluoronitromethane were performed by various Hartree-Fock and electron correlation methods. In those calculations, staggered and eclipsed conformations are of primary concern. These results indicated that for CH₃NO₂ and CH₃BF₂ the staggered conformations are more stable, while CF₃NO₂ has a more stable conformation in an eclipsed form. Both conformations do not differ significantly, which may account for the low internal rotational barrier of each molecule. Values of the barrier calculated by the Møller-Plesset perturbation and the quadratic configuration interaction methods did not match the experimental results. However, better internal rotational barrier values of each molecule were observed when the improved better basis sets and the Hartree-Fock method were selected. © 1997 John Wiley & Sons, Inc.     

Suitability of density functional methods for calculation of electrostatic properties

A systematic analysis was performed on the suitability of the molecular electrostatic potential (MEP) and MEP-derived properties determined by means of density functional (DFT) methods. Attention was paid to the electrostatic potential (ESP) derived charges, the ESP and exact quantum mechanical dipole moments, the depth of MEP minima, and the MEP distribution in layers around the molecule for a large series of molecules. The electrostatic properties were determined at either local or nonlocal DFT levels using different functionals. The results were compared with the values estimated from quantum mechanical calculations performed at Hartree–Fock, Møller–Plesset up to fourth order, and CIPSI levels. The suitability of the MEP-derived properties estimated from DFT methods is discussed for application in different areas of chemical interest. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 980–991, 1997     

Slow convergence of the møller-plesset perturbation series: the dissociation energy of hydrogen cyanide and the electron affinity of the cyano radical

Møller-Plesset perturbation expansions for hydrogen cyanide (HCN) and for cyanide anion (CN ⁻) converge rapidly, whereas that for cyano radical CN ) converges only slowly. As a result, fourth-order Møller-Plesset theory leads to estimates of the dissociation energy of HCN and of the electron affinity of CN which are considerably overestimated. The results for cyano radical indicate that slow convergence of the UMP series in the case of strongly spin-contaminated wavefunctions can occur not only for stretched molecules but also for equilibrium structures.     

Density functional theory and post-Hartree-Fock studies on molecular structure and harmonic vibrational spectrum of formaldehyde

Density functional theory (DFT) with the Becke's three-parameter exchange correlation functional and the functional of Lee, Yang and Parr, gradient-corrected functionals of Perdew, and Perdew and Wang [the DFT(B3LYP), DFT(B3P86) and DFT(B3PW91) methods, respectively], and several levels of conventional ab initio post-Hartree-Fock theory (second- and fourth-order perturbation theory M?ller-Plesset MP2 and MP4(SDTQ), coupled cluster with the single and double excitations (CCSD), and CCSD with perturbative triple excitation [CCSD(T)], configuration interaction with the single and double excitations [CISD], and quadratic configuration interaction method [QCISD(T)], using several basis sets [ranging from a simple 6-31G(d,p) basis set to a 6-311+ +G(3df, 2pd) one], were applied to study of the molecular structure (geometrical parameters, rotational constants, dipole moment) and harmonized infrared (IR) spectrum of formaldehyde (CH₂O). High-level ab initio methods CCSD(T) and QCISD(T) with the 6-311+ +G(3df, 2pd) predict correctly molecular parameters, vibrational harmonic wavenumbers and the shifts of the harmonic IR spectrum of ¹²CH₂ ¹⁶O upon isotopic substitution. Received: 30 January 1997 / Accepted: 7 May 1997     

Pyrrolidinium-based ionic liquids as electrolytes for lithium batteries: A Computational Study

Electrochemical windows (ECWs) of the cyclic ammonium based ionic liquids formed by the combination of two common pyrrolidinium cations—N,N-butylmethyl pyrrolidinum(P_yr14) and N,N-hexylmethyl pyrrolidinium(P_yr16) and five anions—dicyanamide, trifluoroacetate, fluoromethane sulfonate, bis((trifluoromethylsulfonyl)imide, and bis(fluorosulfonyl)imide were investigated. The ECW of each ionic liquid was obtained from the oxidation and reduction potentials of these ionic liquids with respect to a Li⁺/Li reference electrode by using thermodynamic cycle method. The work reveals that the ECWs of these ionic liquids are solely decided by the HOMO energy of pairing anions. The ECWs were also computed using HOMO-LUMO method employing Møller-Plesset perturbation theory to the second order and M06L methods with a basis set of 6-31 + G(d, p). The ECW computed using M06L functional with an extended basis set of 6-311++G(d, p) showed better agreement with experimental values suggesting accurate computation of ECW is possible at lower computational cost.     

Accurate electron affinities of several diatomic and triatomic molecules

The electron affinity of several diatomic and triatomic molecules is computed with an error of less than 0.1 eV using the second-order Møller-Plesset method and a 6.311 + G(2d,2p) basis set. The importance of the zero-point energy correction is tested and a comparison with the results obtained with other basis sets is made.     

Comparison of Density Functional and Correlated Wave Function Methods for the Prediction of Cu(II) Hyperfine Coupling Constants

The reliable prediction of Cu(II) hyperfine coupling constants remains a challenge for quantum chemistry. Until recently only density functional theory (DFT) could target this property for systems of realistic size. However, wave function based methods become increasingly applicable. In the present work, we define a large set of Cu(II) complexes with experimentally known hyperfine coupling constants and use it to investigate the performance of modern quantum chemical methods for the prediction of this challenging spectroscopic parameter. DFT methods are evaluated against orbital-optimized second-order Møller-Plesset (OO-MP2) theory and coupled cluster calculations including singles and doubles excitations, driven by the domain-based local pair natural orbital approach (DLPNO-CCSD). Special attention is paid to the definition of a basis set that converges adequately toward the basis set limit for the given property for all methods considered in this study, and a specifically optimized basis set is proposed for this purpose. The results suggest that wave function based methods can supplant but do not outcompete DFT for the calculation of Cu(II) hyperfine coupling constants. Mainstream hybrid functionals such as B3PW91 remain on average the best choice.     

Theoretical study of structure, vibrational frequencies, and electronic spectra of dibenzofuran and its polychlorinated derivatives

Minimum structures and harmonic vibrational frequencies of dibenzofuran (DF), 2,3,7,8-tetrachlorodibenzofuran (TCDF), and octachlorodibenzofuran (OCDF) were calculated using the multiconfigurational complete active space self-consistent field (CASSCF) and density functional theory (DFT) methods. The electronic transitions in these compounds were studied via the single-state multireference second-order perturbation theory (CASPT2) based on the CASSCF(14,13) references, as well as the time-dependent DFT (TD-B3P86) employing the cc-pVDZ (CASSCF/CASPT2) and 6-31G(d,p) (TD-B3P86) basis sets. The B3P86 geometry and harmonic vibrational frequencies of ground state DF agree very well with the experimental data, and the CASSCF/CASPT2 excitation energies and oscillator strengths are accurate enough to provide a reliable assignment of the absorption bands in the 200-300 nm region. The close agreements with experiment for the parent DF give the present theoretical approaches a valuable credit in predicting the properties of the environmentally toxic polychlorinated congeners, which is all the more important considering the difficulties and hazards in obtaining the experimental data.     

State‐specific multireference perturbation theory with improved virtual orbitals: Taming the ground state of F2, Be2, and N2

Adaptation of improved virtual orbitals (IVOs) in state‐specific multireference perturbation theory using Møller–Plesset multipartitioning of the Hamiltonian (IVO‐SSMRPT) is examined in which the IVO‐complete active space configuration interaction (CASCI) is used as an inexpensive alternative to the more involved CAS‐self‐consistent field (CASSCF) orbitals. Unlike the CASSCF approach, IVO‐CASCI does not bear tedious and costly iterations beyond those in the initial SCF calculation. The IVO‐SSMRPT is intruder‐free, and explicitly size‐extensive. In the present preliminary study, the IVO‐SSMRPT method which relies on a small reference space is applied to study potential energy surfaces (PES) of the ground state of challenging, multiconfigurational F₂, Be₂, and N₂ molecules. These systems provide a serious challenge to any ab initio methodology due to the presence of an intricate interplay of nondynamical and dynamical correlations to the entire PES. The quality of the computed PES has been judged by extracting spectroscopic parameters and vibrational levels. The reported results illustrate that the IVO‐SSMRPT method has a potential to yield accuracies as good as the CASSCF‐SSMRPT one with reduced computational labor. Even with small reference spaces, our estimates demonstrate a good agreement with the available experimental values, and some benchmark computations. The blend of accuracy and low computational cost of IVO‐SSMRPT should deserve future attention for the accurate treatment of electronic states of small to large molecular systems for which the wavefunction is characterized by various configurations. © 2015 Wiley Periodicals, Inc.     

A Comparison of the Interacting Quantum Atoms (IQA) Analysis of the Two-Particle Density-Matrices of MP4SDQ and CCSD

Within the quantum topological energy partitioning method called Interacting Quantum Atoms (IQA) we transition from Møller-Plesset (MP4SDQ) to CCSD in calculating intra- and interatomic electron correlation energies for a set of hydrides, diatomics, a few simple molecules and non-covalently bonded complexes, using the uncontracted basis set 6-31++G(2d,2p). CCSD-IQA allows a more rigorous analysis of atomic electron correlation than that offered by Møller-Plesset, which returns IQA contributions that are identical to Hartree–Fock counterparts except for two-electron terms. The CCSD-IQA analysis returns bond and other interatomic correlation energies that are typically much larger in magnitude than the MP4SDQ values. Crisp patterns of energy transferability are detected in water clusters, both for intra-atomic and interatomic correlation energies. CCSD determines that the intra-atomic correlation energy of an oxygen drops by 15 kJ · mol^–1 for donating a hydrogen and by 25 kJ · mol^–1 for accepting a hydrogen.     

The structure of propadienone (CH2CCO)

A complete r_o structure has been obtained for propadienone (CH₂CCCO) with the aid of ab initio molecular-orbital calculations. The effect of electron correlation has been investigated using third order Møller-Plesset perturbation theory. The molecule is found to be planar bent (CCC145°) and the calculated structure yields rotational constants which are in good agreemant with experimental values.