Simultaneous analytical optimization of variational parameters in Gaussian-type functions with full configuration interaction of multicomponent molecular orbital method by elimination of translational and rotational motions: application to isotopomers of the hydrogen molecule

We have extended the multicomponent molecular orbital (MCMO) method to the full-configuration interaction (full-CI) fully variational molecular orbital method by elimination of translational and rotational motion components from total Hamiltonian. In the MCMO scheme, the quantum effects of protons and deuterons as well as electrons can be directly taken into account. All variational parameters in the full-CI scheme, i.e., exponents and centers (alpha and R) in the Gaussian-type function (GTF) basis set as well as the CI coefficients, are simultaneously optimized by using their analytical gradients. The total energy of the H(2) molecule calculated using the electronic [6s3p2d1f] and nuclear [1s1p1d1f] GTFs is -1.161 726 hartree, which can be compared to the energy of -1.164 025 hartree reported using a 512 term-explicitly correlated GTF calculation. Although the d- and f-type nuclear GTFs contribute to the improvement of energy convergence, the convergence of electron-nucleus correlation energy is slower than that of electron-electron one. The nuclear wave functions are delocalized due to the electron-nucleus correlation effect compared to the result of Hartree-Fock level of MCMO method. In addition, the average internuclear distances of all diatomic molecules are within 0.001 A of the previously reported experimental results. The dipole moment of the HD molecule estimated by our method is 8.4 x 10(-4) D, which is in excellent agreement with the experimental result of (8-10) x 10(-4) D.     

Analysis of exponent values in Gaussian‐type functions for development of protonic and deuteronic basis functions

We analyzed the exponent (α) values in Gaussian‐type functions (GTF) for protons and deuterons in BH₃, CH₄, NH₃, H₂O, HF, and their deuterated molecules for the development of nuclear basis functions, which are used for molecular orbital (MO) calculations that directly include nuclear quantum effects. The optimized α (α_opt) value in the single s‐type ([1s]) GTF for protons is changed due to the difference in flexibility of the electronic basis sets. The difference between the energy obtained by using the α_opt value for each molecule and that obtained by using the average α (α_ave) value for these exponents with the 6‐31G(d,p) electronic basis function is only 2 × 10^?5 a.u. The α_ave values of protonic and deuteronic [1s] GTFs by the present calculation are 24.1825 and 35.6214, respectively. We found that the α_ave values enable the evaluation of the total energy and the geometrical changes in hydrogen bonding, such as O…H? O, O…H? N, and O…H? C, while the α_opt value became small by forming a hydrogen bond. The result using only the [1s] GTF for the protonic and deuteronic basis functions is sufficient to explain the differences of energy and geometry induced by the H/D isotope effect, although the total energy of ～5 × 10^?4 a.u. was improved by using the s‐, p‐, and d‐type ([1s1p1d]) GTFs for protons and deuterons. We clearly demonstrate that the protonic and deuteronic basis functions based on the α_ave value enable us to apply the method to other sample molecules (glycine, malonaldehyde, and formic acid dimer). The protonic and deuteronic basis functions we developed treat the quantum effects of protons and deuterons effectively and extend the application range of the MO calculation to include nuclear quantum effects. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Hydrogen/deuterium adsorption and absorption properties on and in palladium using a combined plane wave and localized basis set method

Detailed information on the H/D isotope effects for adsorption on the surface and absorption in the bulk is important for understanding the nuclear quantum effect. To achieve this, we developed a new theoretical approach, namely, the combined plane wave and localized basis set (CPLB) method. By using the multicomponent quantum chemical method, which takes into account the quantum effect of a proton or deuteron, with the localized part of the CPLB method, direct analysis of the H/D isotope effect about adsorption and absorption is carried out. In this study, we performed a theoretical investigation of the H/D isotope effects for adsorption on a Pd(111) surface and absorption in bulk Pd. We clearly showed an H/D isotope effect on geometry during adsorption and absorption. Our developed CPLB approach is a powerful tool for analyzing the quantum nature of H/D in surface, bulk, and inhomogeneous systems.     

Multicomponent Molecular Orbital–Climbing Image–Nudged Elastic Band Method to Analyze Chemical Reactions Including Nuclear Quantum Effect

To analyze the H/D isotope effects on hydrogen transfer reactions in XHCHCHCHY?XCHCHCHYH (X, Y=O, NH, or CH₂) including the nuclear quantum effect of proton and deuteron, we propose a multicomponent molecular orbital‐climbing image‐nudged elastic band (MC_MO–CI–NEB) method. We obtain not only transition state structures but also minimum‐energy paths (MEPs) on the MC_MO effective potential energy surface by using MC_MO–CI–NEB method. We find that nuclear quantum effect affects not only stationary‐point geometries but also MEPs and electronic structures in the reactions. We clearly demonstrate the importance of including nuclear quantum effects for H/D isotope effect on rate constants (k_H/k_D).     

Analysis of exponent values of Gaussian‐type functions on quantum protons and deuterons in charged or polarized systems

The optimal exponent α values (α_opt) in s‐type Gaussian‐type functions (GTFs) for quantum protons and deuterons, which are used for multicomponent molecular orbital calculations including nuclear quantum nature of protons and deuterons, are analyzed for several charged or polarized systems and their deuterated species. Ishimoto and coworkers (Ishimoto, Int. J. Quantum Chem. 2006 , 106, 1465) have already proposed the average exponent values for five neutral molecules (α_ave), and demonstrated that their α_ave enables us to evaluate the H/D isotope effect on energies and geometries of various neutral species. The differences between total energies of several charged or polarized systems with previous α_ave and our α_opt correspond to only less than 0.004% of the total energy (0.47 kcal·mol^?1) except for HeH⁺ and HeD⁺ molecules, while the difference between interaction energies of H₂OH^+…OH₂ and H₂OD^+…OH₂ systems with previous α_ave is 19% (0.22 kcal·mol^?1) smaller than that with our α_opt. Meanwhile, the difference between O? H bond lengths in H₂OH^+…OH₂ system with α_ave and α_opt values is 0.027 Å. We also found that the interaction energies with α_opt value at the geometry optimized with previous α_ave value (α_sp) well reproduce those at the geometry optimized with α_opt value. We have demonstrated that the nuclear basis functions based on s‐type GTFs with previous α_ave values enable us to evaluate the H/D isotope effect on energies and geometries of charged or polarized systems. © 2016 Wiley Periodicals, Inc.     

High-precision quantum thermochemistry on nonquasiharmonic potentials: converged path-integral free energies and a systematically convergent family of generalized Pitzer-Gwinn approximations

Accurate quantum mechanical (QM) vibrational-rotational partition functions for HOOD, D(2)O(2), H(18)OOH, H(2)(18)O(2), D(18)OOH, and H(18)OOD are determined using a realistic potential energy surface for temperatures ranging from 300 to 2400 K by using the TT-FPI-ESPE path-integral Monte Carlo method. These data, together with our prior results for H(2)O(2), provide benchmarks for testing approximate methods of estimating isotope effects for systems with torsional motions. Harmonic approximations yield poor accuracy for these systems, and although the well-known Pitzer-Gwinn (PG) approximation provides better results for absolute partition functions, it yields the same results as the harmonic approximation for isotope effects because these are intrinsically quantal phenomena. We present QM generalizations of the PG approximation that can provide high accuracy for both isotope effects and absolute partition functions. These approximations can be systematically improved until they approach the accurate result and converge rapidly. These methods can also be used to obtain affordable estimates of zero-point energies from accurate partition functions-even those at relatively high temperatures.     

Simulation of tunneling in enzyme catalysis by combining a biased propagation approach and the quantum classical path method: application to lipoxygenase

The ability of using wave function propagation approaches to simulate isotope effects in enzymes is explored, focusing on the large H/D kinetic isotope effect of soybean lipoxygenase-1 (SLO-1). The H/D kinetic isotope effect (KIE) is calculated as the ratio of the rate constants for hydrogen and deuterium transfer. The rate constants are calculated from the time course of the H and D nuclear wave functions. The propagations are done using one-dimensional proton potentials generated as sections from the full multidimensional surface of the reacting system in the protein. The sections are obtained during a classical empirical valence bond (EVB) molecular dynamics simulation of SLO-1. Since the propagations require an extremely long time for treating realistic activation barriers, it is essential to use an effective biasing approach. Thus, we develop here an approach that uses the classical quantum path (QCP) method to evaluate the quantum free energy change associated with the biasing potential. This approach provides an interesting alternative to full QCP simulations and to other current approaches for simulating isotope effects in proteins. In particular, this approach can be used to evaluate the quantum mechanical transmission factor or other dynamical effects, while still obtaining reliable quantized activation free energies due to the QCP correction.     

Deuterium Discrimination in P--H/P--D Exchange of Phosphorous Acid

Deuterium discrimination in P--H/P--D exchange is first reported. Quantitative 1 H and 31 P NMR analyses of the phosphorous acid in H 2 O/D 2 O solutions indicate that there is a strong discrimination against deuterium bonding with phosphorus. The ([PD]/[PH]) nmr ratio, where [PD] nmr and [PH] nmr are the NMR determined concentration of phosphorus attached to deuterium and proton, respectively, is only 67% of the stoichiometrical D/H ratio in the studied solutions. The very strong isotope discrimination should originate from the isotope effect in tautomerization involving an intermediate having the structure of P(OH) 3 where the three OH's are equivalent.     

H/D isotope effect on charge‐inverted hydrogen‐bonded systems: Systematic classification of three different types in H3XH…YH3 (X = C,Si, or Ge,and Y = B,Al, or Ga) with multicomponent calculation

Three different H/D isotope effect in nine H₃XH(D)^…YH₃ (X = C, Si, or Ge, and Y = B, Al, or Ga) hydrogen‐bonded (HB) systems are classified using MP2 level of multicomponent molecular orbital method, which can take account of the nuclear quantum nature of proton and deuteron. First, in the case of H₃CH(D)^…YH₃ (Y = B, Al, or Ge) HB systems, the deuterium (D) substitution induces the usual H/D geometrical isotope effect such as the contraction of covalent R(C? H(D)) bonds and the elongation of intermolecular R(H(D)^…Y) and R(C^…Y) distances. Second, in the case of H₃XH(D)^…YH₃ (X = Si or Ge, and Y = Al or Ge) HB systems, where H atom is negatively charged called as charge‐inverted hydrogen‐bonded (CIHB) systems, the D substitution leads to the contraction of intermolecular R(H(D)^…Y) and R(X^…Y) distances. Finally, in the case of H₃XH(D)^…BH₃ (X = Si or Ge) HB systems, these intermolecular R(H(D)^…Y) and R(X^…Y) distances also contract with the D substitution, in which the origin of the contraction is not the same as that in CIHB systems. The H/D isotope effect on interaction energies and spatial distribution of nuclear wavefunctions are also analyzed. © 2015 Wiley Periodicals, Inc.     

Density functional theory treatment of electron correlation in the nuclear-electronic orbital approach

This paper presents the nuclear-electronic orbital density functional theory [NEO-DFT(ee)] method for including electron-electron correlation and nuclear quantum effects self-consistently in quantum chemical calculations. The NEO approach is designed to treat a relatively small number of nuclei quantum mechanically, while the remaining nuclei are treated classically. In the NEO-DFT(ee) approach, the correlated electron density is used to obtain the nuclear molecular orbitals, and the resulting nuclear density is used to obtain the correlated electron density during an iterative procedure that continues until convergence of both the nuclear and electronic densities. This approach includes feedback between the correlated electron density and the nuclear wavefunction. The application of this approach to bihalides and acetylene indicates that the nuclear quantum effects do not significantly impact the electron correlation energy, but the quantum nuclear energy is enhanced in the NEO-DFT(ee) B3LYP method. The excellent agreement of the NEO-DFT(ee)-optimized bihalide structures with the vibrationally averaged geometries from grid-based quantum dynamical methods provides validation for the NEO-DFT(ee) approach. Electron-proton correlation could be included by the development of an electron-nucleus correlation functional. Alternatively, explicit electron-proton correlation could be included directly into the NEO self-consistent-field framework with Gaussian-type geminal functions.     

Enantiomerisation of tetrahedral homochiral [M4L6] clusters: synchronised four Bailar twists and six atropenantiomerisation processes monitored by temperature-dependent dynamic 1H NMR spectroscopy

Temperature-dependent 1H NMR studies prove homochiral, racemic [([symbol: see text])/([symbol: see text])]-((NH4)4[symbol: see text] [Mg4(L1)6]) (1) to be kinetically stable on the NMR timescale. Due to steric reasons, rotation around the central C-C single bond in (L1)2- is blocked, which prevents 1 from enantiomerisation. Most interestingly, however, the 1H NMR spectrum of racemic 2a reveals dynamic temperature dependence. This phenomenon can be explained by simultaneous Bailar twists at the four octahedrally coordinated magnesium centres, synchronised with the sterically unhindered atropenantiomerisation processes around the C-C single bonds of the six ligands (L2)2-, leading to the unprecedented enantiomerisation ([symbol: see text])-2a [symbol: see text] ([symbol: see text])-2a. The profound nondissociative rearrangement occurs without the formation of diastereoisomers. Supplementary support for the interpretation of the temperature-dependent dynamic 1H NMR spectra of 2a is presented by additional studies of [([symbol: see text])/([symbol: see text])]-((EtNH3)4 [symbol: see text] [Mg4(L2)6]) (2b). In 2a and 2b, the ether methylene protons exhibit identical temperature dependence. However, with addition, the methylene protons of the ethyl ammonium groups of 2b display similar temperature dependence as the ligand ether methylene protons.     

H/D isotope effect on porphine and porphycene molecules with multicomponent hybrid density functional theory

To analyze the H/D isotope effect on porphine and porphycene molecules including the protonic/deuteronic quantum nature and electron correlation efficiently, the authors have developed the new scheme of the multicomponent hybrid density functional theory [MC_(HF+DFT)]. The optimized geometries of porphine, porphycene, and these deuterated isotopomers by our MC_(HF+DFT) method are in good agreement with the experimental "high-symmetric" structures, contrary to the "low-symmetric" geometries optimized by pure multicomponent Hartree-Fock method. The optimized geometries for HD-porphine and HD-porphycene molecules, in which an inner hydrogen is replaced to a deuterium, are found to be low symmetric. Such drastic geometrical change induces the electronic polarization, and gives rise to the slight dipole moment values in these HD species. Their results clearly indicate that the difference of the nuclear quantum nature between inner proton and inner deuteron directly influences the molecular geometry and electronic structure.     

Performance of Hyperspherical Harmonic Expansionon the Low-lying Pand D States of Helium Atom

IntroductionThe hyperspherical coordinate and corresponding hyperspherical harmonics (HH) havebeen applied to various areas of physics, such as three--body scattering, nuclear and atomicphysics as well as quantum chemistry['J, since the 1950's. The HH--generalized Laguerrefunction method (referred to as HHGLF) [2'3] and several modified versions developed by Dengand his coworkers, such as the potential harmonic--generalized Laguerre function(PHGLF )L'], and the correlation fun ct ion --…     

Entanglement of protons in organic molecules: an attosecond neutron scattering study of C [bond] H bond breaking.

Interactions between adjacent particles of condensed phases can lead to quantum correlation phenomena, like quantum interference, entanglement, delocalization, and "Schr?dinger's cat" states. Such correlations are theoretically expected to be extremely short-lived because of environmental disturbances. Here, we present experimental evidence for quantum entanglement between well localized protons of C [bond] H bonds of 2-isobutoxyethanol dissolved in D(2)O. The applied experimental method is neutron Compton scattering (NCS), which has a characteristic time window in the subfemtosecond time range. Our NCS results reveal that, in the subfemtosecond time scale, the measured cross-section density, and thus, in simple terms, the effectively present concentration, of the H atoms is "anomalously" reduced by approximately 20%. Affecting the microdynamics of protons of covalent C [bond] H bonds, this novel effect may have a broad range of chemical and biological applications.     

HD isotope effect of methyl internal rotation for acetaldehyde in ground state as calculated from a multicomponent molecular orbital method

We have analyzed the differences in the methyl internal rotation induced by the HD isotope effect for acetaldehyde (CH(3)CHO) and deuterated acetaldehyde (CD(3)CDO) in ground state by means of the multicomponent molecular orbital (MC_MO) method, which directly accounts for the quantum effects of protons and deuterons. The rotational constant of CH(3)CHO was in reasonable agreement with experimental one due to the adequate treatment of the protonic quantum effect by the MC_MO method. The C-D bond distances were about 0.007 A shorter than the C-H distances because of the effect of anharmonicity of the potential. The Mulliken population for CD(3) in CD(3)CDO is larger than that for CH(3) in CH(3)CHO because the distribution of wavefunctions for the deuterons was more localized than that for the protons. The barrier height obtained by the MC_MO method for CH(3)CHO was estimated as 401.4 cm(-1), which was in excellent agreement with the experimentally determined barrier height. We predicted the barrier height of CD(3)CDO as 392.5 cm(-1). We suggest that the internal rotation of the CD(3) group was more facile than that of the CH(3) group because the C-D bond distance was observed to be shorter than the C-H distance. Additionally the localized electrons surrounding the CD(3) group in CD(3)CDO caused the extent of hyperconjugation between the CD(3) and CDO groups to be smaller than that in the case of CH(3)CHO, which may have also contributed to the observed differences in methyl internal rotation. The differences in bond distances and electronic populations induced by the H/D isotope effect were controlled by the difference in the distribution of wavefunctions between the protons and deuterons.     

2D NMR studies of acrylonitrile-methyl acrylate copolymers

The microstructure of acrylonitrile-methyl acrylate copolymers prepared by the solution polymerization using 2,2′-azobisisobutyronitrile (AIBN) as free radical initiator was investigated by two-dimensional NMR techniques. 2D-heteronuclear single quantum correlation (HSQC) and the total correlation spectroscopy (TOCSY) have been utilized to resolve the complex ¹H NMR spectrum and to establish the compositional and configurational sequences of acrylonitrile-methyl acrylate copolymers. 2D HSQC and TOCSY showed compositional and configurational sensitivity of methine protons of A and M units upto the triad level. Heteronuclear multiple-bond correlation (HMBC) spectroscopy has been used to study carbon (carbonyl/nitrile)-proton coupling. The carbonyl and nitrile carbons showed compositional sensitivity upto the triad level. The values of reactivity ratios were determined by Kelen-Tudos (KT) and non-linear error in variable method (RREVM).     

Nuclear quantum and H/D isotope effects on three-centered bonding diborane: Path integral molecular dynamics simulations

Nuclear quantum and H/D isotope effects of bridging and terminal hydrogen atoms of diborane (B₂H₆) molecules were systematically studied by classical ab initio molecular dynamics (CLMD) and ab initio path integral molecular dynamics (PIMD) simulations with BHandHLYP/6-31++G** level of theory at room temperature (298.15 K). Calculated results clearly show that H/D isotope effect appears in the distribution of hydrogen (deuterium) of B₂H₆ (B₂D₆). Geometry of B₂H₆ also plays a significant role in the nuclear quantum effect proved by PIMD simulations, but slightly deviated from its equilibrium structure when simulated via CLMD simulation. The bond lengths between boron atoms R (B1 … B2) and the bridging hydrogen atoms R_HH (H_B1 … H_B2) of the B₂H₆ molecule obtained from PIMD simulations are slightly longer than those of the deuterated form of the diborane (B₂D₆) molecule. The principal component analysis (PCA) was also employed to distinguish the important modes of bridging hydrogen as related to the nuclear quantum and H/D isotope effects. The highest level of contribution obtained from PCA of PIMD simulations is bending, while various mixed vibrations with less contribution were also found. Therefore, the nuclear quantum and H/D isotope effects need to be taken into account for a better understanding of diborane geometry.     

Structure of copper(II)-histidine based complexes in frozen aqueous solutions as determined from high-field pulsed electron nuclear double resonance

W-band (95 GHz) pulsed EPR and electron-nuclear double resonance (ENDOR) spectroscopic techniques were used to determine the hyperfine couplings of different protons of Cu(II)-histidine complexes in frozen solutions. The results were then used to obtain the coordination mode of the tridentate histidine molecule and to serve as a reference for Cu(II)-histidine complexation in other, more complex systems. Cu(II) complexes with L-histidine and DL-histidine-alpha-d,beta-d2 were prepared in H2O and in D2O, and orientation-selective W-band 1H and 2H pulsed ENDOR spectra of these complexes were recorded at 4.5 K. These measurements lead to the unambiguous assignment of the signals of the H alpha, H beta, imidazole H epsilon, and the exchangeable amino, Ham, protons. The 14N superhyperfine splitting observed in the X-band EPR spectrum and the presence of only one type of H alpha and H beta protons in the W-band ENDOR spectra show that the complex is a symmetric bis complex. Its g parallel is along the molecular symmetry axis, perpendicular to the equatorial plane that consists of four coordinated nitrogens in histamine-like coordinations (NNNN). Simulations of orientation-selective ENDOR spectra provided the principal components of the protons' hyperfine interaction and the orientation of their principal axes with respect to g parallel. From the anisotropic part of the hyperfine interaction of H alpha and H beta and applying the point-dipole approximation, a structural model was derived. An unexpectedly large isotropic hyperfine coupling, 10.9 MHz, was found for H alpha. In contrast, H alpha of the Cu(II)-1-methyl-histidine complex where only the amino nitrogen is coordinated, showed a much smaller coupling. Thus, the hyperfine coupling of H alpha can serve as a signature for a histamine coordination where both the amino and imino nitrogens of the same molecule bind to the Cu(II), forming a six-membered chelating ring. Unlike H alpha the hyperfine coupling of H epsilon is not as sensitive to the presence of a coordinated amino nitrogen of the same histidine molecule.     

One- and two-dimensional NMR studies of methyl acrylate/vinyl acetate/N-vinyl carbazole terpolymers

Terpolymers of methyl acrylate/vinyl acetate/N-vinyl carbazole (M/A/C) with different compositions were synthesized by solution polymerization using AIBN as an initiator. Composition of terpolymers was determined from quantitative ¹³C{¹H} NMR spectrum. Two-dimensional heteronuclear single quantum correlation (HSQC) and total correlated spectroscopy (TOCSY) were used to assign the methylene and methine carbon resonances by analyzing two and three bond order couplings. Various resonance signals were assigned to different compositional and configurational sequences with the help of one- and two-dimensional NMR spectra. Three and four bond order coupling between carbonyl carbon and other neighboring protons have been investigated with the help of 2D heteronuclear multiple bond correlation (HMBC) spectra. The complex and overlapped ¹H NMR spectrum of terpolymer was analyzed completely with the help of 2D HSQC and TOCSY spectra.     

Highly oxygenated triterpenes from the roots of Atropa acuminata

Two new oleanane triterpenes; 2alpha,3alpha,24-trihydroxyolean-12-ene-28,30-dioic acid ([structure: see text]) and 2alpha,3alpha,24,28-tetrahydroxyolean-12-ene ([structure: see text]) have been isolated from the roots of Atropa acuminata. Anti-oxidant p-hydroxyphenethyl trans-ferulate ([structure: see text]), beta-sitosterol-3-O-beta-D-glucopyranoside ([structure: see text]) and oleanolic acid ([structure: see text]) have also been reported for the first time from this species. The structures were determined by spectroscopic studies including 2D-NMR.