The sticking probability of D(2)O-water on ice: Isotope effects and the influence of vibrational excitation

The present study measures the sticking probability of heavy water (D(2)O) on H(2)O- and on D(2)O-ice and probes the influence of selective OD-stretch excitation on D(2)O sticking on these ices. Molecular beam techniques are combined with infrared laser excitation to allow for precise control of incident angle, translational energy, and vibrational state of the incident molecules. For a translational energy of 69 kJ∕mol and large incident angles (θ ≥ 45°), the sticking probability of D(2)O on H(2)O-ice was found to be 1% lower than on D(2)O-ice. OD-stretch excitation by IR laser pumping of the incident D(2)O molecules produces no detectable change of the D(2)O sticking probability (<10(-3)). The results are compared with other gas∕surface systems for which the effect of vibrational excitation on trapping has been probed experimentally.     

Effect of surface modes on the six-dimensional molecule-surface scattering dynamics of H2-Cu(100) and D2-Cu(111) systems

We include the phonon modes originating from the three layers of Cu(100)/Cu(111) surface atoms on the dynamics of molecular [H(2)(v,j)/D(2)(v,j)] degrees of freedom (DOFs) through a mean field approach, where the surface temperature is incorporated into the effective Hamiltonian (potential) either by considering Boltzmann probability (BP) or by including the Bose-Einstein probability (BEP) factor for the initial state distribution of the surface modes. The formulation of effective potential has been carried out by invoking the expression of transition probabilities for phonon modes known from the "stochastic" treatment of linearly forced harmonic oscillator (LFHO). We perform four-dimensional (4D?2D) as well as six-dimensional (6D) quantum dynamics on a parametrically time and temperature-dependent effective Hamiltonian to calculate elastic/inelastic scattering cross-section of the scattered molecule for the H(2)(v,j)-Cu(100) system, and dissociative chemisorption-physisorption for both H(2)(v,j)-Cu(100) and D(2)(v,j)-Cu(111) systems. Calculated sticking probabilities by either 4D?2D or 6D quantum dynamics on an effective potential constructed by using BP factor for the initial state distribution of the phonon modes could not show any surface temperature dependence. In the BEP case, (a) both 4D?2D and 6D quantum dynamics demonstrate that the phonon modes of the Cu(100) surface affect the state-to-state transition probabilities of the scattered H(2) molecule substantially, and (b) the sticking probabilities due to the collision of H(2) on Cu(100) and D(2) on Cu(111) surfaces show noticeable and substantial change, respectively, as function of surface temperature only when the quantum dynamics of all six molecular DOFs are treated in a fully correlated manner (6D).     

Distribution of the cationic state over the chlorophyll pair of the photosystem II reaction center

The reaction center chlorophylls a (Chla) of photosystem II (PSII) are composed of six Chla molecules including the special pair Chla P(D1)/P(D2) harbored by the D1/D2 heterodimer. They serve as the ultimate electron abstractors for water oxidation in the oxygen-evolving Mn(4)CaO(5) cluster. Using the PSII crystal structure analyzed at 1.9 ? resolution, the redox potentials of P(D1)/P(D2) for one-electron oxidation (E(m)) were calculated by considering all PSII subunits and the protonation pattern of all titratable residues. The E(m)(Chla) values were calculated to be 1015-1132 mV for P(D1) and 1141-1201 mV for P(D2), depending on the protonation state of the Mn(4)CaO(5) cluster. The results showed that E(m)(P(D1)) was lower than E(m)(P(D2)), favoring localization of the charge of the cationic state more on P(D1). The P(D1)(?+)/P(D2)(?+) charge ratio determined by the large-scale QM/MM calculations with the explicit PSII protein environment yielded a P(D1)(?+)/P(D2)(?+) ratio of ~80/~20, which was found to be due to the asymmetry in electrostatic characters of several conserved D1/D2 residue pairs that cause the E(m)(P(D1))/E(m)(P(D2)) difference, e.g., D1-Asn181/D2-Arg180, D1-Asn298/D2-Arg294, D1-Asp61/D2-His61, D1-Glu189/D2-Phe188, and D1-Asp170/D2-Phe169. The larger P(D1)(?+) population than P(D2)(?+) appears to be an inevitable fate of the intact PSII that possesses water oxidation activity.     

Structure and spectral features of H+(H2O)7: Eigen versus Zundel forms

The two dimensional (2D) to three dimensional (3D) transition for the protonated water cluster has been controversial, in particular, for H(+)(H(2)O)(7). For H(+)(H(2)O)(7) the 3D structure is predicted to be lower in energy than the 2D structure at most levels of theory without zero-point energy (ZPE) correction. On the other hand, with ZPE correction it is predicted to be either 2D or 3D depending on the calculational levels. Although the ZPE correction favors the 3D structure at the level of coupled cluster theory with singles, doubles, and perturbative triples excitations [CCSD(T)] using the aug-cc-pVDZ basis set, the result based on the anharmonic zero-point vibrational energy correction favors the 2D structure. Therefore, the authors investigated the energies based on the complete basis set limit scheme (which we devised in an unbiased way) at the resolution of the identity approximation Moller-Plesset second order perturbation theory and CCSD(T) levels, and found that the 2D structure has the lowest energy for H(+)(H(2)O)(7) [though nearly isoenergetic to the 3D structure for D(+)(D(2)O)(7)]. This structure has the Zundel-type configuration, but it shows the quantum probabilistic distribution including some of the Eigen-type configuration. The vibrational spectra of MP2/aug-cc-pVDZ calculations and Car-Parrinello molecular dynamics simulations, taking into account the thermal and dynamic effects, show that the 2D Zundel-type form is in good agreement with experiments.     

Water adsorption on Rh(111) at 20 K: from monomer to bulk amorphous ice

The adsorption of water (D(2)O) molecules on Rh(111) at 20 K was investigated using infrared reflection absorption spectroscopy (IRAS). At the initial stage of adsorption, water molecules exist as monomers on Rh(111). With increasing water coverage, monomers aggregate into dimers, larger clusters (n = 3-6), and two-dimensional (2D) islands. Further exposure of water molecules leads to the formation of three-dimensional (3D) water islands and finally to a bulk amorphous ice layer. Upon heating, the monomer and dimer species thermally migrate on the surface and aggregate to form larger clusters and 2D islands. Based on the temperature dependence of OD stretching peaks, we succeeded in distinguishing water molecules inside 2D islands from those at the edge of 2D islands. From the comparison with the previous vibrational spectra of water clusters on other metal surfaces, we conclude that the number of water molecules at the edge of 2D islands is comparable with that of water molecules inside 2D islands on the Rh(111) surface at 20 K. This indicates that the surface migration of water molecules on Rh(111) is hindered as compared with the cases on Pt(111) and Ni(111) and thus the size of 2D islands on Rh(111) is relatively small.     

Molecular dynamics simulations of D2O ice photodesorption

Molecular dynamics (MD) calculations have been performed to study the ultraviolet (UV) photodissociation of D(2)O in an amorphous D(2)O ice surface at 10, 20, 60, and 90 K, in order to investigate the influence of isotope effects on the photodesorption processes. As for H(2)O, the main processes after UV photodissociation are trapping and desorption of either fragments or D(2)O molecules. Trapping mainly takes place in the deeper monolayers of the ice, whereas desorption occurs in the uppermost layers. There are three desorption processes: D atom, OD radical, and D(2)O molecule photodesorption. D(2)O desorption takes places either by direct desorption of a recombined D(2)O molecule, or when an energetic D atom produced by photodissociation kicks a surrounding D(2)O molecule out of the surface by transferring part of its momentum. Desorption probabilities are calculated for photoexcitation of D(2)O in the top four monolayers and are compared quantitatively with those for H(2)O obtained from previous MD simulations of UV photodissociation of amorphous water ice at different ice temperatures [Arasa et al., J. Chem. Phys. 132, 184510 (2010)]. The main conclusions are the same, but the average D atom photodesorption probability is smaller than that of the H atom (by about a factor of 0.9) because D has lower kinetic energy than H, whereas the average OD radical photodesorption probability is larger than that of OH (by about a factor of 2.5-2.9 depending on ice temperature) because OD has higher translational energy than OH for every ice temperature studied. The average D(2)O photodesorption probability is larger than that of H(2)O (by about a factor of 1.4-2.3 depending on ice temperature), and this is entirely due to a larger contribution of the D(2)O kick-out mechanism. This is an isotope effect: the kick-out mechanism is more efficient for D(2)O ice, because the D atom formed after D(2)O photodissociation has a larger momentum than photogenerated H atoms from H(2)O, and D transfers momentum more easily to D(2)O than H to H(2)O. The total (OD + D(2)O) yield has been compared with experiments and the total (OH + H(2)O) yield from previous simulations. We find better agreement when we compare experimental yields with calculated yields for D(2)O ice than when we compare with calculated yields for H(2)O ice.     

Interactions of D2O with methane and fluoromethane surfaces

TOF-SIMS is used to investigate the interactions between D2O and hydrophobic molecules, such as CH4, CH3F, CH2F2, CHF3, and CF4, at cryogenic temperatures (15 K). By irradiation with a 1.5-keV He+ beam, the D(+)(D2O)n ions are ejected efficiently from the D2O nanoclusters physisorbed on the CF4 layer due to Coulomb explosion: the ion yields are by about two orders of magnitude higher than those from a thick D2O layer via the kinetic sputtering. The D(+)(D2O)n yields decrease on the CHnF(4-n) layer with increasing the number of the C-H group. This is because the Coulombic fission is quenched due to the delocalization of valence holes through the C-H...H-C and C-H...D2O contacts. A pure D2O film is hardly grown on the CH4 layer as a consequence of intermixing whereas the D2O molecules basically adsorb on the surfaces of fluoromethanes, suggesting the attractive (water-repellent) interactions in the C-H...D2O (C-F...D2O) contacts. The C-H...O bond behaves like a conventional O-H...O hydrogen bond as far as the collision-induced proton transfer reaction is concerned.     

Structure, stability, thermodynamic properties, and infrared spectra of the protonated water octamer H(+)(H2O)8

We investigated various two-dimensional (2D) and three-dimensional (3D) structures of H (+)(H 2O) 8, using density functional theory (DFT), Moller-Plesset second-order perturbation theory (MP2), and coupled cluster theory with single, double, and perturbative triple excitations (CCSD(T)). The 3D structure is more stable than the 2D structure at all levels of theory on the Born-Oppenheimer surface. With the zero-point energy (ZPE) correction, the predicted structure varies depending on the level of theory. The DFT employing Becke's three parameters with Lee-Yang-Parr functionals (B3LYP) favors the 2D structure. At the complete basis set (CBS) limit, the MP2 calculation favors the 3D structure by 0.29 kcal/mol, and the CCSD(T) calculation favors the 3D structure by 0.27 kcal/mol. It is thus expected that both 2D and 3D structures are nearly isoenergetic near 0 K. At 100 K, all the calculations show that the 2D structure is much more stable in free binding energy than the 3D structure. The DFT and MP2 vibrational spectra of the 2D structure are consistent with the experimental spectra. First-principles Car-Parrinello molecular dynamics (CPMD) simulations show that the 2D Zundel-type vibrational spectra are in good agreement with the experiment.     

Two-Dimensional Planar Chromatography with a Closed Adsorbent Layer

A new two-dimensional chromatography process on closed plates is proposed. A previously described device with ethanol as a mobile phase is used to experimentally study two-dimensional thin-layer chromatography (2D TLC) on plates with 5 × 5 and 10 × 10 cm sizes. This work includes the experimental study and comparison of the following TLC versions: (1) the proposed 2D TLC version with a closed adsorbent layer with 1D separation on closed plates (an ascending mobile phase flow) and (2) conventional 2D TLC with an open adsorbent layer. The ascending version of 2D TLC with a closed adsorbent layer considerably (byR~55%) shortens the chromatographic time, especially with the use of 5 × 5 cm plates in the 2D separation version compared with the 1D version on 10 × 10 cm plates.     

On retentivity tuning by flow in the second column of different comprehensive two dimensional gas chromatographic configurations

Retentivity tuning in comprehensive two dimensional GC separations of aliphatics (linear and cyclic hydrocarbons) and aromatics in gasoline by changing the carrier gas flows in the column series at constant working temperature parameters of both columns is discussed. Comprehensive 2D techniques studied include GC×GC with cryogenic and differential flow modulation and non-modulated transfer (NMT). In all configurations, the first dimension was a non-polar column and the second dimension a polar column. Using three different flows (0.6, 1.0 and 1.4mL/min) of helium carrier gas in cryogenic modulated GC×GC illustrated that, as expected, retention of the solutes on the (1)D and (2)D columns increased but the separation quality was nearly constant. A change of carrier gas pressure (p(m)=175-125kPa) on the (1)D and (2)D columns joint point at constant inlet pressure (p(i)=525kPa) in NMT, induces an increase of the carrier gas flow rate on the (1)D and a decrease on the (2)D column, respectively. The higher retentivity of the (2)D column improved the group type separation of aliphatic/cyclic hydrocarbons and aromatics and a higher distribution of aromatics on the 2D retention plane was noted. Retentivity tuning was also performed in flow modulated GC×GC by operating the (1)D column at 0.8mL/min and the (2)D column at 20 and 26mL/min. The higher retentivity at 20mL/min improved the group type separation of aliphatic/cyclic hydrocarbons and aromatics in the 2D retention plane.     

Visualizations of transition dipoles, charge transfer, and electron-hole coherence on electronic state transitions between excited states for two-photon absorption

The one-photon absorption (OPA) properties of donor-pi-bridge-acceptor-pi-bridge-donor (D-pi-A-pi-D)-type 2,1,3-benzothiadiazoles (BTD) were studied with two dimensional (2D) site and three dimensional (3D) cube representations. The 2D site representation reveals the electron-hole coherence on electronic state transitions from the ground state. The 3D representation shows the orientation of transition dipole moment with transition density, and the charge redistribution on the excited states with charge difference density. In this paper, we further developed the 2D site and 3D cube representations to investigate the two-photon absorption (TPA) properties of D-pi-A-pi-D-type BTD on electronic transitions between excited states. With the new developed 2D site and 3D cube representations, the orientation of transition dipole moment, the charge redistribution, and the electron-hole coherence for TPA of D-pi-A-pi-D-type BTD on electronic state transitions between excited states were visualized, which promote deeper understanding to the optical and electronic properties for OPA and TPA.     

A 3D QSAR study on a set of dopamine D4 receptor antagonists

The molecular alignments obtained from a previously reported pharmacophore model have been employed in a three-dimensional quantitative structure-activity relationship (3D QSAR) study, to obtain a more detailed insight into the structure-activity relationships for D(2) and D(4) receptor antagonists. The frequently applied CoMFA method and the related CoMSIA method were used. Statistically significant models have been derived with these two methods, based on a set of 32 structurally diverse D(2) and D(4) receptor antagonists. The CoMSIA and the CoMFA methods produced equally good models expressed in terms of q(2) values. The predictive power of the derived models were demonstrated to be high. Graphical interpretation of the results, provided by the CoMSIA method, brings to light important structural features of the compounds related to either low- or high-affinity D(2) or D(4) antagonism. The results of the 3D QSAR studies indicate that bulky N-substituents decrease D(2) binding, whereas D(4) binding is enhanced. Electrostatically favorable and unfavorable regions exclusive to D(2) receptor binding were identified. Likewise, certain hydrogen-bond acceptors can be used to lower D(2) affinity. These observations may be exploited for the design of novel dopamine D(4) selective antagonists.     

Cux (x=1-4)团簇在CeO2(111)表面的吸附

用基于密度泛函理论的第一性原理方法研究了Cu团簇(Cu_x, x=1-4)在CeO₂(111)表面的吸附. 研究发现当团簇比较小时(x=2, 3), 倾向于平铺表面; 当x=4时, Cu团簇在CeO₂(111)表面以三维的四面体结构吸附较为稳定, 从Cu 3d到Ce 4f的电荷转移使Cu团簇带正电荷. 由二维的菱形结构到三维的四面体结构的转变势垒为1.05 eV, 并且其中一个Cu原子直接迁移到另外三个Cu原子的空位顶部的转变路径比较有利. 在Cu团簇与CeO₂的相互作用过程中, Cu-O和Cu-Cu相互作用的竞争最终决定了Cu团簇在CeO₂上的形貌. 这种CeO₂(111)负载的带正电的三维Cu团簇将对水分解, 进而对水煤气反应具有高的催化活性.     

Electron spin resonance study on H6+, H5D+, H4D2+, and H2D4+ in solid parahydrogen

We carried out an electron spin resonance (ESR) study on hydrogen ion radicals produced by radiolysis of solid para-H(2). In addition to quartet ESR lines proposed to be H(2) (+)-core H(6) (+) (D(2d)) ions in solid para-H(2) [T. Kumada et al., Phys. Chem. Chem. Phys. 7, 776 (2005)], we newly observed totally more than 50 resolved lines in gamma-ray irradiated solid para-H(2)-ortho-D(2) (1 mol %) and para-H(2)-HD (1 mol %) mixtures. We assigned these lines to be isotope substituents of H(2) (+)-core H(6) (+) ions such as H(5)D(+), H(4)D(2) (+), and H(2)D(4) (+) throughout the comparison of their ESR parameters with theoretical results. These results provide a conclusive evidence that H(2) (+)-core H(6) (+) ions are generated in irradiated solid hydrogens. Analysis of the EPR spectrum and ab initio calculations predicts D(2d) symmetry of the H(6) (+) ions, whereas a lowering symmetry (D(2d)-->C(2v)) induced by asymmetric nuclear wave function is observed in H(5)D(+) and H(4)D(2) (+). We also observed isotope-substitution reactions such as H(6) (+)+D(2)-->H(4)D(2) (+)+H(2) and H(6) (+)+HD-->H(5)D(+)+H(2), which are analogous to the well-known isotope-condensation reactions of H(3) (+) in dark nebula, H(3) (+)+HD-->HD(2) (+)+H(2) and HD(2) (+)+HD-->D(3) (+)+H(2).     

Possibility of a 2D SiC monolayer formation on Mg(0001) and MgO(111) substrates

The geometrical characteristics of a 2D SiC monolayer on Mg(0001) and MgO(111) plates regarded as potential materials for growing two-dimensional silicon carbide were studied. The most favorable positions of the atoms of 2D SiC on the substrates were determined. In the 2D SiC/Mg(0001) system, unlike in 2D SiC/MgO(111), the deviation of the carbon atom from the silicon carbide monolayer was insignificant (0.08 Å). Consequently, magnesium can be used as a substrate for growing two-dimensional silicon carbide. The use of MgO(111) is not recommended because of a significant distortion of the 2D SiC surface.     

Capture and dissociation in the complex-forming CH(v = 0,1) + D2 → CHD + D, CD2 + H, CD + HD reactions and comparison with CH(v = 0,1) + H2

Rate coefficients for the CH(v = 0,1) + D(2) reaction have been determined for all possible channels (T: 200-1200 K), using the quasiclassical trajectory method and a suitable treatment of the zero point energy. Calculations have also been performed on the CH(v = 1) + H(2) reaction and the CH(v = 1) + D(2) → CH(v = 0) + D(2) process. Most of the results can be understood considering the key role played by the deep minimum of the potential energy surface (PES), the barrierless character of the PES, the energy of the reaction channels, and the kinematics. The good agreement found between theory and experiment for the rate coefficients of the capture process of CH(v = 0) + D(2), the total reactivity of CH(v = 1) + D(2), H(2), as well as the good agreement observed for the related CH(v = 0) + H(2) system (capture and abstraction), gives confidence on the theoretical rate coefficients obtained for the capture processes of CH(v = 1) + D(2), H(2), the individual reactive processes of CH(v = 1) + D(2), H(2), the abstraction and abstraction-exchange reactions for CH(v = 0) + D(2), and the inelastic process mentioned above, for which there are no experimental data available, and that can be useful in combustion chemistry and astrochemistry.     

High-throughput 3D spheroid culture and drug testing using a 384 hanging drop array

Culture of cells as three-dimensional (3D) aggregates can enhance in vitro tests for basic biological research as well as for therapeutics development. Such 3D culture models, however, are often more complicated, cumbersome, and expensive than two-dimensional (2D) cultures. This paper describes a 384-well format hanging drop culture plate that makes spheroid formation, culture, and subsequent drug testing on the obtained 3D cellular constructs as straightforward to perform and adapt to existing high-throughput screening (HTS) instruments as conventional 2D cultures. Using this platform, we show that drugs with different modes of action produce distinct responses in the physiological 3D cell spheroids compared to conventional 2D cell monolayers. Specifically, the anticancer drug 5-fluorouracil (5-FU) has higher anti-proliferative effects on 2D cultures whereas the hypoxia activated drug commonly referred to as tirapazamine (TPZ) are more effective against 3D cultures. The multiplexed 3D hanging drop culture and testing plate provides an efficient way to obtain biological insights that are often lost in 2D platforms.     

Observation and analysis of the 2g(1D) ion-pair state of I2: the g/u mixing between the 1u(1D) and 2g(1D) states

We report the analysis of the 2g(1D) ion-pair state of I2 by perturbation-facilitated optical-optical double resonance. The present study began with the observation of the 2g(1D)-A' 3Pi(2u) emission at around 230 nm during the analysis of the ultraviolet emissions originating form the 1u(1D) ion-pair state. The identification of this new transition helped us to specify the wavelengths for detecting the 2g(1D) state by emission, and also to estimate its absolute position. The intermediate states used to observe the 2g(1D) state were the B 3Pi(0u(+))-b' 2u mixed states by the hyperfine interaction, which allowed us to combine the X 1Sigmag(+) ground state with the 2g(1D) state in the (1+1) photon excitation following the optical selection rules for one-photon transitions: 2g(1D)<--b' 2u-B 3Pi(0u(+))<--X 1Sigmag(+). Our analysis covered the 2g(1D) state in the 0< or =v< or =12 and 9< or =J< or =40 ranges. The molecular constants and Rydberg-Klein-Rees (RKR) potential of the 2g(1D) state were reported. We discussed the occurrence of the 2g(1D)-A' 3Pi(2u) emission, when exciting to the 1u(1D) v=0 state, and attributed it to the g/u mixing between the 2g(1D) and 1u(1D) states by the hyperfine interaction. The effect of the perturbation on measured line intensities and lifetimes was evident.     

Quantum sieving effect of three-dimensional Cu-based organic framework for H2 and D2

The crystal structure of [Cu(4,4'-bipyridine) 2(CF 3SO 3) 2] n metal-organic framework (CuBOTf) of one-dimensional pore networks after pre-evacuation at 383 K was determined with synchrotron X-ray powder diffraction measurement. Effective nanoporosity of the pre-evacuated CuBOTf was determined with N 2 adsorption at 77 K. The experimental H 2 and D 2 adsorption isotherms of CuBOTf at 40 and 77 K were measured and then compared with GCMC-simulated isotherms using the effective nanoporosity. The quantum-simulated H 2 and D 2 isotherms at 77 K using the Feynman-Hibbs effective potential coincided with the experimental ones, giving a direct evidence on the quantum molecular sieving effect for adsorption of H 2 and D 2 on CuBOTf. However, the selectivity for the 1:1 mixed gas of H 2 and D 2 was 1.2. On the contrary, experimental H 2 and D 2 isotherms at 40 K had an explicit adsorption hysteresis, originating from the marked pore blocking effect on measuring the adsorption branch. The blocking effect for quantum H 2 is more prominent than that for quantum D 2; the selectivity for D 2 over H 2 at 40 K was in the range of 2.6 to 5.8. The possibility of the quantum molecular sieving effect for H 2 and D 2 adsorption on [Cu 3(benzene-1,3,5-tricarboxylate) 2(H 2O) 3] n of three-dimensional pore networks was also shown at 77 K.     

Tunneling chemical reactions D + H2 --> DH + H and D + DH --> D2 + H in solid D2-H2 and HD-H2 mixtures: an electron-spin-resonance study

Tunneling chemical reactions D + H2 --> DH + H and D + DH --> D2 + H in solid HD-H2 and D2-H2 mixtures were studied in the temperature range between 4 and 8 K. These reactions were initiated by UV photolysis of DI molecules doped in these solids for 30 s and followed by measuring the time course of electron-spin-resonance (ESR) intensities of D and H atoms. ESR intensity of D atoms produced by the photolysis decreases but that of H atoms increases with time. Time course of the D and H intensities has the fast and slow processes. The fast process, which finishes within approximately 300 s after the photolysis, is assigned to the reaction of D atom with one of its nearest-neighboring H2 molecules, D(H2)n(HD)(12-n) --> H(H2)(n-1)(HD)(13-n) or D(H2)n(D2)(12-n) --> H(HD)(H2)(n-1)(D2)(12-n) for 12 > or = n > or = 1. Rate constant for the D + H2 reaction between neighboring D atom-H2 molecule pair is determined to be (7.5 +/- 0.7) x 10(-3) s(-1) in solid HD-H2 and (1.3+/-0.3) x 10(-2) s(-1) in D2-H2 at 4.1 K, which is very close to that calculated based on the theory of chemical reaction in gas phase by Hancock et al. [J. Chem. Phys. 91, 3492 (1989)] and Takayanagi and Sato [J. Chem. Phys. 92, 2862 (1990)]. This rate constant was found to be independent of temperature up to 7 K within experimental error of +/-30%. The slow process is assigned to the reaction of D atom produced in a cage fully surrounded by HD or D2 molecules, D(HD)12 or D(D2)12. This D atom undergoes the D + DH reaction with one of its nearest-neighboring HD molecules in solid HD-H2 or diffuses to the neighbor of H2 molecules to allow the D + H2 reaction in solid HD-H2 and D2-H2. The former is the main channel in solid HD-H2 below 6 K where D atoms diffuse very slowly, whereas the latter dominates over the former above 6 K. Rate for the reactions in the slow process is independent of temperature below 6 K but increases with the increase in temperature above 6 K. We found that the increase is due to the increase in hopping rate of D atoms to the neighbor of H2 molecules. Rate constant for the D + DH reaction was found to be independent of temperature up to 7 K as well.