Density functional theoretical assessment of titanium metal for adsorption of hydrogen, deuterium and tritium isotopes

Titanium, a high-temperature tolerance metal, is preferred as neutron targets due to high hydrogen storage capacity. Therefore, there is a need to understand the interaction and dynamical behaviours of hydrogen isotopes with Ti which is investigated by means of linear combination of atomic orbitals and projector augmented wave (PAW) potential within the density functional theoretical framework. The hydrogen isotope is studied by incorporating zero point energy and the harmonic transition state theory (HTST) was used to determine the rate constant. The values of surface adsorption energy of hydrogen isotopes were predicted to follow the trend: Ead(H2) > Ead(D2) > Ead(T2). The activation energy barrier from top to bridge and top to hollow sites was negative for H atom indicating barrier less diffusion. The computed total density of states and partial density of states confirmed that the hollow site offers the most stable site for H atom adsorption than that by bridge and top sites. The calculated barrier height for dissociation was 0.4 eV at surface coverage of θH > 0.5 ML, whereas the barrier height for recombination was found to be much higher than that of dissociation. The calculated dissociation rate constant using HTST was found to be quite fast, whereas the rate constant for recombination was determined to be very slow as expected. The ZPE corrected activation heights for bulk diffusion in Ti from one Td void to nearby Td void for H, D and T were computed to be 0.118, 0.126 and 0.129 eV, respectively, at the PAW level. The calculated diffusivity establishes that the lighter H atom migrates faster than that of heavier D and T atoms. The classical barrier height was observed to be reduced after quantum correction.


Introduction
Isotopes of hydrogen are fused simultaneously by portable linear particle accelerator to generate controlled neutron flux. The accelerated positively charged ions of hydrogen isotopes are subjected to metal hydride target also containing hydrogen isotopes and the whole compact system is popularly known as neutron generator. The metal hydride target could be either in the solid or gas state with deuterium (D) or tritium (T) inside. The deuterium-and tritium-based target is known as DD and DT neutron, respectively [1][2][3][4]. The metal hydride target should have high mechanical strength to withstand the bombardment by high energetic particle, high thermal stability and heat conductivity. Additionally, the metal hydride target of the neutron generator should possess high storage capacity of hydrogen isotope to convey an uninterrupted neutron stream. Researchers throughout the world have tried with the thin films fabricated from different pure metals like: Lithium, Titanium, Yttrium, Vanadium, Zirconium, Hafnium, Niobium, Lanthanum and Thorium and many more as well as alloys for the storage of hydrogen and its isotopes [5]. Among all of the studied materials, thin film of Titanium was established to be the preferred substance for metal hydride targets because of its very high hydrogen isotope storage capacity (H/Ti ~ 2) that leads to a high neutron yield [6,7]. Apart from this, Ti is quite cheap, easily available and displays high-temperature tolerance.
Titanium hydride, TiH 2 , is widely deployed as an efficient storage material for hydrogen isotopes [6,7]. Ti in Ti-H can be present either as α-Ti with a hexagonal close-packed lattice (hcp), δ-Ti with a face-centered cubic lattice (fcc) or β-Ti with a body-centered cubic lattice (bcc) depending on the environment [8]. Titanium has been considered as the preferred target material for deuterium or tritium loaded neutron generator as it has the capacity of holding a higher density of hydrogen isotopes than the other available metalhydride target materials [9]. However, bcc-type Ti-V alloys have attracted interest for storage hydrogen because they can absorb and release hydrogen in large amounts and at lower temperature than pure titanium. So, it is interesting to study the behavior of H isotopes with pure bcc-Ti before moving to alloys [10].
In view of the aforementioned applications, the atomistic understanding of Ti-H system is of immense importance which includes adsorption, dissociation and absorption of hydrogen isotopes in bulk and surface Ti. Numerous studies have been reported on the metal-H system employing ab initio calculations to have fundamental insights of hydrogen behavior through evaluation of hydrogen solubility and diffusivity [11][12][13][14][15][16][17]. First-principles calculations on Ti-H system also have been reported by many research group. Connetable et al. [18] have reported diffusion of hydrogen in hcp-titanium using density functional theory. The point defects in titanium using ab initio calculations have been explored by Nayak et al. [19]. Density Functional Theory (DFT) with generalized gradient approximation was adopted to study the adsorption of hydrogen on a titanium atom incorporated benzene molecule [20]. Further, vacancy and self-interstitials in hcp titanium were studied using first principles methods [21]. Combined ab initio and positron lifetime spectroscopy were used to investigate vacancy-hydrogen interaction in α-Ti [22]. DFT was used to study the H-H interaction with α-Ti [23]. The hydride stability in the Ti-H system for tetragonal γ-TiH phase and the fcc-based δ-TiH 2 phase was investigated by first-principles theory [24]. The chemical bonding in TiH 2 systems was reported earlier using the linear-combination-of-atomic-orbital (LCAO) technique for a cluster model [25].
The function of titanium in dissociative chemisorption of hydrogen molecule was also studied using DFT [26]. Ab initio modeling on the effect of H, N, C and O interstitial atoms on the deformation mechanism of α-Ti was reported [27,28]. Earlier, the hydrogen solubility in TiH n was reported using ab initio calculated free energies [29]. The face-centered cubic, δ phase and ɛ phase structures of TiHx with were investigated using first-principles calculation [30]. The solution energy of H and He in hcp Ti at the DFT level of theory has been reported [31]. Diffusivity of titanium in the alpha Ti-H n and pure α-Ti was determined using the pseudopotential means [32]. Though plenty of studies have been carried out on hcp-Ti, the study of bcc-Ti is rather limited. Earlier, the lattice dynamics of bcc Ti was conducted to evaluate the phonon frequency [33]. Recently, superionic like diffusion in bcc Titanium has been reported by performing classical and ab initio molecular dynamics [34] simultaneously. An integral modelling approach for understanding the strengthening mechanisms in bcc-Ti alloys has earlier been reported [35]. Earlier, the interaction and dynamical behaviors of hydrogen isotopes in pure metals were studied using DFT [36][37][38][39].
In spite of very high potential application, the experimental and computational studies on the conduct of hydrogen isotopes in bcc-Ti are rather limited. For an efficient Ti filmbased neutron generator, the fundamental understanding on the hydrogen isotopes adsorption and diffusion in bulk Ti and surface is very much needed. Therefore, our aim in this work is to establish the chemisorption and diffusion pathway of H isotopes in the clean Ti lattice by applying ab initio density functional theory. We present the computational methodology in Sect. 2, and the results and discussion in Sect. 3. The validation of computational methodology is presented in 3.1, whereas Sect. 3.2 contains about dissociation of H 2 molecule. The adsorption and diffusion of H isotopes in Ti are described in 3.3 to 3.6. and the work is concluded in Sect. 4.

Computational protocol
In this work we have conducted first principles calculations using Vienna Ab-initio Simulation code [40,41]. The effects of exchange and correlation (XC) were treated using the generalized gradient approximation in the form of Perdew-Burke-Ernzerhof (PBE) density functional [42][43][44] including spin polarization. The projector augmented wave (PAW) potentials [45,46] with an energy cut-off of 350 eV were employed to embody the ionic cores, whereas the integration of the Brillouin zone was taken care by the special k-points of Monkhorst-Pack [47]. Both the atomic positions and supercell were allowed to relax for attaining equilibrium. The forces on all the atoms are kept less than 0.01eVÅ −1 . The zero point energy (= 1/2∑ i hν i , ν i is the frequency) was determined from the H atom frequency by performing phonon calculations by freezing the Ti atoms. The contribution of metal atoms to the total ZPE corrections can be safely ignored compared to lighter H isotopes due to lower mass as reported by earlier studies [48,49]. A k-point sampling of 3 × 3 × 3 for bulk Ti 54 was used, whereas a 2 × 2 surface cell with 6 layers of metal and a k-point sampling of 8 × 8 × 1 was followed for H atom at the surface of Ti(100). Furthermore, 10 Å of vacuum was provided for the calculations of surface. The nudged elastic band (NEB) method [50] is performed to find the minimum energy paths and the transition states for H atom diffusion into Ti through Ti(100) [using the surface (2 × 2) cell] and bulk Ti. The convergence criterion was maintained by setting the force of about 0.01 eV/Å or less acting on an atom for all the images. The calculations are also conducted using Kohn-Sham (KS) DFT employing Perdew-Burke-Ernzerhof (PBE) density functional [42][43][44] with generalized gradient approximation (GGA) and double zeta polarized basis set (LCAO basis sets) as implemented in the Atomistic Toolkits (ATK) [51][52][53]. The climbing image nudged elastic band (CINEB) technique was employed to find the minimum energy paths for H atom migration using ATK.

Computational method validation
We have validated the present computational methods by comparing the calculated values of lattice parameter (a), cohesive energy (E coh ) and bulk modulus (B) for the bulk Ti with the available experimental data which are tabulated Table 1. The computed results obtained using LCAO and PAW basis sets are quite well in agreement with the results of reported literature and experiments and thus confirms the correctness of the used computational techniques in the present study. The calculated elastic constant (29.14 GPa), shear modulus (29.39 GPa) and Poisson ratio (0.375) using LCAO basis set are in accord with the reported experimental data [54][55][56].
The LCAO-based basis set was further tested by evaluating the molecular parameters of single hydrogen molecule. The H-H bond length (0.76 Å), vibrational frequency (ν = 531.27 meV), binding energy (E b = − 4.47 eV), and zero point energy (25.63 kJ/mol) were found to be in accord with the published experimental data [63][64][65].
The much studied slab model was considered for surface calculations. The optimized number of layers for the slab was fixed by allowing relaxations of surface comprising of 4, 5, 6, 7 and 8 layers.
The surface energy was calculated as, where E DFT slab represents total energy of the slab with N atoms and € represents bulk energy per Ti atom, A is the surface area. The computed surface energies for Ti(100) surface with different layers are tabulated in Table 2, whereas the various surface layers are displayed in Fig. 1. The calculated surface energies were seen to be converged to ~ 7 meV/Å 2 right after 6 atomic layers using LCAO for ATK and for VASP, the value is ~ 2 meV/Å 2 with PAW potential.

Dissociative adsorption of hydrogen molecule and its isotopes on Ti (100) surface
The physisorption of hydrogen molecule and its isotopes on the surface of titanium and subsequently dissociation to atoms happens very quickly with almost zero energy barrier. The mechanism of dissociation at the atomistic level is yet to be matured. Therefore, there is a need to elucidate the dissociation mechanism of H 2 molecule on Ti (100) surface from an atomistic level as well as technological curiosity.
There are three potential sites available for initial attachment of H 2 molecule namely top, bridge and hollow. The H 2 molecule is initially placed on the bridge and top sites parallel to the surface and subsequently was made to move towards the surface in progression and was allowed to relax parallel to the surface. Figure 2 portraits the dissociation of H 2 molecule at the near proximity of the Ti (100) surface. From Fig. 3, it can be seen that the H…H interatomic bond length increases continuously from the equilibrium bond length of 0.75 Å as H 2 molecule approaches the Ti atom at the Ti (100) surface followed by dissociation to atoms at a distance of 1.5 Å from the surface. The hydrogen atoms after dissociation were seen to reside in the hollow position. In the beginning, the hydrogen molecule is found to be adsorbed as a molecule at a distance of 2.5 Å from the Ti (100) surface and then starts dissociating as approaching nearer to the surface which is clearly reflected in the profile of adsorption energy. At the start, the calculated adsorption energy of H 2 was positive at a distance of 3.5-3.0 Å (non-interacting)   from the surface and then turns into negative energy signifying the molecular H 2 adsorption and thereafter becomes more negative (~ − 0.72 eV) in the range of 1.25-0.75 Å from the surface (dissociation in to atoms). This is due to decrease in the H-H interaction compared to Ti-H interaction as H 2 molecule is approaching towards the surface. The increase in the interaction of Ti with H atom is due to the interaction of H (1s) orbitals with Ti (4s) and (4p) orbital (explanation is provided through DOS, Fig. 7). Also, from Fig. 2a  Further, in order to determine the barrier energy for dissociation of hydrogen molecule, CI-NEB calculation was performed using LCAO basis set as implemented in ATK software. The energy versus reaction coordinate is plotted in Fig. 4a for LCAO and Fig. 4b for PAW calculations.
The calculated values are listed in Table 3. The calculated barrier height for dissociation was 0.4 eV at surface coverage of θ H > 0.5ML. Almost similar value (0.46 eV) was obtained by PAW calculation. It is interesting to explore the barrier for the recombination of two H atoms to H 2 molecule. CI-NEB and NEB calculation was performed to evaluate the barrier energy for recombination using both LCAO and PAW basis sets. The barrier height for recombination was found to be much higher than that of dissociation. In case of recombination the H atom has to be detached from the binding of Ti atom and it recombines with another H atom to form H 2 molecule and this requires higher activation energy which is generally provided by applying external temperature. The calculated value using both LCAO and PAW are very close to each other. The classical barrier height was observed to be reduced after quantum correction. The calculated dissociation rate constant using HTST was found to be quite fast, whereas the rate constant for recombination was determined to be very slow as expected.

Adsorption of hydrogen isotopes on Ti (100) surface
In the preceding section we described the dissociation mechanism of hydrogen molecule and its isotopes. Now, we will discuss the adsorption of isotopes of H atom in different potential sites of Ti (100) surface. The configuration of Ti (100) surface containing one H atom surrounded by four Ti atoms on the surface (0.25 ML coverage) was allowed to relax and the relaxed minimum energy configuration is depicted in Fig. 5. The computed values of surface adsorption energy over a wide coverage are given in Tables 4 and 5. The surface adsorption energy (E ad ) for hydrogen atom on Ti (100) surface was evaluated by the following expression:  Here, E H2, E Ti(slab) and E nH-Ti(slab) represent the total electronic energy of isolated H 2 molecule, Ti(100) slab and H atom containing Ti(100) slab, respectively.
The hydrogen atom in the hollow site is found to be adsorbed most strongly over bridge and top sites at the PAW level of calculations, whereas bridge site is predicted to be preferred over hollow and top sites at the LCAO level. Nevertheless, top is the least preferred for H adsorption. From the Bader charge analysis, it is observed that more charge was transferred from Ti atoms to H in the case of bridge and hollow (~ 0.60 and 0.63 e − ) site adsorption compared to top position (0.46 e − ). These values suggest ionic type of bond between H and Ti atoms. Further, ZPE correction was performed to study the effect of isotopes. In the case of hollow site, the heavier isotope is a little softly adsorbed, whereas in bridge site, the heavier isotope is to some extent strongly adsorbed.
The calculated values of adsorption energy, E ad for H atom both in the bridge and hollow sites are seen to be greater with increase in the coverage of Ti (100) (Fig. 6). Next, to obtain more insights about the preferred adsorption of H atom in the hollow position, the total density of states (TDOS) and projected density of states (PDOS) for H/Ti (100) system at hollow, bridge and top positions were evaluated. The calculated TDOS and PDOS for H/Ti (100) and pure Ti (100) system are depicted in Fig. 7a, b and  On the other hand, a significant shift in the 4s and 4p orbitals of Ti atom compared to DOS of pure Ti (100), due to the presence of 1s orbital of H atom indicates a strong interaction with Ti atom in the hollow and bridge sites. Overall, the computed TDOS and PDOS confirms that the hollow site offers the most stable site for H atom adsorption than that by bridge and top sites.

Diffusion of H atom from top to hollow and top to bridge site
From previous section we have confirmed that H atom adsorption at top position is not energetically feasible, whereas at bridge and hollow sites H adsorption is energetically feasible. Therefore, it will be appealing and imperative to unearth the diffusional energy barrier for H atom to jump from top to bridge, top to hollow, and bridge to hollow site which is the most stable site. The diffusional energy barrier of H atom jumping from top to bridge, top to hollow, and bridge to hollow sites was determined by performing CINEB calculations on the constructed images between initial and final structures. The computed potential energy surface for minimum energy path is displayed in Fig. 8. The activation energy barrier from top to bridge and top to hollow sites was negative for H atom indicating barrier less diffusion. From Fig. 8, it was observed that the move of H atom from the bridge site to hollow site takes place via a transition state in which the adsorbed H atom is seen to be coordinated to three Ti atoms in trigonal mode with barrier energy of 0.0156 eV.

Subsurface absorption of H atoms
Further, DFT calculations were performed to study the migration of H atoms from surface to subsequent sub surfaces. The computed potential energy surface and relaxed geometries are depicted in Fig. 9. The first subsurface (T1) adsorption energy ( − 0.34 eV) is although exothermic, it is less exothermic compared to adsorption energy at bridge and hollow sites. The activation barrier from hollow site to first subsurface (T1) is found to be 0.75 eV and from T1 to second subsurface is 0.18 eV. The second subsurface (T2) adsorption energy (0.47 eV) is predicted to be endothermic as expected.

Bulk absorption of H atoms
After arriving in the subsurface, the H atoms will start migrating to bulk and will be absorbed in the available voids of the bulk lattice. The conduct of H atoms within bulk Ti lattice can be well described by the value of absorption energy of H atom which can be evaluated by the following expression: Here E (TinH) and E (Tin) denote the total electronic energy of the bulk supercell containing n Ti atoms with H and without H atom, respectively. The computed relaxed bulk structures of Ti 54 , Ti 54 -H T , Ti 54 -H o are displayed in Fig. 10 ("T" denotes tetrahedral

Activated diffusion of isotopes of hydrogen into bulk Titanium
The diffusion of interstitial atoms in solid is commonly expressed as: with D 0 is typically the temperature independent pre-exponential factor, kT is the Boltzmann constant time temperature. Here, E a represents the activation barrier which has to be surmounted by the interstitial atom from an equilibrium site to move forwards along the diffusion path to another equilibrium site. The diffusion rate of an atom using the diffusion theory of Wert and Zener [66] can be written as where "l" is the jump length from one interstitial void to another interstitial void and Γ represents jump rate which can be calculated using the activated complex model of Eyring [67,68] within the transition state formula by Wigner [69,70] as Here, Q # and Q represent the total partition function of activated and stable sites of the molecular complex. ΔE denotes the energy difference between the activated and stable sites. The vibrational partition function under the classical mechanics solution leads to Vineyard's [71] result which can be expressed as where, ϑ j and ϑj # denote the real frequencies of the complex at the stable and the transition state. The quantum vibrational partition function can be applied to evaluate the jump rate and is expressed as: with ΔE = E a + ΔZPE, is the ZPE corrected activation barrier energy.

Effect of tunnelling
The jump rate obtained using TST is mostly valid at temperatures where the tunneling effect is considered to be unimportant. But, tunneling effect of H becomes quite significant at temperatures below certain crossover and must be accounted. The theory of tunneling is quite well studied. There are few theoretical models which take care the effect of tunneling by proposing a correction factor to the jump rate, Γ hTST . One such correction factor was introduced by Wigner, and Hirschfelder and Wigner [70,72]. They offered a harmonic correction factor x*/sin x* by assuming the tunneling barrier as an infinite, one-dimensional parabola with an imaginary frequency on the saddle point and arrived at an expression for the jump rate: Here ν* denotes the imaginary frequency at the transition state.
The crossover temperature (T c ) for H atom in bulk Ti based on the Wigner's model can be written as: T c = h * 2 k . The tunnelling effect becomes significant at lower temperature and contributes significantly than hTST at certain crossover temperature. However, there is a drawback in the use of Eq. (9) as it is not continuous for all temperature range. As T approaches T c , Eq. (7) diverges to infinity. In order to circumvent this divergence, Fermann and Auerbach [73] introduced a separable semi-classical TST (SC-TST) in which the diffusion rate becomes steady during the entire range of temperature. The correction due to tunneling, Γ corr within the SC-TST model can be written as Here 0 is the maximum barrier penetration integral and is defined as, 0 = ΔE h| * | . The integral in the Eq. (10) is solved numerically. The jump rate after taking care of tunneling over the entire temperature range is expressed as The crossover temperature with SC-TST model is written as The activated diffusion of H atom among adjacent T-sites in Ti 54 lattice takes place through a transition state where (12) T c = (h| * |ΔE)∕k 2 ΔE − h| * | ln 2  the H atom is found to be coordinated to 3 Ti atoms in a trigonal mode as illustrated in Fig. 11. The calculated values of diffusivity of H atom are listed in  54 bulk lattice as per earlier adopted methods using LCAO basis set and the results are illustrated in Fig. 12. The computed activation barrier energy, E a (3.1 eV) was found to be very high for the migration of H atom from O-site to adjacent O-site. In order to test the accuracy of the LCAO results, similar calculations were performed using PAW basis set as implemented in VASP.
The calculated values of diffusion energy barrier for both T-site to adjacent T-site and O-site to adjacent O-site are presented in Fig. 13. The calculated values of diffusion energy barrier for T-site to adjacent T-site and O-site to adjacent O-site using PAW potential were found to be 0.144 eV and 2.62 eV which were similar to the results obtained using LCAO basis set. The calculated values of energy barrier for H atom diffusion from O-site to adjacent O-site at both LCAO and PAW level were found to be much higher than that of T-site to adjacent T-site which seems to be quite high and hence was not studied further.
Next, the calculated values of jump rate against temperature using different models for H, D and T isotopes are shown in Fig. 14. From the calculations, it is observed that, the jump rate is lower for T compared to its lower mass isotopes namely H and D. The jump rate found to be increased with increase in the temperature. The Wigner corrected hTST shown increase in the jump rate till T c at lower temperatures. Below Tc, the jump rate is diverged, whereas SC-TST model shown increase in the jump rate even after T c at lower temperatures. The crossover temperature (T c ) using Wigner and SC-TST methods are computed and is presented in Table 8. The obtained cross over temperature was higher for H (T c = 157 K using Wigner and 170 K by SC-TST) due to lower mass and lower for T (T c = 91 K using Wigner and 95 K by SC-TST) due to heavier mass. The prediction of higher T c using SC-TST model over Wigner has earlier been observed for W [74]. The imaginary frequency at the saddle point is used for calculating T c . The calculated frequency for H (630.36 cm −1 ) is seen to be higher compared to T (363.94 cm −1 ). In the case of SC-TST method, the calculated T c is more than Wigner model due to 2ПΔE > hν*ln (2). When, 2ПΔE > > hν*ln(2) i.e. larger barrier heights, the Eq. (12) truncates to T c = h * 2 k which is Wigner crossover temperature.
The calculated values of diffusion coefficient using different models are presented in Fig. 15. The calculated diffusion coefficient values are in similar line with jump rates. Due to unavailability of experimental results, the calculated results cannot be compared. The increase in diffusion was observed at lower temperatures compared to hTST and Classical using Wigner + hTST and SC-TST models, whereas below T c , one has to use SC-TST method for the estimation of diffusion coefficients. For e.g., from 200 to 100 K the tunneling corrected diffusion coefficients for H atom using SC-TST differs by 70-99% in comparison to hTST and 90-99% to classical predicted values.

Conclusions
Density functional theoretical calculations employing LCAO and PAW basis set were carried out to obtain atomistic level insights on the structural, energetic and dynamical aspects of H isotopes in Ti bulk lattice and Ti (100) surface. The computed lattice constant and bulk modulus using LCAO and PAW basis set are very close to each other and also well in agreement with the experimental results. The percentage accuracy of lattice constant and bulk modulus are within 3.5% of the experimental values using both LCAO and PAW methods. The calculated elastic constant (29.14 GPa), shear modulus (29.39 GPa) and Poisson ratio (0.375) using LCAO basis set is in good agreement with the available experimental results. The computational time of LCAO method is approximately 10 times lower compared to its PAW methods for surface calculations. It was noticed that the H….H interatomic bond length increases continuously from the equilibrium bond  length of 0.75 Å as H 2 molecule approaches the Ti atom at the Ti (100) surface followed by dissociation to atoms at a distance of 1.5 Å from the surface. The hydrogen atoms after dissociation were seen to reside in the hollow position. The activation energy barrier from top to bridge and top to hollow sites was negative for H atom indicating barrier less diffusion. The computed total density of states (TDOS) and partial density of states (PDOS) confirmed that the hollow site offers the most stable site for H atom adsorption than that by bridge and top sites. The calculated barrier height for dissociation was 0.4 eV at surface coverage of θ H > 0.5ML, whereas the barrier height for recombination was found to be much higher than that of dissociation. The calculated dissociation rate constant using HTST was found to be quite fast, whereas the rate constant for recombination was determined to be very slow as expected. The computed results of adsorption energy of hydrogen isotopes on Ti (100) surface were found to follow the ascending trend: E ad (H 2 ); − 1.846 > E ad (D 2 ); -1.779 > E ad (T 2 ); − 1.750 eV. The calculated barrier height for dissociation was 0.4 eV. Almost similar value (0.46 eV) was obtained by PAW calculation. It is interesting to explore the barrier for the recombination of two H atoms to H 2 molecule. CI-NEB calculation was performed or evaluate the barrier energy for recombination using both LCAO and PAW basis sets. The barrier height for recombination was found to be much higher than that of dissociation. The computed values of activation diffusion barrier after zero point energy correction for H, D and T was computed to be 0.118, 0.126 and 0.129 eV, respectively, at the PAW level which are higher compared to the corresponding values obtained using LCAO method. This phenomena resulted in the higher rate and diffusion constants of H isotopes with LCAO method compared to PAW method. The calculated diffusivity establishes that the lighter H atom migrates faster than that of heavier D and T atoms. The classical barrier height was observed to be reduced after quantum correction.