Design and control of dynamical quantum processes  
in ortho-para H2 conversion on surfaces  
-From atomic-scale understanding to meter-scale application- 
 
Rifki Muhida*, Riza Muhida1, Wilson A. Diño2, Hiroshi Nakanishi2, Hideaki Kasai2 
 
*Department of Science in Engineering, International Islamic University Malaysia,  
Jalan Gombak Kuala Lumpur 53100 Malaysia 
e-mail: rifki@iiu.edu.my 
 
1Department of Mechatronics Engineering, International Islamic University Malaysia,  
Jalan Gombak Kuala Lumpur 53100 Malaysia 
e-mail: muhida@iiu.edu.my 
 
2Department of Precision Science & Technology and Applied Physics, Osaka University, 
2-1 Yamadaoka, Suita, Osaka 565-0871, Japan. 
e-mail: wilson@dyn.ap.eng.osaka-u.ac.jp, hiro@dy.ap.eng.osaka-u.ac.jp, kasai@dyn.ap.eng.osaka-u.ac.jp 
 
 
Abstract 
We present here a novel, cost-effective method for 
increasing and controlling the ortho-para H2 (o-p H2) 
conversion yield. First, we invoke two processes derived 
from fundamental, surface science insights, based on the 
effect of molecular orientation on the hydrogen-solid 
surface reaction, i.e., dynamical quantum filtering and 
steering, and apply them to enhance the o-p H2 conversion 
yield.  Second, we find an important factor that can 
significantly influence the yield i.e., inhomogeneity of spin 
density distribution. This factor gives us a promising 
possibility to increase the yield and to find the best catalyst 
e.g., design of materials that can function as catalysts for 
the o-p H2 conversion. 
1 
Introduction 
Now, issues on global warming, Arctic meltdown, and 
disappearance of rich ecosystems become central issue in 
the world, especially after Kyoto’s protocol [1]. It has been 
explained that the temperature increases faster in the last 
two decades [2]. This temperature change causes the Arctic 
ice pack to melt at a big rate, indicating that since the 
1950s, the thickness of summer polar ice shows a 40-
percent reduction [2]. To resolve these global problems we 
must give up a carbon-based technology which is not 
compensated by photosynthesis and simple inefficient 
combustion practices which cause an emission of NOx, SOx 
and other fragments of hydrocarbons [2]. The world 
currently relies on natural gases, oil, and coal as main 
sources of electricity generation. Within the next century, if 
energy consumers continue to rely on resources such as 
coal, petroleum, and other fossil fuels at the current rate, 
society will deplete its fuel reserves, specifically petroleum, 
then we are headed towards a global energy crisis. The 
energy crisis causes panic concerning not only electrical 
power shortages but environmental issues too.  
Alternative power sources become necessary to maintain 
current standards of living based on power sources. The 
problem involves ensuring global preparedness when low 
energy reserves mandate the use of renewable energy 
resources through proper allocation of renewable energy 
technology, ethical support from the public and the 
government, 
financial 
flexibility, 
and 
environmental 
sustainability. This reliance requires an energy source both 
efficient and long-term. Efficiency includes effectiveness of 
production while watching out for the environment too. 
Hydrogen is one solution to overcome the global problems.  
Hydrogen is probably the most important of all elements, 
and it is in abundance in the universe [3]. From an 
environmental point-of-view, hydrogen has been attracting 
a lot of attention. With water as the only emission from 
hydrogen combustion, hydrogen is being promoted as the 
energy source of the future. In order to support this 
developing hydrogen economy [4], infrastructures have to 
be built. Development of efficient processes for hydrogen 
extraction, and efficient processes and materials for 
hydrogen storage [5] would also be necessary. Thus, from 
an economics point-of-view, the transition to an economy 
based on hydrogen (energy) could, in the long run, also 
serve as a key to solving the problems we are currently 
facing.  
We will give several examples to give us illustration on 
hydrogen technology problems and point out where is our 
position to overcome one of the problems. The first problem 
is on hydrogen production. Hydrogen can not be produced 
directly by drilling a well or mining. It must be extracted 
chemically from hydrogen-riched materials such as natural 
gas, water or plant matters. Large-scale production 
techniques that are now being used include steam filtering 
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from natural gas, clean up of industrial by-product gases 
and electrolysis of water. A number of other technologies 
being studied include production of hydrogen from water or 
biomass using solar or other forms of renewable energy. 
Second problem is in the transportation of hydrogen 
gas/liquid. Hydrogen is very explosive when mixed with 
oxygen. In its pure state, it poses no explosive threat so is 
perfectly safe to ship in pipelines. Although the use of 
liquid hydrogen as a fuel source has a great potential,  
(particularly on jet airplanes and the future vehicle) the 
technical problems associated with the storage and delivery 
have not yet been overcome. In this article we will 
concentrate on how to overcome the storage problem 
resulting from ortho-para H2 (o-p H2) conversion. Through 
this study, we hope that we can reduce the cost of storing 
liquid hydrogen [6]. We hope that through systematic 
theoretical studies, we can present a simple, cost-effective 
method for solving a timely and urgent problem in the 
hydrogen technology. 
The idea of using hydrogen as fuel is not a new one, but 
interest in it has grown in recent years, as a result of the 
intense efforts of the United States Government through the 
Department of Energy (DOE) to realize and implement 
hydrogen fuel technology for hydrogen-powered vehicle 
[7]. One important facet of this growing hydrogen 
technology is concerned with the storage of liquid 
hydrogen. When we store the hydrogen fuel, e.g., in the 
hydrogen fuel stations, in the rockets for space programs, in 
the fuel tanks of an automobile to run for 300 to 400 miles, 
we have to concentrate the hydrogen into a small volume. 
That can be done by cooling the hydrogen to an extremely 
low temperature or by compressing it under very high 
pressure as liquid. In the storage tank of liquid hydrogen, 
some 
particular 
procedures 
(e.g., 
extra/expensive 
refrigeration equipment/system) are required to keep the 
composition (proportion) of the two types of hydrogen 
molecules, 
known 
as 
orthohydrogen 
(o-H2) 
and 
parahydrogen (p-H2) [8]. Without the particular procedure, 
o-H2 in the storage tanks would slowly but spontaneously 
convert to p-H2 over a period of days or weeks, releasing 
enough heat to evaporate most of the liquid [7, 9]. For 
example, when cooling and liquefying a normal mixture 
(25% p-H2, 75 % o-H2) of hydrogen, about 40 % of the 
original content of the tank evaporates after 100 hours of 
storage [6]. In order to limit the boil-off to low levels, it is 
necessary to fill the tank with liquid hydrogen that has 
already been converted to an equilibrium composition close 
to 100 % p-H2 [6, 7, 9].  
The existence of the types of hydrogen is a quantum 
mechanical phenomenon involving the concept of spin, 
Pauli principle and Fermi statistics [8,10,11]. In hydrogen 
molecules, the three (symmetric) nuclear spin states (|↑↑〉, 
|↑↓〉+|↓↑〉, |↓↓〉) are associated with odd j levels, to give the 
o-H2 (j is the rotational quantum number). The one 
(antisymmetric) state (|↑↓〉-|↓↑〉) is associated with even j 
levels, to give p-H2. At the lowest o-H2 and p-H2 states the 
energy difference has a value of 15.08 meV [8,10]. At T=0 
K, only the j=0 rotational state is occupied, so at thermal 
equilibrium at low temperatures a sample of hydrogen gas 
is pure p-H2. At high temperatures, the gas is a mixture of 
both forms in the ratio of 3 parts o-H2 to 1 part p-H2. The 
two forms have different rotational contributions to the heat 
capacity on account of the difference in availability of 
rotational states. The two forms of H2 also differ in their 
magnetic properties, in addition to their difference in 
thermal properties [9]. The realignment of nuclear spins is 
slow in the absence of dissociative adsorption or 
paramagnetic materials, and the 3:1 mixture persist for long 
periods at low temperatures.  
There are generally two methods of inducing an o-p H2 
transition. One method consists of dissociating H2 and then 
inducing the two H atoms to recombine. When dissociated, 
the nuclear spin states of the two atomic nuclei are no 
longer orientationally restricted by rotational states of the 
H2. Upon recombination, H2 is formed according to the 
equilibrium 
energy 
distribution 
determined 
by 
the 
temperature of the system. The other method involves the 
interaction between a magnetic field, produced by some 
catalysts e.g., magnetic material [9,11]. The magnetic field 
is applied along the axis of rotation of the nuclear spin, such 
that the external field causes a reversal of spin in one of the 
nuclei. This spin reversal is equivalent to an o-p H2 
transition [9]. In order to induce an o-p H2 conversion by 
the catalyst, the H2 must be brought close enough to the 
magnetic material/catalyst [9]. Without an o-p H2 
conversion catalyst, extra refrigeration equipment is 
required to remove the heat generated by natural o-p H2 
conversion. This extra refrigeration equipment will increase 
the cost of storing liquid hydrogen. The method to induce 
and enhance the o-H2 to p-H2 (o-p H2) conversion is thus an 
essential in the hydrogen technology. In this article we 
introduce a new method to increase the o-p H2 conversion 
yield on the catalysts surfaces by using molecular 
orientation dependence (steric effect (SE)) of o-p H2 
conversion yield (chapter 2) [12-15] and  inhomogeneity of 
spin density distribution to finding the best catalyst for o-p 
H2 conversion (chapter 3) [16]. In chapter 4 we introduce a 
reaction design of o-p H2 conversion [17-20] to enhance the 
yield using dynamical quantum filtering (DQF) process in 
the associative desorption of H2 from surfaces [21-23] and 
steric effect (SE). We summarize our results and 
conclusions in chapter 5. 
2. Increasing the yield using molecular orientation 
(steric effect)  
In this chapter, we will show how the molecular orientation 
of H2 plays an important role in influencing the o-p H2 
conversion yield. To demonstrate this, in this article we 
consider the molecular orientation dependence of o-p H2 
conversion yield on Fe(OH)3 catalyst. Fe(OH)3 is known to 
be a good catalyst for the o-p H2 conversion [11,24,25] and 
has been used widely in the industry to overcome problems 
related to storing liquid hydrogen [11,25]. Although the 
experiment of o-p H2 conversion on Fe(OH)3 catalyst has 
been done by Buyanov in 1960 [24], the detailed 
mechanism as to how this material can induce o-p H2 
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conversion has not yet been understood. One major hurdle 
to a theoretical explanation of the mechanism of o-p H2 
conversion in Buyanov's experiments is that the structure of 
the Fe(OH)3 could not be determined using X ray and 
electron photographs [11,24]. Efforts to determine the 
structure of Fe(OH)3 are now being done by many 
researchers [26-28].  
In the last ten to twenty years, we have seen great progress 
in 
computational 
physics. 
Through 
first 
principles 
calculations, we can now determine the structure of many 
materials and directly relate these to experimental results 
with a high degree of accuracy. In particular, it is now 
possible to theoretically explore the structure of Fe(OH)3 
and even simulate catalytic processes involving its 
interaction with H2, e.g., the o-p H2 conversion process. 
The stable structure of Fe(OH)3 [Fig. 2.1(a)] and the relative 
configuration between interacting H2 and Fe(OH)3 is shown 
in Fig. 2.1 (b)[51]. We assume that H2 sits on top of the Fe 
atom in Fe(OH)3 and θ is the H2 molecular orientation angle 
with respect to Fe(OH)3 surface normal, while Z is the H2 
center-of-mass (CM) distance from the Fe(OH)3 surface. 
The stable structure of Fe(OH)3 is determined by an 
optimization calculation using GAUSSIAN 03 [29] via a 
series of density functional theory (DFT) [30] based total 
energy calculations, adopting Becke's three-parameter 
functional [31], Perdew and Wang's gradient-corrected 
correlation functional [32], and Dunning [33], Hay and 
Wadt's basis sets [34]. The obtained structure of Fe(OH)3 is 
comparable with previous results [35]. The ground state of 
Fe(OH)3 has S=5/2 (S is the total spin). 
We have examined the 〈S.S〉=ħ values (S is the electron 
spin operator), and compared them to the S(S+1) values for 
each total spin of the Fe(OH)3 system, to check for spin 
contamination. In the ground state of the Fe(OH)3 system 
the S(S+1) value is 8.76 [51]. This value has the spin 
contamination around 0.1% where it is much smaller than 
the maximum value that can be allowed, i.e., 10% [36]. 
The molecular orientation dependence of the o-p H2 
conversion yield of H2 on Fe(OH)3 is investigated using the 
anti-symmetric part of the hyperfine contact interaction 
[11,12]. We can write the anti-symmetric part of the 
hyperfine contact interaction between each electron spin 
and two H2 nuclear spins by  
(
)
(
) (
)
(
)
[
]
α
α
α
α
δ
δ
λ
θ
r
r
r
r
I
I
S
−
−
−
−
=
∑
=
b
a
N
b
a
C
HC Z
H
1
.
,
 (2.1).             
Here, Ia  and Ib  are the operators for the nuclear spin of the 
two protons a and b of H2. δ(ra-rα) and δ(rb-rα) represent the 
Dirac operators. rn(n=a,b) and rα are the proton and electron 
coordinates (the position vectors) with respect to the M ion, 
respectively. Sα is the electron spin operator and λC is the 
hyperfine contact constant. 
The o-p H2 conversion yield as functions of the H2 CM 
distance with respect to Fe ion and the H2 molecular 
orientation angle with respect to the surface normal θ  is 
proportional to the hyperfine contact contribution [12] and 
can be written as  
                                
(
)
(
)
2
,
,
θ
ξ
θ
Z
Z
W
∝
,                 
(2.2)                
where  
       (
)
(
)
(
)
(
)
θ
ψ
χ
θ
χ
θ
ψ
θ
ξ
α
α
,
,
,
,
,
,
Z
Z
H
Z
Z
el
o
HC
p
el
r
r
=
(2.3)                 
ξ(Z,θ) is the hyperfine contact interaction that contributes to 
the o-p H2 conversion yields. ψel(rel, Z,θ) is the unperturbed 
wave function for the electron system obtained from 
GAUSSIAN 03. The H2 nuclear spin wave function of the 
o-H2 can be expressed as 
 
Figure 2.2. The matrix element of the hyperfine contact 
interaction ξ(Z,θ) for θ=10o and θ=70o as a function of the H2 
center-of-mass (CM) distance from the Fe(OH)3 surface. 
 
 
Figure 2.1. (a) The structure of Fe(OH)3. The structure is 
obtained by optimization calculation using GAUSSIAN 03. (b) 
The relative configuration between interacting H2 and Fe(OH)3. 
The H2 is sitting on the top of the Fe ion of Fe(OH) 3 with the H2 
center-of-mass (CM) distance Z from the Fe(OH)3 surface and θ 
is its molecular orientation angle with respect to the surface 
normal. ra and rb are the position vectors of protons a and b with 
respect to the Fe ion, respectively. 
 
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(
)
⎪
⎪
⎩
⎪⎪
⎨
⎧
↓↓
↓↑
+
↑↓
↑↑
=
       
          
      
          
o
2
χ
,          
 (2.4)                                                   
while the H2 nuclear spin wave function of the p-H2 can be 
expressed  as  
  
 
(
)
↓↑
−
↑↓
=
2
1
p
χ
.           
(2.5)                                                        
Fig. 2.2 shows the matrix element of the hyperfine contact 
interaction ξ(Z,θ) for θ =10o and θ =70o. We can see that 
ξ(Z,θ) for θ =10o is larger than that for θ =70o. The strong 
dependence on the H2 molecular orientation angle θ is due 
to the antisymmetric part of the hyperfine contact 
interaction in Eq. (2.1) [52]. The maxima and minima for θ 
=10o are found at Z=0.5 Å and Z=1.2 Å, respectively, 
whereas the maxima and minima for θ =70o are found at 
Z=0.5 Å and Z=1.0 Å, respectively. These extrema 
correspond to the maximum contacts between the nuclear 
spin of H2 and the electron spin density distribution of 
Fe(OH)3-H2 system[52].  
The o-p H2 conversion yield has shown that a perpendicular 
orientation is preferred to a parallel orientation. We expect 
that the behavior of the o-p H2 conversion yield like this is a 
general behavior, as we have shown in the previous studies 
on the o-p H2 conversion on metal oxide surfaces [12-14] 
and metal surfaces [15]. These results will give us steric 
effect (SE) where o-p H2 conversion yield for H2 with a H2 
doing cartwheel-like rotation (CLR H2) is higher than that 
for a H2 doing helicopter-like rotation HLR H2 [14]. These 
results indicate that there is a promising possibility to 
enhance the o-p H2 conversion yield by using steric effect 
(SE). 
3 
Increasing the yield using inhomogeneity of 
spin density of surface catalyst  
We are now extending this study to investigate other factors 
that can influence the yield, e.g., inhomogeneity of spin 
density 
distribution. 
To 
demonstrate 
how 
the 
inhomogeneity of spin density distribution can influence the 
o-p H2 conversion yield we consider the interaction of H2 
with new magnetic material clusters, i.e., organometallic 
compounds of multiple-decked sandwich clusters viz., 
M(C6H6)2 (M=Mn, Fe, Co) that have been synthesized 
experimentally, e.g., by Cloke et al. [37] and Kaya's group 
[38]. Also, they have become the subject of many studies 
for the past several decades. 
  
The electronic structures of these materials have been 
investigated by Miyajima et al. [39], and it has been shown 
that these materials exhibit semiconducting and even 
conducting properties in the solid states [39]. The magnetic 
properties of these novel materials were investigated for the 
first time by Yasuike et al.[40], when they investigated the 
spin state of V2(C6H6)3 system. However, they could not 
exactly determine which state is more stable, i.e., triplet or 
singlet. Pandey et al., [41] calculated the spin multiplicity 
of Mn(C6H6)n+1 (M=Sc, Ti, V, Cr, Mn, Fe, Co, Ni, and n = 
1,2) systems, and obtained agreements with electron spin 
resonant experiments done by Cloke et al. [42]. We have 
investigated the spin polarization and have determined local 
magnetic moments of the transition metal atom M and the 
benzene, in the M(C6H6)2 clusters [43-45].  
 
The model we use to investigate the o-p H2 conversion on 
M(C6H6)2 clusters is shown in Fig. 3.1[16]. We assume that 
H2 impinges on the atom M with its CM position Y lying 
along the y-axis (H2 is in the xy-plane). The molecular 
orientation angle with respect to the y-axis is given by θ. 
Optimization of the M(C6H6)2 structure is obtained by 
performing a series of density functional theory (DFT) that 
has been formulated in chapter 2 using GAUSSIAN 03.  
 
We have checked the existence of spin contamination in 
this system, e.g., Fe(C6H6)2 in the ground state, the <S.S>=ħ 
value takes 2.0641, while S(S+1) = 2,0. This value is much 
smaller than the maximum value that can be allowed, 10% 
[36]. To compare with previous studies by Pandey et al. 
[41], we have also considered the V(C6H6)2 system. We 
have found that the magnetic moment of V(C6H6)2 system is 
1.0 Bohr magneton (µB) corresponding to the spin 
multiplicity 2.0. This multiplicity value agrees with the 
experiment by Cloke et al. [42] and it also agrees with 
previous studies by Pandey et al. [41]. The local magnetic 
moment of M in M(C6H6)2 system has been determined in 
the previous studies [43-45]. The magnetic moments of Mn, 
        
 
Figure 3.1. Model system of an interaction between H2 and 
multiple-decked sandwich clusters of M(C6H6)2 (M=Mn,Fe,Co). 
H2 impinges on the atom M with its CM position Y along the y-
axis (H2 is in the xy-plane), as shown in the figure. ra and rb 
denote the position vectors of proton a and b with respect to the 
M, respectively. The H2 molecular orientation angle with respect 
to the surface normal is given by θ. Here, a is the distance from 
the transition metal atom to the center of benzene plane. b is the 
distance between the two C atoms in benzene, and c is the 
distance between the C atom and the H atom in benzene. The 
benzene ring is parallel to the xy-plane while the z-axis is 
perpendicular to the plane of benzene. The a, b and c values for 
Mn, Fe and Co systems are shown in the Table. 
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Fe and Co in M(C6H6)2 system are found 1.1695 µB, 2.3816 
µB and 1.4273 µB, respectively [43]. These magnetic 
moments are lower than isolated case for Mn, Fe and Co 
ions. Decreased magnetic moments in M in these materials 
have been discussed in the references [43, 44]. When H2 
impinges on the M(C6H6)2 system, e.g., when H2 CM 
distance from the atom M is 1.8 Å and the H2 molecular 
orientation angle θ =100, the magnetic moment of Mn in 
Mn(C6H6)2 system becomes 3.1 µB. For the Fe(C6H6)2 and 
Co(C6H6)2 systems the magnetic moments become 2.3 µB 
and 1.3 µB, respectively. The increases in the magnetic 
moments are attributed to the H2. For example, when the H2 
CM position is 1.8 Å from the atom M, the local magnetic 
moments of atoms of H2 in the Mn(C6H6)2 system increase 
to 0.068 µB and -0.0034 µB, for atoms a and b, respectively. 
 
To determine the o-p H2 conversion yield, we use the 
previous method that was explained in chapter 2. In Fig. 3.2 
we 
show 
the 
hyperfine 
contact 
contribution  
ξ(Y,θ) for the H2 molecular orientation angle θ = 100 as a 
function the H2 CM distance from the atom M. The 
behavior of those curves is due to the spin interaction 
between the two protons of H2 and the electron spin density 
of H2-M(C6H6)2 systems. It can be seen that the dip in ξ(Y,θ) 
for H2 on Mn(C6H6)2 system is larger than those of H2 on 
Fe(C6H6)2 and Co(C6H6)2 systems. To explain this, we show 
the spin density distribution of the H2-Mn(C6H6)2 [Fig. 
3.3(a)], the H2-Fe(C6H6)2 [Fig. 3.3(b)] and the H2-
Co(C6H6)2 [Fig. 3.3(c)] systems when the H2 CM distance 
from the atom M is 1.8 Å. Inhomogeneity of spin density 
distribution along the y-axis for the H2-Mn(C6H6)2 system is 
the largest, followed by the H2-Fe(C6H6)2 and H2-Co(C6H6)2 
systems. This inhomogeneity can be known by checking 
spin density distribution at the H2 nuclear positions of those 
systems. For the H2-Mn(C6H6)2 system, the spin density 
distribution at ra and rb are -0.0688 and 0.0225, 
respectively, resulting to net -0.0912 beta spin density. For 
the H2-Fe(C6H6)2 system, the spin density at ra and rb are -
0.01466 and -0.0008, respectively, resulting to net 0.0155 
alpha spin density. For the H2-Co(C6H6)2 system, the spin 
density at ra and rb are -0.00954 and -0.00032, respectively, 
resulting to net 0.0092 alpha spin density. Although the 
local magnetic moment of Fe is the largest in Fe(C6H6)2 
system, the inhomogeneity of spin density distribution 
along the y-axis of H2-Fe(C6H6)2 system material is lower 
than that of the H2-Mn(C6H6)2 system. 
 
Increasing magnetic moments that followed by increasing 
conversion yield has been clarified experimentally by 
Ashmead et al. [46] in 1964, and Selwood [47,48] in 1970. 
Our results also show a strong dependence on the H2 CM 
distance from M (Fig. 2).  For the distances far from M, the 
conversion yield is small while when H2 gets the closer to 
M (e. g, in the physisorbed H2) the yield increases. This 
behavior has agreement with experiments of the o-p H2 
conversion on surface catalysts [49]. 
 
This result gives us a promising possibility to increase this 
conversion by finding the best catalyst e.g., design of 
materials that can function as catalysts for the o-p H2 
conversion. Inhomogeneity of spin density distribution thus 
can be considered as an important factor to look for the best 
catalyst for the o-p H2 conversion. 
4 
Reaction Design of ortho-para H2 Conversion  
In chapter 2 we have shown a promising possibility to 
increase the o-p H2 conversion yield using molecular 
orientation of H2 on catalyst surfaces. This molecular 
orientation will give us steric effect [14], where the o-p H2 
conversion yield for a H2 doing cartwheel-like rotation 
(CLR H2) shows a larger value than that for a H2 doing 
helicopter-like rotation (HLR H2). Based on this effect, we 
can increase the o-p H2 conversion yield if we orient the 
rotational axis of H2 parallel to the catalyst surface. The 
problem now is how to control the H2 orientation so that we 
only have a CLR H2 with respect to the surface (i.e., the H2 
rotational axis is parallel to the surface). This could be 
achieved through the dynamical quantum filtering (DQF) 
process via associative desorption [21-23].  
 
 
Figure 3.3. Two-dimensional contour (xy-plane) of spin density 
distribution when H2 interacts with M(C6H6)2 (M=Mn,Fe,Co). 
The H2 CM distance from the atom M is 1.8 Å and the H2 
molecular orientation angle θ = 100. (a) Spin density distribution 
of H2-Mn(C6H6)2 system, (b) spin density distribution of H2-
Fe(C6H6)2 system, (c) spin density distribution of H2-Co(C6H6)2 
system. 
 
Figure 3.2. The hyperfine contact contribution as a function of 
the H2 CM distance from the atom M of M(C6H6)2 clusters (M = 
Mn, Fe, Co). The H2 molecular orientation angle with respect to 
the surface normal θ = 100. 
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Diño et al. [21-23], when they investigated the orientation-
dependence of H2 interaction with Cu(001) found that metal 
surfaces can, via the orientation-dependence of potential 
energy surface (PES), act or be utilized as rotational 
quantum state filters for molecules and induce, e.g., 
desorbing H2 to exhibit rotational alignment. They showed 
that the resulting alignment of desorbed molecules, as 
determined by the value of quadrupole alignment factor 
Ao
(2)(j), exhibits a nonmonotonic dependence on the 
rotational quantum number j and the translational energy Et. 
From the calculation of desorption probability [21-23], they 
found the corresponding quadrupole alignment factors 
 
            
(
)
[
]
(
)
(
)
∑
∑
+
+
−
=
j
j
j
j
m
tot
n
m
mnjm
m
tot
n
m
mnjm
j
tot
o
E
D
j
j
E
D
j
j
m
E
A
'
'
'
'
2
)
2
(
)1
(
)1
(
3
 
(4.1) 
Here, m, n, m’ and n’ are the quantum numbers for the 
surface parallel translational motion of H2. j and mj are 
quantum numbers for the rotational motion of H2 and j is 
the absolute value of the angular momentum vector j, and 
mj corresponds to the surface normal component of the 
angular momentum vector j. The total energy of the system 
Etot is defined as the sum of the kinetic energy of the surface 
normal translational motion, surface parallel translational 
motion, rotational motion, and vibrational motion of H2. 
Dm’n’mnjmj (Etot) is desorption probability as functions of 
final states of the rotational motion (j,mj), and initial (m’,n’) 
and final (m,n) states of the surface parallel translational 
motion of H2 on the surface. 
  
The quadrupole alignment factor Ao
(2) (Etot) can be 
experimentally determined by using resonance-enhanced 
multiphoton 
ionization 
(REMPI) 
and 
laser-induced 
fluorescence (LIF), and gives us information regarding the 
degree of alignment and orientational preference of H2. It 
assumes values in the range [-1,3j/(j+1)-1]. A CLR H2 
(mj≈0) has Ao
(2) (Etot)<0, while HLR H2 (mj≈j) has 
Ao
(2)(Etot)>0. A spatially isotropic distribution of the angular 
momentum vector j is described by Ao
(2)(Etot)= 0. In Fig. 
4.1, one can see that slowly desorbing H2 [i.e., the fnal 
translational energy (Et) «Vmin] exhibit a CLR H2, while fast 
desorbing H2 [Et »Vmin] exhibit a HLR H2. Vmin is the 
minimum activation barrier for H2 dissociation, with the H-
H bond oriented parallel to the surface [Vmin ≈0.5 eV] [21-
23]. 
 
Now, we propose a new method to enhance the o-p H2 
conversion yield/rate of H2 inter-acting with a solid surface. 
It consists of two steps. The first step involves the DQF 
process [21-23], and the second step relies on the steric 
effect (SE) of the o-p H2 conversion [12-15]. The purpose 
of the DQF process is to align the rotation of o-H2 such that 
we have only a HLR H2 or a CLR H2. This DQF process 
could be performed, e.g., by permeating H atoms through 
some metal crystal. After permeation, the desorbing H2 will 
be exhibiting either a CLR H2 or a HLR H2 depending on 
their final translational energy upon desorption. As shown 
in Fig. 4.1, if we devise a means to either select only slowly 
desorbing molecules or fast desorbing molecules, then we 
can obtain exclusively CLR or HLR H2. In the second step, 
as shown in Fig. 4.2(a), we bring these aligned o-H2 close to 
a catalyst surface. Based on the steric effect, CLR o-H2 will 
be converted to p-H2 with higher rate than HLR o-H2. 
 
To realize this idea we develop a conceptual design of a 
machine that will increase the o-p H2 conversion yield [17-
20,53]. The o-H2 with free rotation, first undergoes the DQF 
process. In the second stage, for the H2 desorption with 
CLR, we put catalyst A in the position as shown in Fig. 
4.2(b), while for the H2 desorption with HLR we use 
catalyst B. This machine will give us higher catalytic 
surface area for the o-p H2 conversion and improves the 
efficiency of the second process. We can use this machine 
during the liquefaction process [17-20]. 
5 
Summary and conclusions  
The o-p H2 conversion process is extremely important in the 
industry, e.g., when considering the production, storage and 
utilization of hydrogen. At low temperature o-H2 is 
unstable, and changes toward the more stable p-H2 over 
time, liberates heat which can cause hydrogen evaporation 
within the storage vessel. Since o-H2 makes up 75 % of 
normal H2 at room temperature, they can considerably 
complicate the job of storing liquid hydrogen. Without an o-
p H2 conversion catalyst, extra refrigeration equipment is 
required to remove the heat generated by natural o-p H2 
conversion. The methods to induce and enhance the o-H2 to 
p-H2 (o-p H2) conversion are thus an essential in the 
hydrogen technology. 
In this article we introduced new methods to increase the o-
p H2 conversion yield on the catalysts surfaces by using: 
1. Molecular orientation. 
We expected that the orientation of H2 on surface 
catalyst would also play an important role in enhancing 
the o-p H2 conversion. As an illustration, we consider 
 
Figure 4.1. Rotational alignment of H2 as a function of the final 
translational energy. Molecules with Ao
(2) (j) > 0 exhibit a HLR 
H2, while molecules with Ao
(2) (j) < 0 exhibit a CLR H2. 
Experiment has been done by Hou et al. [50]. 
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the molecular orientation dependence of o-p H2 
conversion yield on the Fe(OH)3 catalyst that is known 
to be good catalyst for o-p H2 conversion. By using 
steric effect (SE) and dynamical quantum filtering 
(DQF) effect in the associative desorption we propose 
new reaction design of the o-p H2 conversion on 
catalyst surfaces to increase the yield. This design will 
give us higher catalytic surface area for the o-p H2 
conversion and improves the efficiency. 
 
2. Inhomogeneity of spin density distribution. 
Based on our series of studies on magnetic properties 
of nanoclusters and its interactions with H2 [16,43-45], 
we found that the inhomogeneity of spin density 
distribution can influence the o-p H2 conversion yield. 
This result gives us a promising possibility to increase 
this conversion by finding the best catalyst e.g., design 
of materials that can function as catalysts for the o-p H2 
conversion. Inhomogeneity of spin density distribution 
thus can be considered as an important factor to look 
for the best catalyst for the o-p H2 conversion. 
6 
Acknowledgement  
This work is partly supported by International Islamic 
University Malaysia and the Ministry of Education, Culture, 
Sports, Science and Technology of Japan (MEXT) through 
Grants-in-Aid for Scientific Research on Priority Areas 
(Developing Next Generation Quantum Simulators and 
Quantum-Based Design Techniques), and through Grants-
in-Aid for the 21st Century Center of Excellence (COE) 
Program “Core Research and Advance Education Center for 
Material Science and Nano-Engineering” supported by the 
Japan Society for the Promotion of Science (JSPS) and for 
the New Energy and Industrial Technology Development 
Organization's (NEDO) Materials and Nanotechnology 
Program. 
Calculations 
were 
performed 
using 
the 
supercomputer facilities of the Institute for Solid State 
Physics (ISSP) Supercomputer Center (University of 
Tokyo) and the Japan Atomic Energy Agency (ITBL, 
JAEA). 
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