ARTICLE IN PRESS
Selective control of photodissociation in deutereted
water molecule HOD
S. Adhikaria,b, Sarin Deshpandea,1, Manabendra Sarmaa,
Vandana Kurkala,2, M.K. Mishraa,
a
Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India
Department of Chemistry, Indian Institute of Technology Guwahati, North Guwahati 781 039, India
b
Abstract
Bond dissociation in the deutereted water molecule HOD has been investigated to explore the possibility of selective
control of dissociation of O–H and O–D bonds using simple field profiles and initial states that do not require
high overtone excitations. Preliminary results indicate that considerable selectivity in dissociation of O–H and
O–D bonds can be achieved using fundamental and first overtone excitations only and use of field optimized initial state
(FOIST) based scheme with appropriate choice of field parameters and initial states may enhance both selectivity and
yield.
Keywords: HOD photodissociation; Photodynamic control; Flux maximization; Field optimization; Mixing of initial states; Multi
color lasers
1. Introduction
Attempts to use lasers as molecular scissors to cleave
bonds selectively are being pursued extensively (Crim,
1993; Gordon and Rice, 1997; Rabitz et al., 2000; Rice
and Zhao, 2000; Shapiro and Brumer, 2003; Zare, 1998).
The established theoretical (Brumer and Shapiro, 1992;
Gross et al., 1991; Judson and Rabitz, 1992; Shi et al.,
1988; Tannor and Rice, 1985) and experimental schemes
(Assion et al., 1998; Baumert and Gerber, 1994; Crim,
1990; Cohen et al., 1995; Lu et al., 1992; Vander Wal
et al., 1991) rely on designing appropriate laser pulses to
achieve the desired outcome from photo-dissociation
reactions, often requiring field attributes that cannot be
foreseen on the basis of chemical considerations
(Baumert and Gerber, 1994; Gross et al., 1992) and
may also be difficult to reproduce (Gross et al., 1994) in
normal laboratory conditions.
The deutereted water molecule HOD has been a
popular prototype for investigation of selective control
through vibrational mediation (Amstrup and Henriksen,
1992; Cohen et al., 1995; Crim, 1990; Lu et al., 1992;
Vander Wal et al., 1991). The H–OD ð3693 cm1 Þ and
HO–D ð2717 cm1 Þ stretching frequencies are well
separated. This provides for selective excitation of more
or less pure O–H and O–D modes and the use of either
selectively excited higher O–D overtones (Crim, 1993) or
a combination of IR and UV pulses to first produce
ARTICLE IN PRESS
2107
large quanta of vibrational stretching in the desired
bond and then pump it to the lowest repulsive excited
electronic state for selective dissociation, has been
investigated in detail in many groups (Amstrup and
Henriksen, 1992; Cohen et al., 1995; Crim, 1990; Lu
et al., 1992; Vander Wal et al., 1991). Amstrup and
Henriksen (1992) have theoretically investigated both
active and passive approaches to selective control of
HOD photodissociation except that the UV fields
employed were d-function type or with extremely
narrow 5 fs pulse width and also required large quanta
of vibration ðnOD ¼ 4Þ in the O–D stretch.
It is our purpose in this paper to investigate if
considerable selectivity and yield in HOD dissociation
may be achieved with easily realizable small quanta
vibrational excitations and more realistic UV fields.
Furthermore, we have been advocating the use of field
optimized initial state (FOIST) scheme (Gross et al.,
1996; Vandana et al., 1998; Vandana and Mishra, 1999a, b,
2000a) which attempts to distribute the onus for selective control on both the field attributes and the
molecular initial state to be subjected to the chosen
photolysis pulse both of which can be sampled
separately and economically using simple time-dependent quantum mechanical (TDQM) techniques based on
fast fourier transform (FFT) (Kosloff and Kosloff,
1983) and Lanczos propagation (Leforestier et al., 1991)
to select a combination of field attributes which may be
easier to realize experimentally. Earlier applications of
the FOIST scheme to HI and IBr photodissociations
have provided new insights and encouraging selectivity
and yield (Vandana and Mishra, 2000b) and it is our
purpose here to provide preliminary results from its
application to selective cleaving of O–H and O–D bonds
in the HOD molecule. Results from the first application
of the FOIST scheme to HOD molecule are analyzed to
try and garner features which may facilitate easier routes
to enhanced selectivity and yield.
The systemic and methodological details are presented
in the following section. In Section 3 we discuss our
results and a brief summary of salient observations in
Section 4 concludes this paper.
2. Method
Photofragmentation of the deutereted water molecule
HOD in the first absorption band involving electronic
transition from the ground electronic state to the first
excited electronic state takes place on the repulsive first
excited potential energy surface (Figs. 1a and b). This
lowest energy excitation induces negligible change in the
HOD bending angle, and since the bending is not active
in first absorption band (Amstrup and Henriksen, 1992;
Imre and Zhang, 1989), the internal kinetic energy
operator in terms of the conjugate momenta p^ 1 and p^ 2
associated with the O–H ðr1 Þ and O–D ðr2 Þ stretching
co-ordinates, respectively, is given by
p^ 2
p^ 2
p^ p^
T^ ¼ 1 þ 2 þ 1 2 cos y
2m1 2m2
mo
where
_ q
; j ¼ 1; 2,
i qrj
mH mO
mO mD
; m2 ¼
m1 ¼
ðmH þ mO Þ
ðmO þ mD Þ
p^ j ¼
ð1Þ
and y is the fixed bending angle, 104:52 .
The potential energy surface (PES) of the ground
electronic state (Fig. 1a) is expressed with two Morse
oscillators and a coupling term (Engel et al., 1988;
Reimers and Watts, 1984) among them
V g ðr1 ; r2 Þ ¼ D½1 expðaðr1 r0 ÞÞ2
þ D½1 expðaðr2 r0 ÞÞ2
þ f 12 ðr1 r0 Þðr2 r0 Þ,
f 12 ¼
F 12
,
1 þ expðb½ðr1 r0 Þ þ ðr2 r0 ÞÞ
(2)
where D ¼ 0:2092 hartree, a ¼ 1:1327a1
0 , r0 ¼ 1:81a0 ,
3
2
b ¼ 1:0a1
and
F
¼
6:76
10
hartree=a
12
0
0.
The PES of the first electronically excited state ðV e Þ is
available from ab initio calculations (Staemmler and
Palma, 1985; Zhang et al., 1989) and the same (Fig. 1b)
is used in our computations as well. The transition
dipole moment function calculated in a small region
ðr1 ; r2 p2:6a0 Þ by ab initio method has been fitted to an
analytical function for transition dipole moment as
given below (Amstrup and Henriksen, 1992; Imre and
Zhang, 1989)
mge ¼
2:225
2:225
.
1 þ expðbðr1 r0 ÞÞ 1 þ expðbðr2 r0 ÞÞ
(3)
The transition dipole moment vector, ~
mge , is taken to
be perpendicular to the molecular plane (Zhang et al.,
1989) and the electric field vector of the UV laser field
parallel to dipole vector, whereby the interaction with
single/multi color laser is given by
X
H^ uv ðtÞ ¼ mge ðr1 ; r2 ÞE 0 aðtÞ
cos oiuv t,
(4)
i
where oiuv is the ith UV frequency in the multicolor laser
and the Gaussian envelope is defined by
sffiffiffiffiffiffiffiffiffiffiffiffi
4 ln 2
2
aðtÞ ¼ exp½gðt tuv Þ with FWHM ¼
. (5)
g
ARTICLE IN PRESS
2108
Fig. 1. Potential energy surfaces for (a) ground and (b) first excited state of HOD. Probability density plots for the jnOH ; nOD i modes of
HOD are depicted in: (c) j0; 0i, (d) j0; 1i, (e) j1; 0i and (f) j0; 2i.
ARTICLE IN PRESS
2109
The first and second excited electronic states are well
separated and following earlier investigation (Amstrup
and Henriksen, 1992) we too formulate the HOD
dynamics considering only the ground and the first
excited electronic state (Figs. 1a and b) of the molecule.
The time evolution of the corresponding nuclear motion
can then be performed using the time-dependent
Schrödinger equation
q
i_
qt
Cg
Ce
!
¼
H^ g
H^ uv ðtÞ
H^ uv ðtÞ
H^ e
!
Cg
Ce
!
,
(6)
where Cg ¼ Cg ðr1 ; r2 ; tÞ and Ce ¼ Ce ðr1 ; r2 ; tÞ are the
wave functions associated with nuclear motion in the
ground and first excited electronic state, respectively.
H^ g ¼ T^ þ V^ g and H^ e ¼ T^ þ V^ e are the nuclear Hamiltonians for the two electronic states where H uv couples
as well as perturbs both the electronic states. We solve
Eq. (6) with the ðt ¼ 0Þ initial condition that the ground
state wave function Cg is a single, field free, vibrational
state or a linear combination of more than one
vibrational state(s) of the HOD electronic ground state,
and the excited state wave function Ce ¼ 0, at t ¼ 0.
Vibrational eigenfunctions of the ground electronic
state of the HOD molecule were obtained using the
Fourier grid Hamiltonian (FGH) method (Marston and
Balint-Kurti, 1989) modified for two dimensions (Dutta
et al., 1993), where the total Hamiltonian is partitioned
into individual modes and coupling between them and
for the present system may be written as
p^ p^
H^ g ¼ H^ 1 þ H^ 2 þ V 12 þ 1 2 cos y,
mo
(7)
given by
"
n1
1 X
2 cos½2plði jÞ=nr H ij ¼
fT l g
Dr l¼1
nr
#
þ ð1Þij T n =nr þ V ðri Þdij
ð10Þ
with T l ¼ ð_2 =2mÞðlDkÞ2 , 2n ¼ nr 1 and Dk ¼ 2p=nr Dr.
After solving Eq. (9) we can express cðr1 ; r2 Þ as a
superposition of the product basis sets (Dutta et al.,
1993) generated from H^ 1 and H^ 2 as below
X
cl jFl ðr1 ; r2 Þi
jcðr1 ; r2 Þi ¼
l
¼
nr1 nr2
X
X
i
aij jfi ðr1 Þijfj ðr2 Þi
ð11Þ
j
and form the total Hamiltonian matrix with V 12 and
ðp^ 1 p^ 2 =mo Þ cos y as the coupling terms. Diagonalization
of this Hamiltonian matrix provides vibrational eigenfunctions ðcm Þ of the ground electronic state. Some
eigenfrequencies are tabulated in Table 1 and a few
corresponding eigenmodes are depicted in Figs. 1c–f.
These compare quite well with those used elsewhere
(Amstrup and Henriksen, 1992).
The propagation of the wavefunctions fCg ðtÞ; Ce ðtÞg
has been performed by using Eq. (6) where the effect of
kinetic energy operators of the Hamiltonian on the
wavefunction is evaluated with a two-dimensional FFT
(Kosloff and Kosloff, 1983) algorithm and the time
propagation is carried out using the Lanczos scheme
(Leforestier et al., 1991).
where
p^ 2
H^ 1 ¼ 1 þ V^ OH ,
2m1
Table 1
Eigenfrequencies for first 16 vibrational eigenmodes of HOD
p^ 2
H^ 2 ¼ 2 þ V^ OD ,
2m2
ð8Þ
with V^ OH and V^ OD being the Morse potentials along the
OH and OD modes, respectively. V 12 and ðp^ 1 p^ 2 =mo Þ
cos y are the potential and kinetic coupling between OH
and OD modes.
Eigenvalues and eigenvectors of H^ 1 and H^ 2 are
evaluated using one-dimensional FGH (Marston and
Balint-Kurti, 1989) method
H^ 1 jfi ðr1 Þi ¼ i1 jfi ðr1 Þi;
H^ 2 jfi ðr2 Þi ¼ i2 jfi ðr2 Þi;
i ¼ 1; . . . ; nr1
i ¼ 1; . . . ; nr2 ,
ð9Þ
where nr1 and nr2 are the number of grid points in
the r1 and r2 mode, respectively, and the matrix elements
of H^ 1 and H^ 2 with even number of grid points is
nOH
nOD
Energy ðcm1 Þ
0
0
1
0
1
2
0
1
2
0
3
1
2
0
3
4
0
1
0
2
1
0
3
2
1
4
0
3
2
5
1
0
0
2717
3693
5348
6408
7225
7894
9038
9938
10 355
10 596
11 584
12 567
12 731
13 306
13 807
ARTICLE IN PRESS
2110
and maximization of time integrated Flux functional,
In the FOIST scheme (Gross et al., 1996; Vandana
and Mishra, 1999a, 2000b), we control the product
yield through preparation of the initial wavefunction jCg ðr1 ; r2 Þi as a coherent superposition of
vibrational wavefunctions of the ground electronic
state
Cg ð0Þ ¼
M
X
C m cm ,
f ¼
hCð0ÞjF^ jCð0Þi
,
hCð0ÞjCð0Þi
(13)
where Cð0Þ is defined in Eq. (12) and the time integrated
flux operator F^ is given by
Z T
y
^ 0Þ,
F^ ¼
dt U^ ðt; 0Þj^Uðt;
(14)
(12)
m¼0
0
0.4
0.025
0.3
0.02
Power Spectrum
0.2
E(t)
0.1
0
-0.1
0.015
0.01
-0.2
0.005
-0.3
-0.4
95
97
99
(a)
101
103
105
107
0
46000 48000 50000 52000 54000 56000 58000 60000 62000
109
(b)
Time(fs)
Wave number
0.16
0.1
0.08
0.14
0.06
0.12
Power Spectrum
0.04
E(t)
0.02
0
-0.02
0.1
0.08
0.06
-0.04
0.04
-0.06
0.02
-0.08
-0.1
(c)
0
50
100
Time(fs)
150
0
60000
200
(d)
60500
61000
61500
62000
Wave number
Fig. 2. The UV field plots for (a) The 5 fs field form used by Amstrup and Henriksen (1992) with EðtÞ ¼ AðtÞðcos otÞ;
AðtÞ ¼ 0:3 expðgðt tuv Þ2 Þ; g ¼ log 16=fwhm2 ; fwhm ¼ 5 fs; tuv ¼ 103 fs; o ¼ 54 869 cm1 , (b) Fourier transform of the Field
depicted in (a). (c) The field form employed by us with amplitude value chosen to provide peak intensity of nearly 20 TW=cm2 as given
by EðtÞ ¼ 0:0952446416 expðgðt tuv Þ2 Þðcos otÞ; fwhm ¼ 50 fs; tuv ¼ 100 fs and o ¼ 61169:34 cm1 , (d) Fourier transform of the
field depicted in (c).
ARTICLE IN PRESS
2111
Z
with
¼
^ 0ÞCð0Þ.
CðtÞ ¼ Uðt;
(15)
Alternatively, the product yield in the desired channel is
related to the time-integrated flux
Z T
^
dthCðtÞjjjCðtÞi
f ¼
0
T
y
^ 0ÞjCð0Þi
dthCð0ÞjU^ ðt; 0Þj^Uðt;
0
¼ hCð0ÞjF^ jCð0Þi,
ð16Þ
where j is the channel-specific flux operator and the field
r2 ; t) manifests itself through Uðt; 0Þ ’
dependence of H (~
r1 ;~
eiHt=_
where
H ¼ Hmolecule þ Hmoleculefield interaction .
Fig. 3. Time Evolution of j0; 0i on the ground electronic state induced by field described in Figs. 2c and d.
ARTICLE IN PRESS
2112
Optimization of the channel and field specific flux functional
hCð0ÞjF^ jCð0Þi with respect to the coefficients C m employed
in Eq. (12) leads to the Rayleigh–Ritz eigenvalue problem
FC ¼ fC where the matrix elements of F are given by
(Vandana and Mishra, 1999b)
Nt
X
^ l ðnDtÞi
F kl Dt
hck ðnDtÞjjjc
(17)
n¼0
with
1
j^ ¼
½p^ dðri rdi Þ þ dðri rdi Þp^ i 2mi i
(18)
where mi , p^ i and rdi are the reduced mass, the momentum
operator and a grid point in the asymptotic region of the ith
Fig. 4. Time evolution induced by the field described in Figs. 2c and d of j0; 0i on the first excited electronic state.
ARTICLE IN PRESS
2113
3. Results and discussion
FOIST-based approach attempts to utilize simple field
profiles where yield enhancement can be achieved either
through mixing of other initial states (Vandana and
Mishra, 1999a, b) or mixing of some other colors which
can induce coherent transition to the same final state or
mixing of both initial states and lasers of appropriate
frequencies (Vandana and Mishra, 2000b). This requires
that the frequency spectrum of fields utilized be
sufficiently narrow to fit our chemically motivated
mechanistic models based on excitation from and
dumping to the vibrational levels of the ground state.
The temporal and frequency profiles of 5 fs field
(Amstrup and Henriksen, 1992) utilized by Amstrup
and Henriksen are depicted in Figs. 2a and b and due to
its wide frequency span does not serve our requirements.
The simple Gaussian pulse used by us and its power
spectrum is depicted in Figs. 2c and d, respectively.
Time evolution of the ground vibrational state j0; 0i
(Fig. 1c) under the influence of the simple UV Gaussian
pulse in Figs. 2c and d with carrier frequency
61169:34 cm1 on ground (Fig. 1a) and repulsive excited
surface (Fig. 1b) are shown in Figs. 3 and 4, respectively.
On the ground state surface (Fig. 3) there is only a
simple diminution of amplitude without any change in
the wavefunction profile which implies that due to pure
repulsive nature of the excited PES (Fig. 1b) there is no
time for field-induced dumping of amplitude from
excited PES to ground PES and hence there is no fieldinduced mixing of vibrational states. FOIST-related
enhancement will therefore have to be induced by
mixing of additional vibrational states or additional
colors to the carrier frequency. The accumulated flux in
H þ O2D and H2O þ D channels is plotted in Fig. 5
which shows the kinematic bias of lighter H atom
flowing faster down the H þ O2D channel as reflected
in much larger flux in the H þ O2D channel as
compared to H2O þ D channel (first row of Table 2).
The kinematic factor is also seen to manifest itself in
Fig. 5 as delayed flow of flux in the H2O þ D channel.
However, the flux flow in the two channels is far from a
monotonic build up in the H þ O2D channel since the
probability density flow in the two channels (Fig. 4)
sways back and forth and cannot be predicted from
kinematic considerations alone.
Table 2
Flux obtained using different initial states and frequencies
Initial
state(s)
Frequencies
ðcm1 Þ
O–H flux
(%)
O–D flux
(%)
j0; 0i
j0; 1i
j0; 2i
j0; 0i
61169.34
57776.77
54371.61
61169.34 &
57776.77
61169.34
57776.77
61169.34 &
57776.77
66.77
35.79
11.20
69.19
32.28
61.85
82.44
27.30
36.44
35.80
42.95
57.94
61.86
54.42
j0; 0i þ j0; 1i
j0; 0i þ j0; 1i
j0; 0i þ j0; 1i
0.9
0.8
O-H
0.7
0.6
Flux
channel denoted by reaction coordinate ri , e.g., H þ O2D
or H2O þ D channel as desired.
We propagate the M initial states, included in the
expansion manifold of Eq. (12) where M ¼ 0, 1, and 2
i.e., either c0 , c1 and c2 , individually or as an
appropriate combination depending on value of M,
and calculate accumulated flux matrices ðF ikl Þ both for
the H þ O2D and H2O þ D dissociation channels. The
HþO2D
accumulated F kl
or F H2OþD
matrix are diagonakl
lized and eigenvector ðC m Þ corresponding to the highest
eigenvalue indicates the maximum possible dissociation
yield and defines the initial wavefunction, Cg ð0Þ ¼
P
max
m C m cm which will provide preferential dissociation
in the chosen H þ O2D or H2O þ D channel obtainable for the field used in H moleculefield interaction and the
expansion manifold of field free vibrational states (M)
utilized in the calculation (Vandana and Mishra, 1999b).
In addition, we can also influence selectivity and yield
by supplementing or substituting the mixing of vibrational states by mixing additional frequencies (Vandana
and Mishra, 2000b) to the
P resonant carrier frequency
with a field profile A i cos oiuv t where oiuv are
physically motivated UV frequencies that induce transitions to same final state from different vibrational levels
of the ground state. The frequencies in this multicolor
field are well separated so that mechanistic insights in
terms of excitation from and dumping to specific
vibrational levels may be attempted.
0.5
0.4
O-D
0.3
0.2
0.1
0
0
50
100
150
Time(fs)
200
250
Fig. 5. OH and OD flux from time evolution of j0; 0i under the
influence of the field described earlier in Figs. 2c and d.
ARTICLE IN PRESS
2114
The time evolution of the first excited vibrational state
j0; 1i with one quantum of vibration in the O–D bond
(Fig. 1d) under the influence of UV field with same
profile as that used earlier for the ground vibrational
state j0; 0i except that carrier frequency ð57776:77 cm1 Þ
has been chosen to resonate with that required for
transition from j0; 1i to the excited surface are plotted in
Figs. 6 and 7. The probability flow pattern of j0; 1i on
Fig. 6. Time evolution of j0; 1i on the first excited electronic state using same field form used in Fig. 2c but with carrier frequency
o ¼ 57776:77 cm1 , corresponding to resonant transition from j0; 1i level to the first excited electronic state.
ARTICLE IN PRESS
2115
0.9
0.8
0.7
O-D
Flux
0.6
0.5
O-H
0.4
0.3
0.2
0.1
0
0
50
100
150
Time(fs)
200
250
Fig. 7. Accumulated OH and OD Flux for j0; 1i initial state
using the field form of Fig. 6.
ground surface is similar to that seen earlier for j0; 0i
with simple diminution of amplitude with passage of
time and therefore not shown separately. Probability
density flow on the excited surface is detailed in Fig. 6
and we see that with j0; 1i as the initial state, there is
greater build up of flux in the H2O þ D channel and the
reversal of the natural kinematics favoring greater flux
in H þ O2D channel is reversed quite early and
substantively (Fig. 7). The final flux in the H2O þ D
channel (Fig. 7 and second row of Table 2) is twice as
large as that in the H þ O2D channel and this reversal
of kinematic bias with just one quantum of excitation in
the O–D mode using a simple Gaussian pulse has
perhaps been demonstrated for the first time. A more
detailed examination of Figs. 6 and 7 may also furnish
time scales for termination of field to achieve different
H þ O2D=H2O þ D dissociation ratios.
Use of j0; 2i with two quanta of vibration in the O–D
bond (Fig. 1f) as the initial state and the same Gaussian
pulse with carrier frequency corresponding to transition
from the j0; 2i initial state to the excited state PES
ð54371:61 cm1 Þ provides a surge of probabilty flow in
the H2O þ D channel from very beginning (Fig. 8) and
an overwhelming reversal of the favored dissociation
pattern in H þ O2D channel (Fig. 9 and third row of
Table 2). Dominant selective dissociation in the H2O þ
D channel may therefore be obtained with just two
quanta of excitation in the O–D bond, using an easily
reproducible Gaussian pulse. Both these features should
motivate simple experiments for selective photodynamic
control of the deutereted water molecule HOD.
Results from FOIST-based mixing of additional color
and the j0; 0i and j0; 1i vibrational states with single and
two color laser setups are reported in Table 2. Mixing of
an additional color is intended to provide field-induced
dumping from the excited PES to the j0; 1i vibrational
level of ground PES and thereby facilitate a mixing of
j0; 0i with j0; 1i so that the kinematic bias in favor of
O–H dissociation is decreased. Using the j0; 0i initial
state and a two color photolysis pulse ð61169:34 cm1 þ
57776:77 cm1 Þ where the additional frequency ðo ¼
57776:77 cm1 Þ corresponds to transition between j0; 1i
and the excited PES, however, only ends up reinforcing
the kinematic bias (row 4, Table 2) in favor of H þ
O2D channel. There is an additional 2.5% flux in the
H þ O2D channel with j0; 0i and two color field (row 4,
Table 2) as opposed to when only the single frequency
ðo ¼ 61169:34 cm1 Þ corresponding to resonant transition from j0; 0i level to the excited PES was being used
(row 1, Table 2). Results from rows 5 to 7 in Table 2
however show that FOIST-based mixing of j0; 0i and
j0; 1i using single and two color fields are quite sensitive
to frequencies employed and provide extra means for
manipulation of H þ O2D=H2O þ D ratio.
Although the FOIST results presented here so far do not
provide any enhancement of O–D flux and in some cases
diminution, sensitivity of these results to field attributes
implies that some other combination of field attributes
could provide FOIST-based enhancement of O–D dissociation. Propagation of even a single initial state on two
surfaces is extremely demanding computationally. Propagation of two or more initial states for many different
frequencies as required by FOIST has therefore not been
attempted in this initial investigation. A more systematic
investigation of this dependence is required for any
definitive conclusion and is being explored.
4. Concluding remarks
Selectivity and yield may be influenced by mixing
initial states or color in the UV field or both and further
attempts to use these variations on HOD are still going
on. Preliminary results presented here however provide
fresh impetus for utilizing simple, chemically motivated
field forms and ideas to achieve considerable selectivity
and very high yield in the kinematically unfavorable
H2O þ D channel using simple initial states like j0; 1i
and j0; 2i which should be easy to populate using normal
spectroscopic tools.
The probability density profiles reveal a richness in
the dynamics which, with more detailed analysis, may
provide additional insights for selective control of HOD
and other polyatomics. For example, the remarkable
correlation between the probability density snapshots of
Figs. 4, 6 and 8 with the surge/slowdown and levelling in
the flux plots of Figs. 5, 7 and 9 inspires more detailed
correlation which can provide new avenues for enhanced
photodynamic control. Effects from change of field
width, coupled with a well-calibrated sweep through
frequency and amplitude regimes can provide further
enriching insights as well. An effort along these lines is
underway in our group.
ARTICLE IN PRESS
2116
Fig. 8. Time evolution of j0; 2i on the first excited electronic state using same field form used in Fig. 2c but with carrier frequency
o ¼ 54371:61 cm1 , corresponding to resonant transition from j0; 2i level to the first excited electronic state.
ARTICLE IN PRESS
2117
0.9
O-D
0.8
0.7
Flux
0.6
0.5
0.4
0.3
0.2
O-H
0.1
0
0
50
100
150
Time(fs)
200
250
Fig. 9. Accumulated OH and OD Flux for j0; 2i initial state
using the field form of Fig. 8.
Acknowledgments
M. K. M. acknowledges financial support from the
Board of Research in Nuclear Sciences (Grant No.2001/
37/8/BRNS) of the Department of Atomic Energy,
India. S. A. acknowledges Department of Science and
Technology (DST), Government of India for partial
financial support through the project No. SP/S1/H-53/
01. Manabendra Sarma acknowledges support from
CSIR, India (JRF, F. No. 9/87(336)/2003-EMR-I). We
are grateful to Prof. S. H. Patil for many useful
discussions.
References
Amstrup, B., Henriksen, N.E., 1992. Control of HOD
photodissociation dynamics via bond-selective infrared
multiphoton excitation and a femtosecond ultraviolet laser
pulse. J. Chem. Phys. 97 (11), 8285–8295.
Assion, A., Baumert, T., Bergt, M., Brixner, T., Kiefer, B.,
Seyfried, V., Strehle, M., Gerber, G., 1998. Control of
chemical reactions by feedback-optimized phase-shaped
femtosecond laser pulses. Science 282, 919–922.
Baumert, T., Gerber, G., 1994. Fundamental interactions of
molecules ðNa2 ; Na3 Þ with intense femtosecond laser pulses.
Israel J. Chem. 34 (1), 103–114.
Brumer, P., Shapiro, M., 1992. Laser control of molecular
processes. Annu. Rev. Phys. Chem. 43, 257–282.
Cohen, Y., Bar, I., Rosenwaks, S., 1995. Photodissociation of
HOD ðnOD ¼ 3Þ: demonstration of preferential O–D bond
breaking. J. Chem. Phys. 102 (9), 3612–3616.
Crim, F.F., 1990. State- and bond-selected unimolecular
reactions. Science 249, 1387–1392.
Crim, F.F., 1993. Vibrationally mediated photodissociation:
exploring excited-state surfaces and controlling decomposition pathways. Annu. Rev. Phys. Chem. 44, 397–428.
Dutta, P., Adhikari, S., Bhattacharyya, S.P., 1993. Fourier grid
Hamiltonian method for bound states of multidimensional
systems. Formulations and preliminary applications to
model systems. Chem. Phys. Lett. 212 (6), 677–684.
Engel, V., Schinke, R., Staemmler, V., 1988. Photodissociation
dynamics of H2 O and D2 O in the first absorption band:
a complete ab initio treatment. J. Chem. Phys. 88 (1),
129–148.
Gordon, R.J., Rice, S.A., 1997. Active control of the dynamics
of atoms and molecules. Annu. Rev. Phys. Chem. 48,
601–641.
Gross, P., Neuhauser, D., Rabitz, H., 1991. Optimal control of
unimolecular in the collisional regime. J. Chem. Phys. 94
(2), 1158–1166.
Gross, P., Neuhauser, D., Rabitz, H., 1992. Optimal control of
curve-crossing systems. J. Chem. Phys. 96 (4), 2834–2845.
Gross, P., Bairagi, D.B., Mishra, M.K., Rabitz, H., 1994.
Optimal control of IBr curve-crossing reactions. Chem.
Phys. Lett. 223, 263–268.
Gross, P., Gupta, A.K., Bairagi, D.B., Mishra, M.K., 1996.
Initial state laser control of curve-crossing reactions using
the Rayleigh–Ritz variational procedure. J. Chem. Phys.
104 (18), 7045–7051.
Imre, D.G., Zhang, J., 1989. Dynamics and selective bond
breaking in photodissociation. Chem. Phys. 139, 89–121.
Judson, R.S., Rabitz, H., 1992. Teaching lasers to control
molecules. Phys. Rev. Lett. 68 (10), 1500–1503.
Kosloff, D., Kosloff, R., 1983. A Fourier method solution for
the time dependent Schrödinger equation as a tool in
molecular dynamics. J. Comp. Phys. 52, 35–53.
Leforestier, C., Bisseling, R.H., Cerjan, C., Feit, M.D.,
Friesner, R., Guldberg, A., Hammerich, A., Jolicard, G.,
Karralein, W., Meyer, H.D., Lipkin, M., Roncero, O.,
Kosloff, R., 1991. A comparison of different propagation
schemes for the time dependent Schrödinger equation.
J. Comp. Phys. 94, 59–80.
Lu, S.P., Park, S.M., Xie, Y., Gordon, R.J., 1992. Coherent
laser control of bound-to-bound transitions of HCl and CO.
J. Chem. Phys. 96 (9), 6613–6620.
Marston, C.C., Balint-Kurti, G.G., 1989. The Fourier grid
Hamiltonian method for bound state eigenvalues and
eigenfunctions. J. Chem. Phys. 91 (6), 3571–3576.
Rabitz, H., Riedle, R.D.V., Motzkus, M., Kompa, K., 2000.
Whither the future of controlling quantum phenomena?
Science 288, 824–828.
Reimers, J.R., Watts, R.O., 1984. A local mode potential
function for the water molecule. Mol. Phys. 52 (2),
357–381.
Rice, S.A., Zhao, M., 2000. Optical Control of Molecular
Dynamics. Wiley Interscience, New York.
Shapiro, M., Brumer, P., 2003. Coherent control of molecular
dynamics. Rep. Prog. Phys. 66, 859–942.
Shi, S., Woody, A., Rabitz, H., 1988. Optimal control of
selective vibrational excitation in harmonic linear chain
molecules. J. Chem. Phys. 88 (11), 6870–6883.
Staemmler, V., Palma, A., 1985. CEPA calculations of potential
energy surfaces for open shell systems. IV. Photodissocia1
tion of H2 O in the A~ B1 state. Chem. Phys. 93, 63–69.
Tannor, D.J., Rice, S.A., 1985. Control of selectivity of
chemical reaction via control of wave packet evolution.
J. Chem. Phys. 83 (10), 5013–5018.
Vandana, K., Mishra, M.K., 1999a. Photodynamic control
using field optimized initial state: a mechanistic investiga-
ARTICLE IN PRESS
2118
tion of selective control with application to IBr and HI
photodissociation. J. Chem. Phys. 110 (11), 5140–5148.
Vandana, K., Mishra, M.K., 1999b. Selective photodynamic
control of chemical reactions: a Rayleigh–Ritz variational
approach. Adv. Quant. Chem. 35, 261–281.
Vandana, K., Mishra, M.K., 2000a. Investigation and control of
photodissociation dynamics: an overview. PINSA-A: Proc.
Indian National Sci. Acad. Part A: Phys. Sci. 66 (1), 29–58.
Vandana, K., Mishra, M.K., 2000b. A simplification of
selective control using field optimized initial state with
application to HI and IBr photodissociation. J. Chem. Phys.
113 (6), 2336–2342.
Vandana, K., Bairagi, D.B., Gross, P., Mishra, M.K., 1998.
Field optimized initial state based control of photodissociation. Pramana—J. Phys. 50 (6), 521–534.
Vander Wal, R.L., Scott, J.L., Crim, F.F., Weide, K., Schinke, R.,
1991. An experimental and theoretical study of the bond
selected photodissociation of HOD. J. Chem. Phys. 94 (5),
3548–3555.
Zare, R.N., 1998. Laser control of chemical reactions. Science
279, 1875–1878.
Zhang, J., Imre, D.G., Frederick, J.H., 1989. HOD spectroscopy and photodissociation dynamics: selectivity in OH/
OD bond breaking. J. Phys. Chem. 93 (5), 1840–1851.