Supplemental Materials
The photoexcitation of crystalline ice and amorphous solid water: A molecular dynamics study
of outcomes at 11 K and 125 K
Jeff Crouse, Hans-Peter Loock* and Natalie M. Cann*
Department of Chemistry, Queen’s University, Kingston, Ontario, Canada K7L 3N6
Telephone:
613-533-2651
FAX:
613-533-6669
E-mail:
ncann@chem.queensu.ca, hploock@chem.queensu.ca
Supplemental A: Rigid Molecule Structure Assignation Procedure
To assign atomic coordinates and velocities for the photoexcited water molecule in the rigidwater simulations, we follow a method similar to that followed by Andersson et al.1 and van
Harrevelt et al.2.
At the instant of photoexcitation, the initial atomic positions and velocities are chosen from a
Wigner type phase-space distribution function.
PW  q1 , q2 , q3 , p1 , p2 , p3     q1   q2   q3    p1    p2    p3  
2
(S1)
where qi and pi represent the three normal modes and the corresponding conjugate momenta.
𝜓(𝑞𝑖 ) and 𝜑(𝑝𝑖 ) are defined as ground state vibrational wave functions in the quantum harmonic
oscillator approximation3.
1
1
 1  4
 1

   4
  

  qi    i i  exp  i i qi 2  ,   pi   
pi 2 
 exp 
  
 2

 ii 
 2ii

(S2)
In equation (S2) 𝜇𝑖 and 𝜔𝑖 are the reduced mass and vibrational frequency of the ith normal
mode. The Box-Muller4 method is used to generate random values for qi and pi that are consistent
with the distributions in Equation (S2). A Boltzmann probability is calculated for the qi and pi.
pB  e
E  q1 , q2 , q3 
kT
where k is the Boltzmann constant, and T is the temperature of the simulations. The relative
energy of the molecular structure represented by q1, q2, and q3 is
(S3)
E (q1 , q2 , q3 )  E (q1 , q2 , q3 )  E ref (q1 , q2 , q3 ) . When zero point energy is neglected, the energy in
Equation (S3) is relative to the global minimum of the potential energy surface, Eref = Eglobal,
calculated from the Dobbyn-Knowles ground state surface5. If zero point energy is included, then
the reference energy in Equation (S3) includes the zero point energy of water in the harmonic
approximation.
1
1
1
E ref  E global  1  2  3
2
2
2
(S4)
A Monte Carlo criterion, based on Pf  Pw pB , is employed to accept or reject the randomly
generated set of qi and pi values. Specifically, a random number between 0 and 1 is generated
and if this number is less than Pf, the set of coordinates and momenta is assigned to the
photoexcited molecule and the simulation continues. Otherwise, a new set of qi and pi are
generated and tested, until a set of positions and momenta is accepted.
Supplemental B: Calculation of the Vibrational Spectrum
The parameters for the flexible fSPC model were chosen6 to reproduce the vibrational spectrum
of water. From simulations, the calculated vibrational spectrum is obtained starting from the
hydrogen atom velocity autocorrelation function, AH(t)(shown in Figure S1 for water, and Figure
S3 for crystalline ice).
AH  t  
vH  s   v H  s  t 
vH  s   v H  s 
(S5)
The real part of the fast Fourier transform of AH(t) yields the vibrational spectrum
Φ H    Re  FFT  AH  t   
(S6)
Figure S2 shows ΦH(ω) calculated for liquid water at 325 K. Three broad features centered at
~500 cm-1, ~1850 cm-1, and ~3150 – 3450 cm-1 are evident from the spectrum. The first of these
corresponds to libration, the second to the H-O-H bending mode, and the third to a combination
of the symmetric and asymmetric O-H stretching modes. Raman7 studies of liquid water have
observed these features at ~450 cm-1, ~1630 cm-1, and 3220 – 3460 cm-1.
IR and Raman experiments on ice7-9 show that libration shifts to higher energy (600 - 800 cm-1),
the bending mode broadens and also shifts to higher energy to ~1650 cm-1, while the
symmetric/asymmetric stretch shifts to lower energy ( 3150 – 3380 cm-1). In other
experiments10,11 features at ~220 cm-1 were observed and attributed to the hydrogen bond stretch
while those at ~3969 cm-1 were attributed to stretching of OH groups that were not hydrogen
bonded to other groups in the matrix (dangling OH monomers). The simulated vibrational
spectrum for crystalline ice at 50 K is shown in Figure S4 and for amorphous solid water at 50 K
in Figure S5. Comparing the calculated crystalline ice spectrum to the simulated liquid water
spectrum we observe a blue shift in the libration mode, which peaks at approximately 600 cm-1
and covers a range of values between 550 cm-1 – 1000 cm-1, the bending mode peaks at
approximately the same frequency, ~1850 cm-1, and the symmetric and asymmetric stretch band
is observed to red shift and separate into two bands, centered at ~ 3050 cm-1 and ~3150 cm-1.
Additionally, in both spectra, a small peak centered at ~3450 cm-1 is observed which we can
attribute to dangling OH. The calculated amorphous solid water spectrum shows peaks at similar
values, i.e. ~550 cm-1 for libration, ~1900 cm-1 for bend, and 3000 to 3300 cm-1 for the
symmetric/asymmetric stretches. IR experiments12, 13 on amorphous solid water have observed
libration near 800 cm-1, the bending mode at ~1650 cm-1, and the symmetric/asymmetric stretch
band at 3100 - 3400 cm-1. The position of the very broad symmetric/asymmetric bands as well as
the libration band are well represented in the calculated spectra. As in experiments, the peak
which corresponds to H-O-H bending does not shift significantly in the transition from liquid
water to crystalline ice to amorphous solid water, although in all cases the peak is displaced from
experimental values by approximately 200 cm-1.
Figure S1: The hydrogen atom velocity autocorrelation function, AH(t) at 325 K.
Figure S2: Simulated water vibrational spectrum at 325 K. Figure S2 is calculated from the Fourier
transform of the autocorrelation function shown in Figure S1.
Figure S3: The hydrogen atom velocity autocorrelation function, AH(t) for 50 K crystalline ice.
Figure S4: Simulated crystalline ice spectrum at 50 K. Calculated from the Fourier transform of the
autocorrelation function shown in Figure S3.
Figure S5: Simulated amorphous solid water spectrum at 50 K. Calculated as in Figure S4.
Supplemental C: H∙∙∙H2O Potential Energy Surface
The H∙∙∙H2O potential energy surface was produced by fitting to the YZCL2 surface of Zheng et
al.14. The form of the potential is identical to that used by Andersson et al.15 but uses new
constants to reflect the Simple Point Charge (SPC)16 geometry. The form of the potential is given
below. The constants are provided in Table S1.
VH
H 2O
 Vdisp ( RHH (1) )  Vdisp ( RHH (2) )  Vdisp ( RHO )
 Vrep ( RHH (1) )  Vrep ( RHH (2) )  Vrep ( RHO )  Vmorse ( RHO )
(S7)
Vdisp ( Ri )  D( Ri )C6i Ri6
(S8)

1.0,
Ri  Rci

2
  Ri
D( Ri )  
 
i
c
exp    R  1  , Ri  Rc
  i
 

(S9)
Vrep ( Ri )  ai exp( bi R i )
(S10)
Vmorse ( RHO )  DHO exp    HO  RHO  Re,HO  
exp   R
HO


HO  Re ,HO    2.0
(S11)
Table S1 - Parameters for the H∙∙∙H2O potential
kJ
5.14355 x105
nm6
C6HH
mol
kJ
2.32932 x105
nm6
C6OH
mol
HH
Rc
0.197079 nm
RcOH
aHH
bHH
aHO
bHO
DHO
 HO
Re , HO
0.501761 nm
kJ
1381.93
mol
1
30.2071
nm
kJ
4417.09
mol
1
28.4494
nm
kJ
65.4171
mol
1
74.5318
nm
0.115553 nm
Supplemental D: OH∙∙∙H2O Potential Energy Surface
The OH∙∙∙H2O potential energy surface was generated using a bond-bond interaction formalism
combined with Coulomb electrostatic interactions. The interactions of the two O-H bonds in
water with the OH radical was modeled using the Improved-Lennard-Jones (ILJ) interaction
potential17.


 Ri 
 Ri 
n
n
6



 Rm ( i )   Rm ( i ) 
6
 Rm ( i )   Rm ( i )  
i
VILJ
( Ri ,  i )   ( i ) 





  Ri 
Ri 
Ri  
 Ri 


n
n

6
6
 Rm ( i ) 
  Rm ( i ) 

 R 
 R 
n 
    4.0 

 Rm    
 Rm    
(S12)
2
(S13)
In this equation Ri is the bond separation and  is the triple of angles a ,b ,   (see Figure S6).
Ri is taken as the separation between the ith bond in water and the bond in the OH radical. This
separation is obtained from approximately the center of mass of the O-H system, and is then
allowed to vary in the fit optimization. The bond angles  a and b are obtained from the inner
product of the separation vector Ri and the O-H bond vector in water and the OH radical
respectively.
cos( a ) 
cos(b ) 
Ri  ROHi
(S14)
Ri ROHi
Ri  ROH r
(S15)
Ri ROH r
In these equations ROHi refers to the ith bond in water and ROHr refers to the OH radical bond. 
is obtained as the angle between the components of the bond vectors, ROHi and ROHr , which are
perpendicular to the bond separation, Ri .
cos( ) 
R
R
OH i
OH i

 R  R

R 
 Ri  ROH r  Ri
i
OH r
(S16)
i
In Equation (S12),   i  and Rm  i  are not fit parameters but rather depend on the atomic
polarizabilities of the species in the bond. For a complete description of these relations the
interested reader is referred to the works of Pirani and Bartolomei18,19. The parameters which are
varied in this potential model are β and the location of the bond – bond interaction site. The
location of the interaction site within the bond is represented as follows.
Rint eract 
rO  Ci rH
1  Ci
(S17)
In this equation Ci is a parameter which is varied for both the OH radical bond (Cr in Table S2)
and for the water OH bonds (Cw in Table S2). rO are the Cartesian coordinates of the O-atom
within the bond, and rH are the Cartesian coordinates of the H-atom. If Ci =
mH
=0.0630 then the
mO
interaction site is the center of mass of the OH bond.
Additionally there is an atom centered Coulomb interaction potential.
Velstat 
qw,i qr , j
(S18)
rij
In this equation, qw,i refers to a charge on either O or H in water, qr , j refers to either O or H in
the OH radical and rij is the atom separation. The charges on the water molecule are those
corresponding to the SPC model and the charges on OH depend linearly on the OH bond length
qO  qH  aq  bq ROH
(S19)
where ROH is the bond length in OH and the parameters aq and bq are chosen to fit to the OH
dipole moment similar to Andersson et al15,20. The total interaction potential for the H2O···OH
system can be written as:
2
VOH
H 2O
k
 Vvdw
( Rk ,  k )  Velstat (rij )
k 1
(S20)
i, j
k
( Rk ,  k ) , includes both OH bonds in water and the
where the sum of bond-bond potentials, VILJ
sum of the electrostatic potentials, Velstat ( rij ) , is runs over all atom pairs to yield the full
interaction potential.
Du et al. 21 have calculated points on the OH∙∙∙H2O potential energy surface at the CCSD(T)/augcc-pVTZ level of theory, which the authors have generously provided to us. The values of the
constants used in this potential are given in Table S2. The energies calculated from Equation S1
are compared with the ab initio in Figures S8 – S16. Figure S7 shows the coordinates used in
Figures S8 – S16.
Table S2 - Parameters for the OH∙∙∙H2O potential
aq

0.69004 e
bq
30.648
e
nm
Cr
0.0753
Cw
0.0079

8.96
Figure S6: Description of the coordinates used in the bond-bond formalism. For a complete description
of the angles see text.
Figure S7: Description of the coordinates used in the potential energy surfaces Figure S8-Figure S16
Figure S8: OH···H2O potential energy interaction as a function of ROO with θ = 90o, φ = 0o, θ’ = 90o, and
φ’ = 69o. (Black) The surface calculated by Du et al.21 at the CCSD(T)/aug-cc-pVTZ level , (red) the
bond-bond description used in this work which was fit to the surface of Du et al., and (green) the
analytical surface used in the works by Andersson et al.15
Figure S9: OH···H2O potential energy interaction as a function of ROO with θ = 54o, φ = 128o, θ’ = 126o,
and φ’ = -52o. All colors the same as in Figure S8.
Figure S10: OH···H2O potential energy interaction as a function of ROO with θ = 90o, φ = -52o, θ’ = 90o,
and φ’ = -52o. All colors the same as in Figure S8.
Figure S11: OH···H2O potential energy interaction as a function of φ’ with ROO = 3.1 Å, θ = 90o, φ = 0o,
and θ’ = 90o. All colors the same as in Figure S8.
Figure S12: OH···H2O potential energy interaction as a function of θ’ with ROO = 2.9 Å, θ = 54o,
φ = 128o, and φ’ = -52o. All colors the same as in Figure S8.
Figure S13: OH···H2O potential energy interaction as a function of θ’ with ROO=3.1 Å, θ =90o, φ=-52o,
and φ’=-52o. All colors the same as in Figure S8.
Figure S14: OH···H2O potential energy interaction as a function of φ’ with ROO = 3.1 Å, θ = 90o,
φ = -52o, and θ’ = 90o. All colors the same as in Figure S8.
Figure S15: OH···H2O potential energy interaction as a function of φ with ROO = 3.1 Å, θ = 90o, θ’ = 90o,
and φ’ = φ. All colors the same as in Figure S8.
Figure S16: OH···H2O potential energy interaction as a function of θ with ROO =3.1 Å, φ = -52o, θ’ = θ,
and φ’=-52o. All colors the same as in Figure S8.
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