Supplementary material for: "Uncovering Molecular

Details of Urea Crystal Growth in the Presence of

Additives"

Matteo Salvalaglio,†,‡ Thomas Vetter,† Federico Giberti,‡ Marco Mazzotti,∗,† and

Michele Parrinello∗,‡,¶

Institute of Process Engineering, ETH Zurich, CH-8092 Zurich, Switzerland, Department of

Chemistry and Applied Biosciences, ETH Zurich, and Facoltà di Informatica, Istituto di Scienze

Computazionali, Università della Svizzera Italiana Via G. Buffi 13, 6900 Lugano Switzerland

E-mail: marco.mazzotti@ipe.mavt.ethz.ch; parrinello@phys.chem.ethz.ch

∗To whom correspondence should be addressed†Institute for Process Engineering, ETH Zurich‡Department of Chemistry and Applied Biosciences, ETH Zurich¶Istituto di Scienze Computazionali, Università della Svizzera Italiana

S1

Force Field Parameters

C

O

C1 C2

H3

H4

H5

H

H1

H2

CC1

N N1

N2

H

H1

H2

H3H4

O

O1

Figure S1: Foreign molecules structures and GAFF atom types.

Table S1: Atom names, atom types, RESP charges, and cartesian coordinates of the biuret and theacetone molecule.

Atom name GAFF atom type RESP charge x y z

C c 0.557188 -0.6694 1.00584 0.00000O o -0.516938 -0.6694 2.22767 0.00000C1 c3 -0.297665 0.64107 0.23609 0.00000H hc 0.092513 0.50594 -0.84607 0.00000H1 hc 0.092513 1.22405 0.52661 -0.88020H2 hc 0.092513 1.22405 0.52661 0.88020C2 c3 -0.297665 -1.97987 0.23609 0.00000H3 hc 0.092513 -1.84474 -0.84607 0.00000H4 hc 0.092513 -2.56285 0.52661 0.88020H5 hc 0.092513 -2.56285 0.52661 -0.88020

Atom name GAFF atom type RESP charge x y z

C c 0.466433 -4.340791 0.552247 -0.000002O o -0.540863 -3.349461 -0.176095 -0.000001H hn 0.260062 -5.569228 -1.050947 0.000001N n -0.236462 -5.620179 -0.041089 0.000001H1 hn 0.371844 -5.188439 2.41595 0.000002H2 hn 0.371844 -3.41572 2.353576 0.000000C1 c 0.466433 -6.865233 0.582529 0.000002O1 o -0.540863 -7.005195 1.81113 -0.000002N1 n -0.681058 -4.314868 1.900237 0.000000H3 hn 0.371844 -7.830834 -1.273121 0.000001N2 n -0.681058 -7.919999 -0.269583 0.000000H4 hn 0.371844 -8.844054 0.131566 -0.000002

acetone

biuret

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Supplementary Results discussion.

Scale of the single urea molecule

Focusing the analysis of the MD trajectories on the dynamics of each urea molecule, differences

between the pseudo-FES landscape associated with the incorporation in the crystal lattice on the

{001} and the {110} faces also emerged. The transition between solution and crystalline states

of a single urea molecule was characterized for both the {001} and the {110} faces through the

collection of the probability distribution p(ni,φi) and the construction of the relative pseudo-FES

as:

F(ni,φi) =−kbT ln p(ni,φi) (1)

The pseudo-FES obtaiened for faces {001} and {110} are reported in Figure S2. For n < 2 and

φi < 0.2 a first basin, corresponding to the solvated state, can be observed in both pseudo-FES, to-

gether with a second basin, corresponding to the lattice bulk, in the region characterized by n > 10

and φi > 0.8. For values of φi > 0.8 and 6 < n < 8 a secondary minimum is observed, correspond-

ing to molecules with a crystalline lattice environment located at the solid/liquid interface. It is

interesting to observe that the transition between solvated and crystalline state, is characterized

by remarkably different pseudo-FES. For the {001} face a low energy barrier (∼ 1.5kbT ) sepa-

rates urea molecules at the solid/liquid interface with a disordered molecular environment from

urea molecules included in the crystal lattice. For the {110} face instead a wider basin can be

associated with liquid-like molecules adsorbed at the interface, and a significantly higher energy

barrier (∼ 3kbT ) is indeed present on the pathway between this state and the basin corresponding

to crystalline structures. Therefore it emerges that also the pseudo-FES associated to the addition

of a single urea molecule to the crystalline lattice intrinsically depends on the molecular structure

of the exposed face and demonstrates that the incorporation of urea molecules in the crystal lattice

in the {001} face is more favorable than in the {110} face.

S3

i

2 4 6 8 10 12 14

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

2

3

4

5

6

7

8

9

10

11

2 4 6 8 10 12 14

{001}

(a) (a)

(b)

(c) (d)

(b)

(c) (d)

(a) (b) (c) (d)

{110}

nn

Figure S2: MD simulations of {001} and {110} faces in water (A and B in ??). Pseudo-FESobtained for the single urea molecule as a function of φi (see the methods section) and the coor-dination number n. The pseudo-FES describes the transition of a urea molecule from the solvatedstate to the crystalline lattice in terms of number of neighbours and relative orientation with respectto the neighbours. Sketches of typical structures characterizing the visited states are reported in theupper part of the figure and refer to the labels included in the pseudo-FES representing: (a) a sol-vated molecule (b) a disordered molecule adsorbed on the crystal surface (c) an ordered moleculeon the crystal surface (d) a urea molecule completely included in the crystal lattice. The ith ureamolecule is depicted with sticks representing all the atoms while neighbours are represented astransparent spheres centred on the urea carbon atom.

S4

Supplementary standard MD simulations.

0.0 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.2100

200

300

400

500

600

700

800

900

1000

time [ s]

Nl

001 growth001 equilibration110 growth110 equilibration

Figure S3: Number of urea molecules in the liquid phase in function of the simulation time. Forthe {001} face it can be observed that the number of urea molecules in the liquid phase equilibratesto a common value for simulations in which both growth and dissolution occur. For the {110} faceinstead it can be observed that growth and dissolution lead to a different number of molecules inthe liquid phase in a 0.2 µs time span. This observation can be attributed to the kinetic limitationsthat characterize the growth on the {110} face, which proceeds with a birth and spread mechanism.

S5

Figure S4: Number of crystalline layers grown on the {110} face during MD simulation for twoperiodic cell sizes. An initial concentration of 6 mol/l is allowed to equilibrate in both cases. Inthe simulation time span (0.04 µs) no crystal growth is observed for the larger model, while in thesmaller model a bith and spread event os recorded after 0.005 µs. This plot shows that finite sizeeffects induced by periodic boundary conditions affect the observed rate of the growth process.The typical step growth discussed in the main paper is however observed also in the smaller modelcase showing that the evolution mechanism is instead not affected by this issue.

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Well Tempered Metadynamics

Metadynamics is a simulation technique aimed at enhancing the sampling of rare events in MD

simulations through the application of a history dependent, Gaussian bias potential to a set of col-

lective variables (CVs, continuous and continuously differentiable functions of the microscopic

cartesian coordinates of the system). Given a set of d CVs, S(R) = [S1(R), ...Sd(R)], the metady-

namics biasing potential at time t, VG(S, t), can be written as:

VG(S, t) =�

t

0ω exp

�−∑

i=1

(Si(R)−Si(R(t �)))2

2σ2i

�dt

� (2)

where ω is an energy rate obtained as the Gaussian height, W , divided by a deposition stride τG

and σi is the standard deviation of the Gaussian distribution for the ith CV. R contains the cartesian

coordinates of all the molecules in the simulation. Moreover VG(S, t → ∞) represents an estimate,

obtained without any additional computational cost, of the negative of the free energy surface

(FES) in function of a set of chosen CVs. The convergence of the free energy estimate is ensured

by the WT metadynamics algorithm, through the introduction of a time dependence for the height

of the Gaussian history dependent bias potential added during the simulation. The bias potential in

WT metadynamics has the following functional form:

V (S, t) = kb∆T ln�

1+ωN(S, t)

kb∆T

�(3)

dV (S, t)dt

=ωδS,S(t)

1+ ωN(S,t)kb∆T

= ωδS,S(t) exp�−V (S, t)

kb∆T

�(4)

where N(S, t) is the histogram of the S variables collected during the simulation, and ∆T the bias

factor, an arbitrary input parameter dimensionally consistent with a temperature. This formulation

can easily be reconnected to standard metadynamics by replacing δS,S(t) with a Gaussian, and in

practice, it is implemented by rescaling the Gaussian height W according to:

W = ωτG exp�−VG(S, t)

kB∆T

�(5)

S7

It was demonstrated that the WT algorithm provides an estimation of the exact FES which con-

verges to a finite error of, which is a function of the bias factor ∆T :

Vg(S, t → ∞) =−∆T

T +∆TF(S)+C (6)

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Supplementary results from WT Metadynamics

Figure S5: FES as a function of CV1 and CV2 computed for the biuret molecule on the {110}; for theacetone molecule on the {001} and {110} faces and for urea on the {001} and {110}. The isoenergy valuesare reported in kbT . The internal molecular vector defining CV2 is defined as a vector parallel to the C-C1axis in biuret and to the C=O bond in both urea and acetone. Biuret does not show strong interactionswith the {110} face. It can be noted that although the three minima are present they are not separated bysignificant energy barriers. The most favoured configuration corresponds to the biuret molecule horizontallyattached to the crystal. This configuration maximizes the interactions between additive and surface withoutanyhow allowing the occupation of crystalline sites at the solid/lliquid interface. The adsorbed state ofacetone does not show strong preferential orientations: the basins corresponding to adsorbed configurationsspan the whole (0,π) range without exhibiting pronounced energy barriers on both the {001} and the {110}faces. Urea shows three minima on the {001}face; two of them (around ±π) correspond to crystal likeorientations of the molecule on the surface while the third (around 100o) correspond to a tilted configurationwith the carbonyl bond pointing towards the crystal and one of the two amine groups pointing towards thesolution. On the {110} face urea does not show a marked preferential orientation.

S9

0 1 2 3 4 5 6x 104

1

1

3

5

frame #

acet

one

G [k

cal m

ol1 ]

{001}

0 2 4 6 8 10x 104

0

2

4

6

frame #

G [k

cal m

ol1 ]

{110}

0 5 10 15x 104

0

2

4

6

8

10

frame #

biur

et

G [k

cal m

ol1 ]

0 2 4 6 8x 104

1

1

3

5

7

frame #

G [k

cal m

ol1 ]

0 0.5 1 1.5 2x 105

0

2

4

6

8

frame #

urea

G [k

cal m

ol1 ]

0 2 4 6 8x 104

0

2

4

6

8

frame #

G [k

cal m

ol1 ]

Figure S6: Time-realization of the ∆Gads during the WT metadynamics simulation. It can beobserved that in all the cases the oscillations in the computed ∆Gads are dumped over time and inthe long time limit tend to converge to a constant as theoretically expected.

S10

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