Molecular Structure Dynamics and Vibrational Spectroscopy of the AcetyleneAmmonia 11 Plastic Co-Crystal at Titan Conditions Atul C. Thakur1and Richard C. Remsing1a

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Molecular Structure, Dynamics, and Vibrational Spectroscopy of the

Acetylene:Ammonia (1:1) Plastic Co-Crystal at Titan Conditions

Atul C. Thakur1and Richard C. Remsing1, a)

Department of Chemistry and Chemical Biology, Rutgers University, Piscataway,

NJ 08854

The Saturnian moon Titan has a thick, organic-rich atmosphere, and condensed phases of small organic

molecules are anticipated to be stable on its surface. Of particular importance are crystalline phases of

organics, known as cryominerals, which can play important roles in surface chemistry and geological pro-

cesses on Titan. Many of these cryominerals could exhibit rich phase behavior, especially multicomponent

cryominerals whose component molecules have multiple solid phases. One such cryomineral is the acety-

lene:ammonia (1:1) co-crystal, and here we use density functional theory-based ab initio molecular dynamics

simulations to quantify its structure and dynamics at Titan conditions. We show that the acetylene:ammonia

(1:1) co-crystal is a plastic co-crystal (or rotator phase) at Titan conditions because the ammonia molecules

are orientationally disordered. Moreover, the ammonia molecules within this co-crystal rotate on picosecond

timescales, and this rotation is accompanied by the breakage and reformation of hydrogen bonds between

the ammonia hydrogens and the π-system of acetylene. The robustness of our predictions is supported by

comparing the predictions of two density functional approximations at diﬀerent levels of theory, as well as

through the prediction of infrared and Raman spectra that agree well with experimental measurements. We

anticipate that these results will aid in understanding geochemistry on the surface of Titan.

INTRODUCTION

Titan, the largest moon of Saturn, is of great interest

to planetary science and prebiotic chemistry communi-

ties because of its similarities to Earth1–5. Like Earth,

Titan has a thick atmosphere, but it is composed mainly

of nitrogen and methane, and atmospheric photochem-

istry creates a rich inventory of organic molecules on Ti-

tan5–9. Titan’s low surface temperature of approximately

94 K — a major diﬀerence between Titan and Earth —

leads to condensation of organic molecules from the at-

mosphere and onto the surface. The surface of Titan has

stable liquids composed mainly of hydrocarbons, which

undergo seasonal rainfall cycles analogous to water-based

cycles on Earth10. In addition to organic liquids, or-

ganic solids can form through condensation or surﬁcial

processes at Titan surface temperatures. Indeed, data

from the Cassini-Huygens mission has provided strong

evidence to suggest that Titan’s surface is dominated by

organic solids11–14. These organic crystals, also referred

to as cryominerals, could play a major role in geology,

geochemistry, and even prebiotic chemistry on Titan’s

surface, similar to the importance of Earth’s minerals in

the terrestrial analogs of these processes15–17.

Titan’s cryominerals are an exciting class of crys-

talline materials that exist as pure phases or multicom-

ponent solids composed of more than one type of or-

ganic molecule — co-crystals15,16,18. These molecular

co-crystals are typically soft because they are held to-

gether mainly by relatively weak intermolecular interac-

tions, such as hydrogen bonding, π-π, or van der Waals

interactions. These diﬀerent types of intermolecular in-

a)rick.remsing@rutgers.edu

teractions act at diﬀerent energy scales, such that molec-

ular crystals often display rich phase behavior consis-

tent with thermal excitations disrupting various interac-

tions at diﬀerent temperatures. For example, molecular

crystals are translationally and orientationally ordered at

low temperatures, resulting in a crystal phase. However,

as the temperature is increased, orientational degrees of

freedom can become disordered without the solid melt-

ing. As a result, the molecular solid is translationally

ordered but orientationally disordered, resulting in a ‘ro-

tator’ or ‘plastic crystal’ phase19.

This complex phase behavior of cryominerals must be

quantiﬁed to gain an understanding of their role in sur-

face processes on Titan. For example, a plastic crystal

typically displays diﬀerent mechanical, thermodynamic,

and chemical properties than those of the perfect crys-

tal. Crystal plasticity usually softens elastic constants

and increases mechanical ﬂexibility20. Anomalies in the

density, thermal expansivity, speciﬁc heat, and electri-

cal properties of molecular solids have also been directly

connected to the presence of plastic phases16,21. The dy-

namic disorder within a plastic phase can facilitate trans-

port through a crystal via molecular paddlewheel mech-

anisms19,22–26. Seismic discontinuities across Earth’s

mantle have also been related to the plastic crystalline

phase within deep Earth minerals27. Together, these ef-

fects may ultimately inﬂuence metamorphism, fractur-

ing, crack propagation, and erosion rates on Titan. Con-

necting these molecular level insights to the large-scale

surface features constitutes an essential step in construct-

ing a foundational understanding of the geological evolu-

tion and possible prebiotic chemistry of Titan.16,20

In this work, we investigate a model Titan cryomin-

eral, the acetylene:ammonia (1:1) co-crystal. The acety-

lene:ammonia (1:1) co-crystal is a prime candidate to dis-

play a plastic phase because both components exhibit

arXiv:2210.12188v1 [physics.chem-ph] 21 Oct 2022

plastic crystal phases28–32. Moreover, the component

molecules that make up the acetylene:ammonia (1:1) co-

crystal have been conﬁrmed in Titan’s atmosphere and

on the surface by instruments onboard Cassini33–38.

Acetylene may be the second most abundant photo-

chemical product in Titan’s hazy atmosphere6,39 and

has been linked to evaporite deposits33,40 and equato-

rial dunes12,39,41 on Titan’s surface. Along with its

pure form, acetylene is also known to co-crystallize with

many small organic molecules forming a variety of poten-

tial Titan cryominerals15,16,42. Like acetylene, ammo-

nia has been detected in Titan’s atmosphere, although

measurement diﬃculties have sparked a debate on these

results33,38,43. Titan’s subsurface ocean is predicted to

be a mixture of water and ammonia, which can erupt

from the surface via cryovolcanism, outgassing, and gey-

sering events that move ammonia from Titan’s interior

to its surface33,44–47. The co-existence of acetylene with

ammonia, either in Titan’s atmosphere or via deposi-

tion of ammonia-rich slurry on top of solid acetylene

rich deposits, can quickly lead to the formation of a co-

crystal that is stable under Titan’s surface conditions and

to methane/ethane ﬂuvial and pluvial events33. As a

consequence, the acetylene:ammonia (1:1) co-crystal is

likely to be found near geochemically and biologically

interesting sites such as cryovolcanic cones, ammonia

eruption pits, and surface ﬂows, in addition to Titan’s

stratosphere.15,33,48,49

Here, we explore the structure and dynamics of the

acetylene:ammonia (1:1) co-crystal using ab initio den-

sity functional theory-based molecular dynamics simu-

lations at T= 30 K and T= 90 K, where the tem-

peratures correspond to a crystal and plastic crystal, re-

spectively. To identify static signatures of the plastic

crystal phase, we quantify the translational and orienta-

tional structure of the co-crystal and identify the orien-

tational disorder in the plastic crystal phase. Through

an examination of translational and rotational dynam-

ics, we show that the acetylene:ammonia (1:1) co-crystal

exhibits rapid dynamic orientational disorder in the plas-

tic phase. We connect the observed orientational disor-

der to the dynamics of N-H· · · πtype hydrogen bonding

within the co-crystal. We end with a discussion of the vi-

brational ﬁngerprints of co-crystal formation while also

reﬂecting on the accuracy of our results through com-

parison of experimentally-measured and computed vibra-

tional spectra. We conclude by highlighting the common-

ality of plastic phases in Titan’s potential cryominerals

and put our results within the broader context of devel-

oping a thorough understanding of Titan’s minerals.

SIMULATION DETAILS

We performed Born-Oppenheimer molecular dynam-

ics (BOMD) simulations using density functional theory

(DFT) within the QUICKSTEP50 electronic structure

module of the CP2K code51–53. QUICKSTEP employs a

dual atom-centered Gaussian and plane wave (GPW)50,54

basis approach for representing wavefunctions and elec-

tron density, leading to an eﬃcient and accurate imple-

mentation of DFT. We used the molecularly optimized

(MOLOPT) Goedecker-Teter-Hutter (GTH) triple-ζsin-

gle polarization (TZVP-MOLOPT-GTH) Gaussian basis

set55 for expanding orbital functions, along with a plane

wave basis set with a cutoﬀ of 500 Ry for representing

the electron density. The core electrons were represented

using GTH pseudopotentials56–58. Exchange-correlation

(XC) interactions were approximated using the Perdew-

Burke-Ernzerhof (PBE) generalized gradient approxima-

tion (GGA) to the exchange-correlation functional59, as

implemented in CP2K. To account for long-ranged dis-

persion interactions, we used Grimme’s D3 van der Waals

correction (PBE+D3)60,61. To assess the accuracy of the

density functional approximation, we also performed sim-

ulations using the r2SCAN meta-GGA62 combined with

the appropriate non-local rVV10 correction for the long-

range dispersion eﬀects (r2SCAN+rVV10)63,64. We de-

termined a planewave cutoﬀ of 700 Ry to be suﬃcient for

describing the system with r2SCAN+rVV10.

We modeled a 2 ×2×2 supercell of the acety-

lene:ammonia (1:1) co-crystal using the structure re-

ported by Boese et al. (Cambridge Structural Database

ID: FOZHOS)65. We equilibrated the system for at least

10 ps in the canonical (NVT) ensemble at constant tem-

peratures of 30 K and 90 K using the canonical velocity

rescaling (CSVR) thermostat66. For the calculation of

dynamic properties, equations of motion were propagated

in the microcanonical (NVE) ensemble for approximately

50 ps using a velocity Verlet integrator with a timestep

of 1 fs. Maximally localized Wannier functions (MLWFs)

were obtained on-the-ﬂy, minimizing the spreads of the

MLWFs according to the general and eﬃcient formula-

tion implemented in CP2K67–69. The centers of the com-

puted MLWFs were used to deﬁne molecular dipoles, and

polarizability tensors which were then used to extract IR

and Raman signatures from the generated BOMD tra-

jectories using the TRAVIS analyzer70–72. The IR and

the Raman spectra were computed from a 20 ps long tra-

jectory with MLWFs obtained at every step. The matrix

elements of the full Raman polarizability tensor were ex-

tracted from the displacements of the MLWF centers re-

computed by applying an electric ﬁeld of strength 0.0005

a.u. along the crystal x,y, and zdirections respectively.

Each simulation with an electric ﬁeld also resulted in pro-

duction runs of 20 ps, such that the Raman spectrum is

estimated from a total of 80 ps of simulation (four 20 ps

trajectories).

The IR spectra were also computed for pure solid

acetylene and solid ammonia. Solid acetylene under-

goes a phase transition into an orthorhombic phase at

133 K. However, to the best of our knowledge, the crys-

tal structure of orthorhombic solid acetylene has not been

determined. Instead, we used the crystal structure for

the orthorhombic phase of dideuteroacetylene (C2D2)

(Cambridge Structural Database ID: ACETYL07) as a

FIG. 1. Snapshot illustrating the zig-zag geometry of the

acetylene:ammonia (1:1) co-crystal with C-H· · · N and N-

H· · · πtype hydrogen bonding interactions shown as dotted

lines. The hydrogen bonds are colored according to the donor

atom. Views from both (a) crystal zand (b) crystal yaxes

are shown.

close approximation, and we replaced the deuterium

atoms with hydrogens in our simulations73. For solid

ammonia, we similarly used the crystal structure for

cubic trideuteroammonia (ND3) (Cambridge Structural

Database ID: 34244)74.

RESULTS AND DISCUSSIONS

Translational Order and Orientational Disorder at Titan

Conditions

The acetylene:ammonia (1:1) co-crystal has a lay-

ered structure consisting of antiparallel planes of zigzag

chains, as shown in Figure 115,33,65,75. The layered ar-

rangement within the co-crystal is primarily held to-

gether via a network of hydrogen bonds and weak van der

Waals interactions. We ﬁnd two types of hydrogen bonds

in the acetylene:ammonia (1:1) co-crystal: C-H· · · N and

N-H· · · πhydrogen bonds33,65,75, shown as blue and red

dashed cylinders in Fig. 1, respectively. The C-H· · · N

hydrogen bonds are formed by electrostatic attractions

between the lone pair electrons of the nitrogen atom

and the H atoms of acetylene molecules. Similarly, elec-

trostatic attractions between the H atoms of ammonia

and the electron-rich π-system of a neighboring acetylene

molecule give rise to N-H· · · πhydrogen bonds. These

C-H· · · N and N-H· · · πinteractions play a crucial role

in determining the structure and dynamics of the acety-

lene:ammonia (1:1) co-crystal.

We quantify the structure of the co-crystal by com-

puting site-site radial distribution functions (RDFs),

gXY (r)76,77, where Xand Yrefer to atomic sites or the

midpoint of the C-C bond when representing the acety-

lene πelectrons. The periodic arrangement of carbon

and nitrogen atoms within the co-crystal is reﬂected in

the periodic nature of C-C and N-N RDFs (Figure 2). In-

tegration of gCC(r) and gNN (r) over the ﬁrst peak yields

coordination numbers of approximately 4 and 6, respec-

tively, consistent the arrangement of atoms within the

co-crystal geometry. Increasing temperature from 30 K

FIG. 2. Site-site radial distribution functions (RDFs),

g(r), computed for (a) acetylene carbons and (b) ammonia

nitrogens within the acetylene:ammonia (1:1) co-crystal at

T= 30 K and T= 90 K. The solid lines indicate the RDFs

evaluated with PBE+D3, and the circles correspond to those

evaluated with r2-SCAN+rVV10.

to 90 K results in broader, lower intensity peaks in the

RDFs, consistent with increased motion in the crystal

due to thermal excitation. These results are largely in-

dependent of density functional approximation, although

the r2-SCAN+rVV10 functional gives slightly larger and

narrower peaks in the C-C and N-N RDFs than those

predicted by PBE+D3.

The hydrogen bonds between acetylene and ammonia

molecules are reﬂected in the various RDFs quantifying

correlations between hydrogen bonding groups, Fig. 3.

The C-H· · · N hydrogen bonds consist of acetylene donat-

ing a hydrogen bond to ammonia. Therefore, these hy-

drogen bonds can be quantiﬁed through C-N and (C)H-N

RDFs, where (C)H is used to indicate that the hydrogen

is bonded to a carbon. The C-N RDF, gCN(r), exhibits

a large ﬁrst peak near 3.5 ˚

A (Figure 3a), the integral of

which gives a coordination number of two. This peak

corresponds to carbon atoms of two diﬀerent acetylene

molecules that are H-bonding with ammonia, highlighted

by the snapshots in Figure 1. There is a second and third

peak soon after (before 5 ˚

A), both of which correspond to

carbons that are not involved in H-bonds with the central

ammonia molecule. This structure is further emphasized

by the (C)H-N RDFs, which exhibit a peak at approxi-

mately 2.25 ˚

A, suggesting that acetylene hydrogens point

directly at the lone pair of the nitrogen to form C-H· · · N

hydrogen bonds (Fig. 3c). Integration of the ﬁrst peak

in this RDF yields a coordination number of two, further

suggesting that the nitrogen atom is, on average, engaged

in hydrogen bonding with two acetylene molecules.

To characterize N-H· · · πhydrogen bonds, we need a

site to represent the πsystem of each acetylene molecule.

Here, we represent the location of the πsystem as a sin-

gle site located at the midpoint of the C-C triple bond,

but note that similar results are found if the centers of

maximally localized Wannier functions are used to repre-

sent the location of πelectrons. The π-N RDF displays

a single, well-deﬁned peak just before 4 ˚

A, suggesting a

single H-bond donated from an ammonia molecule to an

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MolecularStructure,Dynamics,andVibrationalSpectroscopyoftheAcetylene:Ammonia(1:1)PlasticCo-CrystalatTitanConditionsAtulC.Thakur1andRichardC.Remsing1,a)DepartmentofChemistryandChemicalBiology,RutgersUniversity,Piscataway,NJ08854TheSaturnianmoonTitanhasathick,organic-richatmosphere,andcondensedphaseso...

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Molecular Structure Dynamics and Vibrational Spectroscopy of the AcetyleneAmmonia 11 Plastic Co-Crystal at Titan Conditions Atul C. Thakur1and Richard C. Remsing1a

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