Detailed intermolecular structure of molecular liquids containing slightly distorted tetrahedral molecules with C3v symmetry: Chloroform, bromoform, and methyl-iodide

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Detailed intermolecular structure of molecular liquids containing slightly distorted tetrahedral molecules with C3v symmetry: Chloroform, bromoform, and methyl-iodide

Szilvia Pothoczki, , and

Citation: The Journal of Chemical Physics 134, 044521 (2011); doi: 10.1063/1.3517087 View online: http://dx.doi.org/10.1063/1.3517087

View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/134/4?ver=pdfcov Published by the AIP Publishing

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Detailed intermolecular structure of molecular liquids containing slightly distorted tetrahedral molecules with C

_3v

symmetry: Chloroform,

bromoform, and methyl-iodide

Szilvia Pothoczki,^a)László Temleitner,^b)and László Pusztai

Research Institute for Solid State Physics and Optics, Hungarian Academy of Sciences, H-1525 Budapest, P.O. Box 49, Hungary

(Received 26 August 2010; accepted 26 October 2010; published online 27 January 2011)

Analyses of the intermolecular structure of molecular liquids containing slightly distorted tetrahedral molecules of the CXY3-type are described. The process is composed of the determination of several different distance-dependent orientational correlation functions, including ones that are introduced here. As a result, a complete structure classification could be provided for CXY3molecular liquids, namely for liquid chloroform, bromoform, and methyl-iodide. In the present work, the calculations have been conducted on particle configurations resulting from reverse Monte Carlo computer modeling: these particle arrangements have the advantage that they are fully consistent with structure factors from neutron and x-ray diffraction measurements. It has been established that as the separa- tion between neighboring molecules increases, the dominant mutual orientations change from face- to-face to edge-to-edge, via the edge-to-face arrangements. Depending on the actual liquid, these geometrical elements (edges and faces of the distorted tetrahedra) were found to contain different atoms. From the set of liquids studied here, the structure of methyl-iodide was found to be easiest to describe on the basis of pure steric effects (molecular shape, size, and density) and the structure of liquid chloroform seems to be the furthest away from the corresponding “flexible fused hard spheres”

I. INTRODUCTION

The structure of liquids containing perfect tetrahedral molecules has been an evergreen topic in the area (see, e.g., Refs. 1–5 and references therein), indicating that these systems are still considered to be the prototypes of simple molecular liquids. A possible move toward more complex molecular systems, beyond the best known examples like carbon- tetrachloride, CCl4, is the investigation of haloform liquids (CHX3; X: F, Cl, Br, I) whose molecules are of the shape of slightly distorted tetrahedra. Here we consider details of the orientational structure of two representative members of the family: chloroform (CHCl3) and bromoform (CHBr3), in which molecules of the three larger halogen ligands form the basal plane of the tetrahedron. For completeness, an “inverse”

of the above molecules, methyl-iodide (iodomethane, CH3I) is also studied, in which three small H atoms form the basal plane of tetrahedron, making the molecule rather top heavy.

The symmetry of all these molecules is the same: C_3v. Chloroform (trichloromethane) is undoubtedly the best known of the above set of liquids: it is one of the most frequently utilized solvents and reagents in the chemical industry: this is why its microscopic properties have been studied very much in detail (see, e.g.. Refs. 6–9). Studies

a)Present address: Grup de Caracterització de Materials, Departa- ment de Física i Enginyeria Nuclear, ETSEIB, Universitat Politèc- nica de Catalunya, Diagonal 647, 08028 Barcelona, Catalonia, Spain.

Author to whom correspondence should be addressed. Electronic mail:

poth@szfki.hu.

b)Present address: Japan Synchrotron Radiation Research Institute (SPring- 8/JASRI) 1–1-1 Kouto, Sayo-cho, Sayo-gun, Hyogo 679–5198, Japan.

concerned with its liquid structure, including diffraction experiments and computer simulations, have been performed (see, e.g., Refs. 10–13). It may still be concluded that there is no general agreement concerning correlations between molecular orientations. For this reason, a new systematic structural study had been initiated and its first results, including partial radial distribution functions (prdf), molecular ge- ometries in the liquid state, and an average description of orientational correlations, according to Rey,⁴have recently been published.¹⁴ What are still missing are the apparently most informative analyses of orientational correlations that would take into account the different chemical nature of the ligands in liquids of CXY3molecules.

Intermolecular orientational correlations of liquids con- sisting of distorted tetrahedral molecules with C2vsymmetry, where molecules have the general formula of CX2Y2, have been investigated in our previous study.¹⁵ Here, somewhat analogously, first the method applied for the analysis of liquid CCl₄/XY₄ systems^4,5,16–20 is extended, by introducing new subgroups (similarly to Ref. 15), to molecular liquids containing distorted tetrahedral molecules with C_3v symmetry.

These 21 new subgroups, along with the original (six) groups of Rey,⁴are interpreted.

Second, the novel, “subgroup-based,” orientational analyses are complemented with a more traditional study of dipole–dipole (or in other words, “molecular axes”) correlations (see, e.g., Refs.15,21, and22). We wished also to point out the way these methods supplement each other so that their combination provides a supreme understanding of the intermolecular structure.

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044521-2 Pothoczki, Temleitner, and Pusztai J. Chem. Phys.134, 044521 (2011) TABLE I. Some characteristics of the liquids studied and their com-

puter models. X: H (CHCl3), H (CHBr3), I (CH3I). Y: Cl (CHCl3), Br (CHBr3), and H (CH3I).

CHCl3 CHBr3 CH3I

Atomic number density (Å⁻³) 0.0371 0.03425 0.04385

Box length (Å) 65.54432 63.95364 59.14

Fnc(C–X)^a(Å) 1.04–1.16 0.96–1.17 2.07–2.19

Fnc(C–Y) (Å) 1.7–1.82 1.83–2.03 1.02–1.14

Fnc(X–Y) (Å) 2.27–2.39 2.37–2.57 2.55–2.79

Fnc(Y-Y) (Å) 2.84–2.96 3.07–3.28 1.67–1.91

aFnc: tolerances of intramolecular bonding and nonbonding atomic distances.

Our general strategy for understanding the liquid structure (applied also in Refs. 3,5,14, and 15, and 19–22) is first to perform the two most reliable diffraction experiments (neutron diffraction on the deuterated compounds and x- ray diffraction on either the hydrogenated or on the deuterated compounds) and then to model, at the atomic level, the experimental results via the reverse Monte Carlo (RMC) technique.^23–26 These steps have already been reported for chloroform and bromoform,¹⁴as well as for methyl-iodide.²⁷ Particle configurations from RMC could later be analyzed in detail; here, correlation functions mentioned above have been computed (see Sec.IIfor details).

The paper is organized as follows: Sec.IIdeals with computational details. SectionIIIprovides the main findings and finally, in Sec.IV, concluding remarks are given.

II. MODELS AND COMPUTATIONAL DETAILS A. Reverse Monte Carlo modeling

Orientational correlation functions and dipole–dipole correlations have been calculated from configurations resulting from the RMC simulations. (Full description of the RMC method can be found in Refs.23–26.) In our previous works,^14,27 specification of simulation parameters were provided for each studied molecular liquid. For this reason only a short summary of the indispensable details is given here.

Initial configurations consisted of 2000 randomly oriented flexible molecules (10 000 atoms) in cubic boxes with periodic boundary conditions and were defined by the appropriate number densities, intramolecular bondlengths and nonbonding distances, and intermolecular closest approaches between atoms. “Flexibility” means that bondlengths and intramolecular nonbonding distances were allowed to vary slightly within predefined tolerances. Atomic number densities, simulation boxlengths, and limiting values for intramolecular bonding and nonbonding distances are listed in TableI. We note that the tolerances that appear in TableIare larger than they would be in real molecules; this way we al- low for moving molecules around via atomic movements and also, facilitate that the formation of the molecular geometry may be driven also by diffraction data (along with the con- straints given in TableI).

Two types of calculations have been performed: (a) runs modeling both neutron and x-ray diffraction data simultane- ously, resulting particle configurations that were always fully consistent—within errors—with input diffraction data and as

such, that can represent the “real” liquids (code: RMC/NX) and (b) runs without any input diffraction data, the “hard sphere” reference models (code: HS), which were otherwise identical to RMC/NX computations. Comparison between the reference HS and RMC/NX models can exhibit the influence of diffraction data. A similar approach in our earlier studies for other molecular liquids proved to be extremely useful.^5,19–22Further details of diffraction measurements and RMC simulations relevant to the present work can be found in Refs.14and27.

B. Calculation of orientational correlation functions In our previous related work, we utilized Rey’s construction⁴ for the calculation of orientation correlation functions for chloroform (CHCl3) and bromoform liquids (CHBr3) as follows: atoms connected to the central carbon atom (“ligands,” for short) were not distinguished, so that the labeling was carried out in the original way.⁴ That is, given a pair of tetrahedral molecules, we constructed two parallel planes that contain the centers of these molecules and perpen- dicular to the line joining them. Molecular pairs were classified by the number of ligands, belonging to one and the other of the two molecules between these planes; this way, six “original” orientational groups arise.⁴ These groups are the corner-to-corner (1:1), corner-to-edge (1:2), edge-to-edge (2:2), corner-to-face (1:3), edge-to-face (2:3), and face-to- face (3:3) orientations. Note that this classification can be applied for methyl-iodide (for which material analogous results have not been published earlier) and other systems, too, which contain ABC3type of molecules.

Additionally here we introduce two other functions for describing how molecules orient toward each other.

(1) A possible extension to the above classification is when the two types of ligands (in the present cases, hydrogen and halogen atoms) are distinguished. (Note that this extension is not part of the “original” method.) In this way, 21 subgroups derive. For a demonstration, one exam- ple is given here which concerns the most frequent orientation. The edge-to-edge (2:2) orientation for CHCl₃ is composed of the following subgroups: chloride–chloride- to-chloride–chloride (Cl,Cl–Cl,Cl), hydrogen–chloride-to- chloride–chloride (H,Cl–Cl,Cl), and hydrogen–chloride-to- hydrogen–chloride (H,Cl–H,Cl). The complete list with all subgroups can be found in TableII. Schematic representations of the subgroups of the most significant 2:2 group can be seen in Fig.1(Ref.28).

(2) It has to be observed that the molecules of ABC3

liquids frequently possess a permanent dipole moment that assigns a specific molecular axis unambiguously. The rela- tive orientation of two molecules (represented by the two pri- mary molecular axes) can then be characterized by calculat- ing three angles: angles confined by the molecular axes and the line connecting molecular centers and by an additional angle which is defined by the two molecular axes.^21,22 This construction is shown in Fig.2. It has been demonstrated several times^15,21,22that well recognizable arrangements can eas- ily be identified such as “parallel”/“antiparallel,” “chainlike,”

or “T-shaped.” The characteristic cosine values of the three

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TABLE II. Division of the original orientation groups of Rey (Ref.4) into subgroups for CXY3molecular liquids. X: H (CHCl3), H (CHBr3), I (CH3I). Y:

Cl (CHCl3), Br (CHBr3), and H (CH3I).

1:1 1:2 2:2 1:3 2:3 3:3

Corner-to-corner Corner-to-edge Edge-to-edge Corner-to-face Edge-to-face Face-to-face

Y Y Y Y,Y Y,Y Y,Y Y Y,Y,Y Y,Y Y,Y,Y Y,Y,Y Y,Y,Y

X Y X Y,Y X,Y Y,Y X Y,Y,Y X,Y Y,Y,Y Y,Y,Y X,Y,Y

X X Y X,Y X,Y X,Y Y X,Y,Y Y,Y X,Y,Y X,Y,Y X,Y,Y

X X,Y X X,Y,Y X,Y X,Y,Y

angles corresponding to some of the most popular arrangements can be found in TableIII(cosines are mentioned instead of angles since the actual calculation uses cosine values; a de- viation of±0.2 from the ideal cosine value is allowed for a molecular pair to be counted as a “specially oriented” pair).

Some of the most significant special (dipole–dipole) arrangements are depicted in Fig.3, out of the arrangements introduced by TableIII(see Sec.IIIfor more details).

It has to be pointed out that, since only “well recognizable arrangements” are taken into account, not all molecular pairs are classified here; this is a major difference from the group/subgroup representations. The fraction of recognizable arrangements (as compared to the total number of molecular pairs) over the important molecular distance region of 4–5 Å is about 15%.

Please note that our definition of the ‘dipole direction’ is different from the usual convention (see Fig.3), as the dipolar vector in our case points towards the negatively charged part of the molecule. This has no effect on any orientational parameters we have calculated here, neither in our previous paper on CH2X2molecular liquids (see Ref.15).

It is instructive to point out that some of these special orientations may also be categorized in terms of the subgroups defined above. The head-to-head arrangement corresponds to the Cl,Cl,Cl–Cl,Cl,Cl (CHCl3), as well as to the Br,Br,Br–Br,Br,Br (CHBr3) subgroup of the 3:3 group, whereas it corresponds to the I–I subgroup of the 1:1 group for CH3I. The head-to-tail arrangement is analogous with the H–Cl,Cl,Cl (CHCl₃) subgroup as well as the H–Br,Br,Br (CHBr₃) subgroup of the 1:3 original group, and with the

FIG. 1. Subgroups of the 2:2 (edge-to-edge) orientational correlations of CXY3molecular pairs. (a) Cl,Cl–Cl,Cl subgroup for CHCl3; (b) H,Cl–Cl,Cl subgroup for CHCl3; (c) H,Cl–H,Cl subgroup for CHCl3; (d) H,H–H,H subgroup for CH3I; (e) I,H–H,H subgroup for CH3I; (f) I,H–I,H subgroup for CH3I. Green balls, Cl atoms; gray balls, C atoms; light gray balls, H atoms;

violet balls, I atoms.

I–H,H,H subgroup of the 1:3 group for CH₃I. The tail-to- tail arrangement matches the H–H subgroup of the 1:1 group for chloroform and bromoform; on the other hand, it is H,H,H–H,H,H of the 3:3 group in the case of methyl-iodide.

It is important to notice that the representations introduced under points (1) and (2) are distinct and characterize different aspects of correlations between molecular orientations. For a comprehensive description of orientational correlations, it is, therefore, advisable to carry out both kinds of analyses.

The calculations of the above three functions have been performed for each system (HS reference and RMC/NX alike) resulting in various distance-dependent correlation functions.

For all calculations concerning orientational correlations, software developed locally has been used.

III. RESULTS AND DISCUSSIONS

In this section, we concentrate on the analyses of the intermolecular structure of CXY3 molecular liquids (chloroform, bromoform, and methyl-iodide), which are founded on the orientational correlation functions introduced above (see Sec.II B).

A. Orientational correlation functions

Using the original analysis of Rey,⁴with six groups, one finds that, below 4.5 Å, the 2:3 (edge-to-face) orientations dominate while above this distance the 2:2 (edge-to-edge) orientations do. This is true in all six studied systems (HS and RMC/NX systems for CHCl₃, CHBr₃and CH₃I). For some of the original functions of Rey, see Figs. 4–7(cf. also Fig. 6 of Ref.14).

FIG. 2. General arrangement of two CXY3molecules, showing the characteristic axes and angles. (a) chloroform and (b) methyl-iodide. Green balls, Cl atoms; gray balls, C atoms; light gray balls, H atoms; violet balls, I atoms.

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044521-4 Pothoczki, Temleitner, and Pusztai J. Chem. Phys.134, 044521 (2011)

FIG. 3. Some of the special arrangements of molecular axes pairs for CXY3

liquids. (a) “chainlike,” “head-to-head” arrangement for CHCl3; (b) “chainlike,” “head-to-head” arrangement for CH3I; (c) “T-shaped,” “T1-shaped”

arrangement for CHCl3; and (d) “T-shaped,” “T1-shaped” arrangement for CH3I.

Concerning the 2:2 (edge-to-edge) original group, all of its three subgroups are shown by Fig.4for the liquids studied. One of the best visible differences between the three liquids (CHCl₃, CHBr₃, and CH₃I) and between the two systems (HS and NX/RMC), too, can be spotted below 4.2 Å.

A considerable peak appears in the HS system of chloroform, which can also be found in the HS system of bromoform, but there the peak position is shifted by about 0.5 Å toward shorter center–center distances. This peak becomes a shoulder in the RMC/NX system for CHCl3, while its intensity increases in the RMC/NX system for CHBr3. Largely the H, Cl–H,Cl (in CHCl3), and accordingly, the H,Br–H,Br (in CHBr3) subgroups are responsible for these deviations. Inter- estingly, this peak is totally missing in the HS and NX/RMC systems of methyl-iodide. Furthermore, in the case of liquid chloroform and bromoform, the maximum in the HS systems around 5.3 Å splits to form a double peak in the RMC/NX systems. It is conspicuous that the first part of this double peak arises from the H,Cl–Cl,Cl (CHCl₃) and H,Br–Br,Br (CHBr₃)

TABLE III. Definition of the special molecular axes (“dipole—dipole”) arrangements considered in the present work. Wherever possible, the equiv- alent subgroups (see TableII) are also shown. (Note that during the actual calculation, a tolerance of±0.2 in terms of the cosine values was allowed for classifying mutual orientations of molecules into one of the special categories.)

Cosines of angles Arrangement cosα cosβ cosγ

Parallel 0 0 1

Antiparallel 0 0 −1

Chainlike, head-to-head 1 1 −1

Chainlike, head-to-tail 1 −1 1

Chainlike, tail-to-tail −1 −1 −1

T-shaped/1 (T1) 0 −1 0

T-shaped/2 (T2) 1 0 0

Cross-shaped 0 0 0

2 4 6 8 10 12

0.0 0.1 0.2 0.3 0.4 0.5

2 4 6 8 10 12

0.0 0.1 0.2 0.3 0.4 0.5

X,Y-X,Y X,Y-Y,Y

Y,Y-Y,Y edge-to-edge (2:2)

2 4 6 8 10 12

0.0 0.1 0.2 0.3 0.4 0.5

r

_C-C

(Å)

b) CHCl₃ RMC/NX

Percentages/100Percentages/100

e) CH₃I HS

d) CHBr₃ RMC/NX a) CHCl₃ HS

Percentages/100

r

_C-C

(Å)

2 4 6 8 10 12

0.0 0.1 0.2 0.3 0.4

0.5 c) CHBr₃ HS

2 4 6 8 10 12

0.0 0.1 0.2 0.3 0.4

0.5 f) CH₃I RMC/NX

2 4 6 8 10 12

0.0 0.1 0.2 0.3 0.4 0.5

FIG. 4. The 2:2 “original” group with its subgroups for CXY3 liquids.

(a) CHCl3, HS (reference) system; (b) CHCl3, RMC/NX system; (c) CHBr3, HS system; (d) CHBr3, RMC/NX system; (e) CH3I, HS system; and (f) CH3I, RMC/NX system. Black line: “original” 2:2 group; green line with open circles: Y,Y–Y,Y; red line with crosses: X,Y–Y,Y; blue line with solid circles:

X,Y–X,Y [X: H (CHCl3), H (CHBr3), I (CH3I); Y: Cl (CHCl3), Br (CHBr3), H (CH3I)].

2 4 6 8 10 12 0.0

0.1 0.2 0.3 0.4 0.5 0.6

2:3 (edge-to-face) Cl,Cl −−−− Cl,Cl,Cl H,Cl −−−− Cl,Cl,Cl Cl,Cl −−−− H,Cl,Cl H,Cl −−−− H,Cl,Cl

(a) CHCl₃ RMC/NX

r

_C-C

(Å) r

_C-C

(Å)

Percentages/100

2 4 6 8 10 12 0.0

0.1 0.2 0.3 0.4 0.5 0.6

(b) CH₃I RMC/NX

2:3 (edge-to-face) H,H −−−− H,H,H I,H −−−− H,H,H H,H −−−− I,H,H I,H −−−− I,H,H

FIG. 5. The 2:3 “original” group with its subgroups for CXY3 liquids.

(a) CHCl3, RMC/NX system and (b) CH3I, RMC/NX system. Black line:

“original” 2:3 group; blue line with stars: Y,Y–Y,Y,Y; orange line with solid diamonds: X,Y–Y,Y,Y; green line with open circles: Y,Y–X,Y,Y; red line with solid circles: X,Y–X,Y,Y [X: H (CHCl3), I (CH3I); Y: Cl (CHCl3), H (CH3I)].

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3 4 5 6 7 8 0.0

0.2 0.4 0.6 0.8

b) CHCl₃ RMC/NX a) CHCl₃ HS

r

_C-C

(Å) r

_C-C

(Å)

Percentages/100Percentages/100Percentages/100 3:3 (face-to-face)

Y,Y,Y −−−− Y,Y,Y X,Y,Y −−−− Y,Y,Y X,Y,Y −−−− X,Y,Y

3 4 5 6 7 8

0.0 0.2 0.4 0.6 0.8

3 4 5 6 7 8

0.0 0.2

0.4 c) CHBr₃ HS

3 4 5 6 7 8

0.0 0.2

0.4 d) CHBr₃ RMC/NX

3 4 5 6 7 8

0.0 0.2

0.4 e) CH₃I HS

3 4 5 6 7 8

0.0 0.2

0.4 f) CH₃I RMC/NX

FIG. 6. The 3:3 “original” group with its subgroups for CXY3liquids. (a) CHCl3, HS (reference) system; (b) CHCl3, RMC/NX system; (c) CHBr3, HS system; (d) CHBr3, RMC/NX system; (e) CH3I, HS system; and (f) CH3I, RMC/NX system. Black line: “original” 3:3 group; blue line with solid squares: Y,Y,Y–Y,Y,Y; green line with open diamonds: X,Y,Y–Y,Y,Y;

red line with stars: X,Y,Y–X,Y,Y [X: H (CHCl3), H (CHBr3), I (CH3I); Y: Cl (CHCl3), Br (CHBr3), H (CH3I)].

subgroups. The second peak (at larger distances) is composed of the Cl,Cl–Cl,Cl subgroup in CHCl3, and analogously, of the Br,Br–Br,Br subgroups in CHBr3.

A similar double peak can also be observed for methyl- iodide but it is not as characteristic as in the case of the other two liquids; also note that the two systems (HS and RMC/NX) are extremely similar to each other. Both subpeaks of the double peak are due to I,H–H,H arrangements. It is worthwhile noticing that the most populous subgroup is H,H–I,H whose occurrence is twice as large as of the other two subgroups—

as it is also dictated by the larger probability of finding such pairs by randomly selecting participating atoms (X,Y–Y,Y and Y,Y–X,Y pairs are indistinguishable and, therefore, they belong to the same category). Additionally, the occurrence of H,H–H,H contacts exceeds 22% around 3.8 Å in RMC/NX system; note that this subgroup shows the largest differences between the HS reference and the RMC/NX “real liquid”

systems.

Discussing the subgroups of 2:3 (edge-to-face) orientations, we focus, in Fig. 5, on two representative systems, the RMC/NX ones of CHCl₃ and CH₃I which display the most obvious differences. The 2:3 oriented molecular pairs outnumber the 2:2 oriented ones over a very limited distance range, within the first coordination shell of molecular centers. The first, large, peak totally arises from the

H,Cl–H,Cl,Cl subgroup in CHCl3. In the case of methyl- iodide, the H,H–I,H,H and H,H–H,H,H groups share the lead- ing role with occurrences of about 29% and 21%, respectively.

That is, at short distances in methyl-iodide, the less bulky (hy- drogenous) parts favor each other, whereas in the other two liquids the situation is more balanced. The other difference is the shoulder at 5 Å for CHCl₃, which is lacking in RMC/NX system of CH₃I; mainly the Cl,Cl–H,Cl,Cl, arrangement is responsible for this feature.

Subgroups of the 3:3 (face-to-face) orientations, shown in Fig. 6, carry information about mutual orientations of the nearest molecules. It is apparent that the most frequent arrangement of two neighboring (nearly touching) chloroform molecules is Cl,Cl,Cl–Cl,Cl,Cl, whose occurrence towers above 50% in the RMC/NX model, while it is almost undetectable in the HS system. This is an obvious point where the influence of diffraction data can be captured; note that clearly, the bulkier faces of the molecules turn toward each other at these very short distances. This result confirms the conjecture of Bertagnolli et al.¹¹ who suggested that such a

“configuration. . . is possible.” Our result, on the other hand, strongly disagrees with the finding of Dietzet al.,¹²who emphasized the importance of hydrogen atoms approaching each other.

Intensities of the other two subgroups (H,Cl,Cl–Cl,Cl,Cl and H,Cl,Cl–H,Cl,Cl) are nearly same in the two (HS and RMC/NX) model systems. This finding, on the other hand, somewhat weakens the conclusion of the same authors¹¹who stated that a H,Cl,Cl–H,Cl,Cl type “configuration . . . is very likely because it is energetically preferred;” as it is clear from Fig.6, this arrangement is far not the most preferred.

Nearly one third of the molecular pairs (i.e., less than in liquid chloroform) at the shortest center–center distances fall into the 3:3 orientation category in liquid CHBr3 and CH3I.

The I,H,H–H,H,H subgroup is the most frequent for CH3I, while the H,Br,Br–H,Br,Br, is dominant for CHBr₃. It is in- teresting to note that concerning the 3:3 orientations, it is bromoform that looks the most characteristic: a large second maximum follows the first peak at around 4 Å, which cannot

2 4 6 8 10 12 0.00

0.05 0.10 0.15 0.20 0.25

(a) CHBr₃ HS (b) CHBr₃ RMC/NX

r

_C-C

(Å) r

_C-C

(Å)

Percentages/100

1:3 (corner-to-face) Br −−−− Br,Br,Br H −−−− Br,Br,Br Br −−−− H,Br,Br H −−−− H,Br,Br

2 4 6 8 10 12 0.00

0.05 0.10 0.15 0.20 0.25

FIG. 7. The 1:3 “original” group with its subgroups for liquid CHBr3. (a) HS reference system and (b) RMC/NX system. Black line: “original” 1:3 group;

orange line: Br–Br,Br,Br; green line: H–Br,Br,Br; blue line: Br–H,Br,Br; red line: H–H,Br,Br.

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2 4 6 8 10

0.00 0.05 0.10 0.15

MAOCF (arb. units)

tail-to-tail head-to-head head-to-tail

(e) CH₃I HS (c) CHBr₃ HS (a) CHCl₃ HS

MAOCF (arb. units)

2 4 6 8 10

0.00 0.05 0.10 0.15

2 4 6 8 10

0.00 0.05 0.10 0.15

r_C-C(Å) r_C-C(Å)

MAOCF (arb. units)

(d) CHBr₃ RMC/NX (b) CHCl₃ RMC/NX

2 4 6 8 10

0.00 0.05 0.10 0.15 0.20 0.25 0.30

2 4 6 8 10

0.00 0.05 0.10 0.15 0.20 0.25 0.30

2 4 6 8 10

0.00 0.05 0.10 0.15 0.20 0.25

0.30 (f) CH₃I RMC/NX

FIG. 8. Molecular axes orientational correlation functions (MAOCF) for CXY3liquids: “chainlike”distinguished arrangements. (a) CHCl3, HS (reference) system; (b) CHCl3, RMC/NX system; (c) CHBr3, HS system; (d) CHBr3, RMC/NX system; (e) CH3I, HS system; and (f) CH3I, RMC/NX system. Black line with solid circles: “head-to-head” arrangement, red line with open circles: “head-to-tail”arrangement; blue line with crosses:

“tail-to-tail”arrangement.

be found in the other systems. As it is clear from Fig.6, this second peak is already present in the hard sphere reference system; that is, its appearance is due to pure steric effects.

On the other hand, the large first maximum, which appears in each of the liquids investigated, is due to the introduction of diffraction data.

The occurrences of 1:1 (corner-to-corner) and 1:3 (corner-to-face) orientations fall short of 10% (see Ref.14).

Again, bromoform possesses a noteworthy feature: two well recognizable peaks of the 1:3 original group can be observed in the HS system (Fig. 7) at about 3.7 Å and at about 6 Å;

the intensity of both peaks visibly increases in the RMC/NX system. The rising intensity of the first peak is due to the H–H,Br,Br subgroup, while the second peak arises from Br–H,Br,Br arrangements. That is, the first maximum rep- resents a noticeable proportion, of about 22%, of “Apollo- like” arrangements (see Ref.1), which is one of the highest in tetrahedral liquids considered so far (cf. Ref.19, where a similar ratio was found for a particular distance range in liquid SnI₄). Interestingly, the “Apollo”-idea, i.e., the dominance of 1:3 (corner-to-face) mutual molecular arrangements, which had accompanied research on liquids containing perfect

tetrahedral molecules, has not even been mentioned for CXY3

(or, for that matter, CX2Y2) molecular liquids—although, as it has just been exemplified here, it might not be an entirely irrelevant concept.

B. Dipole–dipole (molecular axes) correlations

Molecular axes (“dipolar”) correlations functions are shown in Figs.8and9. Out of the eight arrangements monitored, occurrences of the three “chainlike” (Fig. 8) and the two “T-shaped” arrangements (Fig. 9) are emphasized.

Differences between HS reference and RMC/NX models are noticeable especially at shorter center–center distances in terms of this type of correlation functions. The numbers of classifiable molecular pairs decrease nearly down to the limit of detection beyond about 6 Å.

Concerning “chainlike” arrangements (Fig. 8),head-to- tailorientations are clearly the most frequent in the two haloform liquids around the first maximum of the C–C prdf. In methyl-iodide, they are also the most abundant around 6 Å, where distance is just little higher than the maximum position of the C–C prdf in methyl-iodide;²⁷note that this orientation is only a little more probable in liquid CH3I than others. These findings are qualitatively valid for the HS reference systems,

2 4 6 8 10

0.00 0.01 0.02 0.03 0.04 0.05 0.06

(a) CHCl₃ HS

MAOCF (arb. units)

r

_C-C

(Å)

MAOCF (arb. units)

2 4 6 8 10

0.00 0.01 0.02 0.03 0.04 0.05 0.06

2 4 6 8 10

0.00 0.05 0.10 0.15

(f) CH₃I RMC/NX (e) CH₃I HS

(b) CHCl₃ RMC/NX

r

_C-C

(Å)

2 4 6 8 10

0.00 0.05 0.10 0.15

2 4 6 8 10

0.00 0.01 0.02 0.03 0.04 0.05

0.06 (c) CHBr₃ HS (d) CHBr₃ RMC/NX

MAOCF (arb. units)

2 4 6 8 10

0.00 0.01 0.02 0.03 0.04 0.05 0.06

FIG. 9. Molecular axes orientational correlation functions for CXY3liquids:

“T-shaped”distinguished arrangements. (a) CHCl3, HS (reference) system;

(b) CHCl3, RMC/NX system; (c) CHBr3, HS system; (d) CHBr3, RMC/NX system; (e) CH3I, HS system; and (f) CH3I, RMC/NX system. Black line:

“T1T-shaped” arrangement; red line: “T2T-shaped”arrangement.

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4 2 6 8 0,5 10

(a) -0,5 0,0

0,00 0,05 0,10 0,15 0,20

P(cosθ,rC-C)

rC-C(Å) cosΘ

4 2 6 8 0,5 10

(b) -0,5 0,0

0,00 0,05 0,10 0,15 0,20

rC-C(Å) cosΘ

P(cosθ,rC-C)

FIG. 10. Distance-dependent dipole–dipole correlation functions for chloroform (no special arrangements are distinguished in this representation). (a) HS reference system and (b) RMC/NX system.

too, indicating that steric effects alone can account for these arrangements to form.

Upon introduction of diffraction data, another orientation becomes important at the touching distances (below 4 Å) in each liquid: it ishead-to-headin liquid chloroform and tail-to-tail in liquid bromoform and methyl-iodide. This result corresponds well with the analyses of orientational correlations in terms of subgroups: inspecting Figs.6(a)and6(b) again, the effect can be connected to the increment of the occurrence of the Cl,Cl,Cl–Cl,Cl,Cl subgroup in liquid chloroform (cf. Sec.II B, too). The change is most emphatic in the case of chloroform and the least noticeable in methyl-iodide where the HS reference system shows qualitatively similar result. The considerable ordering when diffraction data are introduced suggests noticeable dipole correlations between the nearest molecules; concerning the actual number of molecules that contribute it is the head-to-tailarrangement that is the most significant.

In terms of T-shaped arrangements (Fig.9), differences between six systems (HS and RMC/NX systems for CHCl3, CHBr3 and for CH3I) are hardly observable. The one excep- tion is methyl-iodide where the occurrence of T1 pairs in- creases significantly, as compared to the HS reference system and matches the occurrences of the head-to-tail pairs.

Otherwise the number of T-shaped pairs does not come near the number of recognised chainlike arrangements.

There is another popular representation of dipole–dipole correlations, which gives the cosines of angles confined by molecular axes (that is the cosines of angle γ, as shown in Fig.2) as a function of the center–center distances. Results for the HS and the RMC/NX systems of chloroform are provided by Fig. 10. The most important observation in both systems is the significant peak at the shortest C–C distances (below 4 Å) at about cos= −1, whose intensity nearly doubles as a result of introducing diffraction data. This feature agrees with both the characteristics of the subgroups of orientational correlation functions (Fig.6) and the characteristics of molecular axes correlations (Fig. 8). It is revealed that the head-to-head(in accordance with the Cl,Cl,Cl–Cl,Cl,Cl) subgroups is a preferred arrangement in liquid chloroform in this distance range.

IV. SUMMARY AND CONCLUSIONS

In this study, we have focused on a detailed charac- terization of orientational correlations between tetrahedral molecules C3vsymmetry (general formula: ABC3; in this paper: CXY3). The original categorization of Rey⁴has been extended by introducing 21 subgroups, characteristic to this kind of molecules. These investigations have been complemented by determining dipole–dipole (molecular axes) correlations.

As a result, the most detailed picture (up to now) of the intermolecular orientations could be provided. The calculations were applied to particle configurations deriving from RMC computer modeling of diffraction data^14,27on CXY₃molecular liquids: chloroform, bromoform, and methyl-iodide.

The most frequent orientation of CXY3molecules, which are separated by more than 4 Å (i.e., around and beyond the first maximum of the C–C prdf) is of the 2:2 (edge-to- edge) type. Within this 2:2 original group the H,Cl–Cl,Cl subgroup in CHCl3, the H,Br–Br,Br subgroup in CHBr3 and the I,H–H,H subgroup for CH3I are the most important.

Concerning shorter range correlations (at and just below 4 Å), two neighboring molecules turn toward each other most frequently according to the 2:3 (edge-to-face) original group;

the dominance of H,Cl–H,Cl,Cl arrangements in chloroform and H,H–I,H,H and H,H–H,H,H arrangements in methyl- iodide are the most noteworthy. In bromoform, the occurrence of 1:3 (corner-to-face or “Apollo”) orientations appear to be significant in a narrow distance range, just below 4 Å.

At the touching distances, at and below about 3.8 Å, the few molecules that are found in this range prefer the 3:3 (face-to-face) arrangements. Interestingly, in liquid chloroform the all-chlorine (Cl,Cl,Cl–Cl,Cl,Cl) arrangements are the most frequent while in the other two liquids, mostly mixed faces (in terms of atom type), such as H,Br,Br–H,Br,Br and I,H,H–H,H,H, turn toward each other.

The strongest dipole–dipole correlations also appear at the shortest distances, around and below 4 Å, upon the introduction of diffraction data. Among the special molecular axes orientations monitored here, the “chainlike” arrangements are more significant. It is worth emphasizing that the head-to-headarrangement in chloroform while thetail-to-tail arrangement in the other two liquids (bromoform, methyl- iodide) are the most populous.

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Finally, we note that although the three liquids studied here do belong to the same symmetry group, C3v, it is not easy to find apparent common features of them; as we have seen, this is mostly because of their different sizes and shapes but also, due to the different interactions between molecules.

Methyl-iodide, in terms of most characteristics, resembles the most to corresponding the hard sphere reference system, whereas the most probable liquid structure of chloroform is the furthest away from the HS reference structure. The liquid structure of bromoform also has some distinct features, for in- stance, the appearance of “Apollo”-pairs. It is, therefore, obvious that, unlike for CH2X2liquids,¹⁵the liquid structure of every single molecular liquid containing ABC3molecules has to be considered individually. The present work, we believe, has introduced and established the appropriate tools for such investigations.

ACKNOWLEDGMENTS

L.T. is grateful to the Japanese Society for the Promotion of Science for a JSPS post-doctoral fellowship.

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