S1

Electronic Supplementary Information:

Cluster-model DFT simulations of the infrared spectra of triazine-based

molecular crystals

Xiaohong Yuan,a Kun Luo,

ab Nan Liu,

a Xueqiang Ji,

a Chao Liu,

a Julong He,

a Guangjun Tian,

b

Yuanchun Zhao*a and Dongli Yu*

a

aState Key Laboratory of Metastable Materials Science and Technology, Yanshan University,

Qinhuangdao 066004, China.

bHebei Key Laboratory of Microstructural Material Physics, School of Science, Yanshan University,

Qinhuangdao 066004, China

*E-mail: yzhao56@ysu.edu.cn (Y.C.Z.); ydl@ysu.edu.cn (D.L.Y.)

Electronic Supplementary Material (ESI) for Physical Chemistry Chemical Physics.This journal is © the Owner Societies 2018

S2

Fig. S1 Crystal structures of (a) melam reported by Lotsch and Schnick in ref. S1 (lattice parameters:

C2/c, a = 18.11 Å, b = 10.87 Å, c = 13.98 Å, and β = 96.31°) and (b) melem reported by Jürgens et al.

in ref. S2 (lattice parameters: P21/c, a = 7.40 Å, b = 8.65 Å, c = 13.38 Å, and β = 99.91°). The C, N, and

H atoms are distinguished with dark grey, blue, and light grey colors, respectively.

Note: The crystal structure and X-ray diffraction pattern of melamine can be found in our previous

work.S3

a

cb

a

cb

(a)

(b)

S3

10 20 30 40 50

Inte

nsity (

a.u

.)

2 (degree)

Melem(b)

Experimental

Theoretical

10 20 30 40 50

Experimental

Inte

nsity (

a.u

.)

2 (degree)

Theoretical

Melam(a)

Fig. S2 Experimental and theoretically generated XRD patterns of (a) melam, and (b) melem.

S4

Fig. S3 Comparison between molecular geometries before and after geometry optimization of (a) the

32-molecule cluster, and (b) the 13-molecule cluster of melamine. The bule(N)-grey(C)-white(H)

colored structures represent the models directly extracted from the crystal structure of melamine, and

the green(N)-grey(C)-white(H) colored structures are those optimized by Gaussian 16 software

package for further IR calculations.

(a)

(b)

S5

Fig. S4 Comparison between molecular geometries before and after geometry optimization of (a) a

single molecule, and (b) the built 16-molecule cluster of melem. The bule(N)-grey(C)-white(H) colored

structures represent the models directly extracted from the crystal structure of melem, and the

green(N)-grey(C)-white(H) colored structures are those optimized by Gaussian 16 software package

for further IR calculations.

(a) 119.6°

127.9°

121.7°121.7°119.3°120.5°

134.8°

121.7°

(b)

S6

Fig. S5 Comparison between molecular geometries before and after geometry optimization of (a) a

single molecule and (b) the 2-molecule cluster, (c) the 17-molecule cluster A, (d) the 16-molecule

cluster B, and (e) the finally built 25-molecule cluster of melam. The bule(N)-grey(C)-white(H) colored

structures represent the models directly extracted from the crystal structure of melam, and the

green(N)-grey(C)-white(H) colored structures are those optimized by Gaussian 16 software package

for further IR calculations.

2.09Å

2.38Å 1.97Å

1.91Å

1.97Å

A B

121.0°

128.9°

118.7°

133.3°

119.9°119.9°116.6°119.5°

120.3°120.4°

(e)

(c)

(b)

(a)

17-molecule cluster A

(d)

16-molecule cluster B

S7

Table S1 Details of the molecules and cluster models designed for IR calculations in this work, which

were directly extracted from the corresponding crystal structures and the geometry optimizations were

performed by the Gaussian 16 software package.

models total atom

numbers

Representative

molecules

numbers of the

surrounding

molecules hydrogen-

bonded with the

representative ones

numbers of the

formed hydrogen

bonds with the

representative

molecules

computational

costsa

melamine 32-molecule cluster 480 4 12 30 31 h

13-molecule cluster 195 1 4 8 4.5 h

melem single molecule 22 1 0 0 0.5 h

16-molecule cluster 352 1 5 8 12.2 h

melam

single molecule 26 1 0 0 0.6 h

2-molecule cluster 52 2 0

from 2 to 3 (before

and after geometry

optimization)

3 h

17-molecule cluster A 442 1 6 10 24 h

16-molecule cluster B 416 1 6 11 19 h

25-molecule cluster 650 2 10 19 65.5 h

aComputer server: Super Sever X10QBL-4, 4 x 2.10 GHz Xeon® Procssor E7-8870 v3/18 Core, 16 x 16 GB ECC DDR3/2133 MHz; the

single-molecule models (melem and melam) and the 2-molecule model of melam were calculated using 20 cores with a memory of 45 GB;

the rest of 6 cluster models were calculated using 60 cores with a memory of 230 GB.

Note: As summarized in Table S1, totally 9 models have been designed for the IR simulations in this

work. By considering the crystallographic equivalence of the corresponding crystal structures, only one

representative molecule has been determined for melamine and melem, respectively; while for melam

two crystallographically independent molecules need to be considered. We have further built specific

cluster models based on the two different molecules of melam A and B (Fig. S5), which present

different molecule numbers as well as distinct hydrogen-bonding environments. For the 2-molecule

cluster of melam, two hydrogen bonds are formed between the considered molecules, whereas after

geometry optimization an additional hydrogen bond is formed with the bridging N−H bond of melam B

(Fig. S5b). The computational costs of all the listed models have also been combined into Table S1 as a

reference.

S8

2600 2800 3000 3200 3400 3600

Experimental

13-molecule cluster

3442

3406

3301

3228

3141

3468

3420

3331

3188

Tra

nsm

itta

nce

(a

.u.)

Wavenumber (cm-1)

3129

H1

H4

H3

H2

H5

H6

Fig. S6 Zoomed FTIR spectra of melamine showing the characteristic NH2 stretching region. The inset

shows the representative molecule and the formed hydrogen bonds, N−H4 and N−H6 are free from

hydrogen bonding and thus show remarkably small intensities at 3406 and 3442 cm-1

in the simulated

spectra.

Table S2 Comparison between the experimental IR absorption peaks and those in the stimulated 13-

molecule-cluster spectrum of melamine related to the characteristic NH2 stretching modes. The

dominant components of each vibration mode have been highlighted, respectively.

wavenumber (cm-1) assignmentsa detailed vibrational componentsb

experimental calculated

3129 3141 νs NH1(m)+NH2(s)+NH3(w)+NH4(w)+NH5(s)+NH6(m)

3188 3228 νs NH1(w)+NH2(w)+NH3(s)+NH4(m)+NH5(w)+NH6(w)

3331 3301 νas NH1(s)+NH2(s)

3420 3406 νas NH3(m)+NH4(s)

3468 3442 νas NH5(m)+NH6(s)

aνs: symmetrical stretching vibration, νas: asymmetrical stretching vibration. bs: strong, m: medium, w: weak.

S9

3141 cm-1 3228 cm-1 3301 cm-1

3406 cm-1 3442 cm-1

H1

H4

H3

H2

H5

H6

Fig. S7 Calculated eigenvectors of the characteristic NH2 stretching modes of melamine at 3141, 3228,

3301, 3406 and 3442 cm-1

. The latter two modes are dominated by the stretching vibrations of N−H4

and N−H6 bonds, which are free from hydrogen bonding. The C, N and H atoms are distinguished by

dark grey, blue, and light grey colors, respectively.

S10

500 1000 1500 2000 2500 3000 3500 4000

Tra

nsm

itta

nce

(a

.u.)

Wavenumber (cm-1)

3325

3424

3487

3119

1612

14701

306

1097

804

16-molecule cluster

Single melem molecule

1640

1612

1555

1518

3426

3462

1167

599

694

771

1060

1480 3

128

3251 3

287493

3534

3401

1646

1581

1522

14501

266

804

1042

Experimental

Fig. S8 Detailed IR peak positions in the experimental and simulated spectra of melem based on

different models.

S11

Table S3 Comparison between the experimental IR absorption peaks and the calculated wavenumbers

of melem based on a single molecule and the built 16-molecule cluster and the corresponding

combinatorial vibration-mode assignments.

calculated experimental

wavenumbers (cm-1) combinatorial vibration-mode

assignmentsa

wavenumbers (cm-1) assignmentsS2 single melem

molecule 16-melem cluster

493,599,694 γ(NH) 478,597,740b

804 771 γ(CN) + γ(NH)

804 the ring-sextant out-of-plane

bending

1042 1060,1090 ρ(NH2) + ν(CN) 1097 NH stretching

1266 1167 ρ(NH2) + ν(CN1)c

1306 CNC bending

1450 1465,1480 ρ(NH2) + δ(NH2) + ν(CN) 1470 side-chain CN breathing

1521 1518 δ(NH2) + ν(CN)OR + ν(CN4,5)

1580 1555 Ring breathing + δ(NH2)

1645 1595,1612,1640 ν(CN2-7) + δ(NH2)

1612 NH2 bending

3401 3128 νs (N8H2) 3119

NH stretching 3251 νas (N8H2) + νs (N9H2) 3325

3534 3287,3426,3462 νas (NH2) 3424,3487

aνs: symmetrical stretching vibration, νas: asymmetrical stretching vibration, ν: stretching vibration, β: in-plane bending vibration, δ:

shearing vibration, ρ: in-plane rocking vibration, γ: out-of-plane bending vibration, R: mode on the ring atoms, OR: mode out of the ring. bThese three peaks are observed in the experimental spectrum in ref. S2 but absent from the spectrum in this study. cN atoms are numbered

in the top panel of Fig. S9.

S12

493 cm-1

599 cm-1

1518 cm-1 1555 cm-1 1612 cm-1

694 cm-1

771 cm-1

1060 cm-1 1090 cm-1

1480 cm-11167 cm-1 1465 cm-1

3128 cm-1 3251 cm-11640 cm-1 3426 cm-1 3462 cm-13287 cm-1

N7

N1

N2

N3

N4N5

N6

N8

N10 N9

Fig. S9 Calculated eigenvectors of the characteristic vibrational modes of melem based on the built 16-

molecule cluster. The C, N and H atoms are distinguished by dark grey, blue, and light grey colors,

respectively.

S13

500 1000 1500 2000 2500 3000 3500 4000

1687

1688

1639

1006

673

566

516

576

Tra

nsm

itta

nce

(a

.u.)

Wavenumber (cm-1)

Single molecule

2-molecule cluster

16-molecule cluster B

17-molecule cluster A

25-molecule cluster

Experimental

3493

15551

429

1491

1339

1252

1452

1516

1614

3074

3180

3321

34161103

3458

808

1589

1245

14181362

1538 1

502

3463

3394

31752955 3522

1330

915

808

1540

984

1241

1327

1498

1593 3

395

3521

1413

674

808

1454

792

1024

1260

1352

1415

1512

1582 1646

3214 3

286

3390

3474

727

3269

3479

3348

32933170

1349

15671

505

1418 1629

1680

1017

1254

787

680

562

692

789

1024

1253

1353

1511

1566 1630

1417

3259

3210

3136

3347

3474

Fig. S10 Detailed IR peak positions in the experimental and simulated spectra of melam based on

different models.

Note: The absorption bands in range of 1200−1700 cm-1

correspond to the vibrational modes of

C−N/C=N stretching and NH/NH2 shearing. As shown in Fig. S10, the peaks at 1253, 1353, 1417, and

1566 cm-1

observed in the 25-molecule-cluster spectrum are dominated by the intramolecular C−N/C=N

stretching (Table S5 and Fig. S11), and the corresponding peaks can be identified in other simulated

spectra, even the one based on a single molecule. However, the vibrational peaks at 1454, 1511, 1630,

and 1687 cm-1

in the 25-molecule-cluster spectrum are mainly related to the NH/NH2 shearing and NH

in-plane rocking, significant differences have been observed in other simulated spectra including those

based on the 17-molecule cluster with melam A and 16-molecule cluster with melam B, indicating these

vibrational modes are more sensitive to the surrounding crystallographic environments.

S14

Table S4 Comparison of the experimental IR absorption peaks and the calculated wavenumbers of

melam based on different models.

experimental absorption

peak

(cm-1)

calculated wavenumbers (cm-1)

25-molecule

cluster

17-molecule cluster

A

16-molecule cluster

B

2-molecule

cluster

single

molecule

562,692 566, 680 516, 576, 727,751 673 674

808 789 787 792 808 808

1103 1024,1060 1017 1024 915,1006 984

1252 1253 1254 1260 1245 1241

1339 1353 1349 1352 1330, 1362 1327

1429 1417 1418 1415 1418 1413

1452 1454 1456 1454 1442 1439

1491,1516 1511 1505 1512 1502,1538 1498,1540

1555 1566 1567 1582 1589 1593

1614 1608 1598 1601 1617

1639 1630 1629 1646 1649

1688 1687 1680

2955

3074 3136,3159 3170 3214 3175

3395

3180 3210

3321

3259 3269

3294 3293 3286

3347 3348

3416 3396,3427 3390,3426 3394,3463 3521

3458 3453,3474 3479 3454,3474 3493,3522

S15

Table S5 Comparison between the experimental IR absorption peaks and calculated wavenumbers of

melam based on the finally built 25-molecule cluster and the corresponding combinatorial vibration-

mode assignments.

calculated (25-molecule cluster) experimental

wavenumbers (cm-1) combinatorial vibration-mode assignmentsa wavenumbers (cm-1) assignmentS1,S4

562,692 γ(NH)

789 γ(CN) + γ(NH)

808 the characteristic sextant ring

bending

1024 (molecule B) ρ(N2H)b

1060 (molecule A)

1253 ρ(NH) + ν(CN)R 1252

C−N/C=N stretching and NH/NH2

shearing

1353 ρ(NH) + ν(CN)OR 1339

1417 δ(NH) + ν(CN)OR 1429

1454 δ(NH) + ν(CN)OR + β(CN2C) 1452

1511 δ(NH) + β(CNH) 1491,1516

1566 δ(N1H) + ρ(N3H) + ν(CN)R 1555

1608 ρ(NH)

1614

1630,1687

3136,3159,3210 νs(NH2) 3074,3180

characteristic N−H stretching

3249,3259 νas(NH2) + ν(N2H) 3321

3294 νs(NH2)

3347 ν(N2H) 3416

3396,3427 νas(NH2)

3458

3453,3474 3562 aνs: symmetrical stretching vibration, νas: asymmetrical stretching vibration, ν: stretching vibration, β: in-plane bending vibration, δ:

shearing vibration, ρ: in-plane rocking vibration, γ: out-of-plane bending vibration, R: mode on the ring atoms, OR: mode out of the ring. bN atoms are numbered in the top panel of Fig. S11.

(to be continued)

562 cm-1

692 cm-1

789 cm-1

1024 cm-1 1253 cm-1 1353 cm-1

1417 cm-1 1454 cm-1 1511 cm-1

1566 cm-1 1608 cm-1 1630 cm-1

N1 N1

N3N3

A B

N2

S16

(continued)

562 cm-1

692 cm-1

789 cm-1

1024, 1060 cm-1 1253 cm-1 1353 cm-1

1417 cm-1 1454 cm-1 1511 cm-1

1566 cm-1 1608 cm-1 1630 cm-1

N1 N1

N3N3

A B

N2

1687 cm-1 3136 cm-1 3159 cm-1

3294 cm-13210 cm-1 3259 cm-1

3347 cm-1 3396 cm-1 3474 cm-1

Fig. S11 Calculated eigenvectors of the characteristic vibrational modes of melam based on the finally

built 25-molecule cluster. The C, N and H atoms are distinguished by dark grey, blue, and light grey

colors, respectively.

S17

References

S1 B. V. Lotsch and W. Schnick, Chem. Eur. J., 2007, 13, 4956−4968.

S2 B. Jürgens, E. Irran, J. Senker, P. Kroll, H. Müller and W. Schnick, J. Am. Chem. Soc., 2003, 125,

10288−10300.

S3 X. Yuan, K. Luo, K. Zhang, J. He, Y. Zhao and D. Yu, J. Phys. Chem. A, 2016, 120, 7427−7433.

S4 E. Wirnhier, M. B. Mesch, J. Senker and W. Schnick, Chem. Eur. J., 2013, 19, 2041−2049.