V Boyko, M Hyla, O Shpotyuk - Chain- and ring-like sulphur clusters modeling within hyperchem program - страница 1

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ВІСНИК ЛЬВІВ. УН-ТУ

Серія фіз. 2009. Bun. 43. С. 233-237

VISNYKLVIV UNIV. Ser. Physics. 2009. Is. 43. P. 233-237

PACS number(s): 61.43.Fs, 31.15.A-

CHAIN- AND RING-LIKE SULPHUR CLUSTERS: MODELING WITHIN HYPERCHEM PROGRAM

V. Boyko1'2, M. Hyla3 ,O. Shpotyuk1

'Lviv Institute of Materials of SRC "Carat" Stryjska Str., 202, 79031 Lviv, UKRAINE e-mail: boykovit@gmail.com 2Lviv Polytechnic National University Bandera Str., 12, 79013 Lviv, UKRAINE 3Institute of Physics of Jan Dlugosz University al. Armii Krajowej, 13/15, 42201 Czestochowa, POLAND

Different types of chain- and ring-like clusters formed of 2-10 sulphur atoms were simulated using HyperChem 7.5 program. It was shown that chains consisting of 5 and more sulphur atoms as well as rings including 6 or 8 sulphur atoms are the most energetically favourable ones within covalent-bonded glassy network.

Key words: sulphur, ab initio calculations.

It well known, there are more then 50 sulphur modifications in dependence on preparation conditions [1, 2]. In general, we can divide these modifications into two large groups - crystalline (rhombohedral or monoclinic) and amorphous, in all these forms sulphur having tendencies to form chain or/and ring-like structural units. If sulphur atoms being interconnected between each others form so called cis-configurations, the ring-like molecules can be formed [2]. It takes place, in particular, provided 8 sulphur atoms are involved. Otherwise, the chain-like configurations of trans-interconnected sulphur atoms are formed. Chain- and ring-like structural units are kept both in crystals and in amorphous sulphur (for example, S8 monoclinic modifications of sulphur [1]). In addition, all these structural units can be found in sulphur-rich chalcogenide glasses depending on their chemical composition, in particular binary As/Ge-S vitreous compounds.

In this work, the possibilities to form ring- and chain-like structural groups of sulphur are analysed using HyperChem 7.5 program. Ab initio calculations with RHF/6-311G* basis set were used to determine the total energies of clusters in dependence on number of sulphur atoms. But, this program can calculate only molecular clusters, such as ring-like sulphur. However, the chain-like clusters are open. We should saturate bonds by hydrogen atoms having very small bond energy [3] to transform them into molecular-like form. After the procedure of geometrical optimization and single point calculations, we receive the total energy of chain-like cluster EE, after that we divide energy of add hydrogen atoms EH and energy of sulphur-hydrogen bond ES-H .

We got formation energy of ring-like and chain-like clusters of sulphur Et: © Boyko V., Hyla M., Shpotyuk O., 2009

Thus, having energy of ring-like and chain-like clusters of sulphur Et, we divide from them energy of all sulphur atoms included in cluster Eat . After that we got formation energy of cluster:

Ej = E, - Eal. (2) We entered average formation energy parameter (AFE) for each our cluster, where N is the total number of atoms in cluster without hydrogen and Ef is formation energy without hydrogen:

AFE-

E1

(3)

Average formation energy of cluster is got by us and set to be the base criterion for determination of possibility of existence of those or other clusters.

Geometrically optimized ring- and chain-like clusters are shown on fig. 1. The bond lengths and angles between atoms are presented in table.

S2

S3

S4

S5

S6

S7

Sn ring

> £ Q &     Ф & &

S2 S3

s4

S5

s6

S7

, Sm chain

Fig. 1. Geometrically optimized ring- and chain-like sulphur clusters

The projection of experimentally determined crystallographic structure of S8 ring is shown on fig. 2 [4, 5]. Our results well correlate with proper information for crystalline analogue (the bond lengths and angles between atoms are practically equal).

Table

The bond lengths and angles between atoms for modelling S8 cluster

Bond lengths, 10-4 nm

2068,7

2069,0

2068,7

2067,9

2068,8

2069,1

2068,6

2068,1

Angles between atoms, grad.

107,50

107,49

107,53

107,51

107,49

107,47

107,53

107,50

Fig. 2. Schematic image bond lengths and angles between atoms for crystalline S8 [5, 6]

-54 • -56 • -58 • -60 • -62 • -64 -66 -68 -70 • -72 • -74

Chain

—•— Ring

-1-1-1-

6

Number of S atoms

10

Fig. 3. Average formation energy in dependence from number of sulphur atoms

The AFE in dependence on number of sulphur atoms for ring- and chain-like clusters is shown on fig. 3. The performed calculations showed that S8- and S6-ring are the most energy favourable for Sn-ring clusters. In case of Sm-chain-like clusters, this

situation is apparently different. The chains involving 5 or more sulphur atoms have the minimal AFE.

The authors acknowledge support from Science and Technology Center in Ukraine under regular STCU Project N 3745.

1. Meyer B. Elemental sulphur // Chem. Rev. 1976. Vol. 79. N 3 P. 267-388.

2. Feltz A. Amorphous inorganic materials and glasses // Weinheim; Basel; Cambridge; New York, NY; VCH, 1993.

3. Phillips J.C Ideally glassy hydrogen-bonded networks // Phys. Rev. B. 2006. Vol.73. P. 024210-1-8.

4. Templeton L.K, Templeton D.H, Zalkin A. Crystal structure of monoclinic sulphur Inorganic Chemistry. 1976. Vol. 15. P. 1999-2001.

5. Pawley G.S., Rinaldi R.P. Constrained refinement of orthorhombic sulphur // Acta Crystallogr., 1972. Vol. 28B. 3605 p.

6. Tronc P., Bensoussan M., Brenac A., Sebenne C. Optical-absorbtion edge and Raman scattering in GexSe1-x glasses // Phys. Rev. B. 1973. Vol. 8. N 12. P. 5947­5956.

7. Lucovsky G., Galeener F.L., Keezer R.C. et al. Structural interpretation of the infrared and Raman spectra of glasses in the alloy system in Ge1-xSx // Phys. Rev. B. 1974. Vol. 10. N 12. P. 5134-5146.

ЛАНЦЮГОВО- ТА КІЛЬЦЕПОДІБНІ СІРКОВІ КЛАСТЕРИ: МОДЕЛЮВАННЯ ЗА ДОПОМОГОЮ ПРОГРАМИ HYPERCHEM

В. Бойко1,2, M. Хиля3, O. Шпотюк1

1 Львівський науково-дослідний інститут матеріалів Науково-виробничого підприємство "Карат " вул. Стрийська, 202, 79031 Львів, Україна 2Національний університет "Львівська політехніка "

вул. С. Бандери, 12, 79013 Львів, Україна 3Институт фізики, Університет ім. Яна Длугоша, ал. Армії Крайової, 13/15, 42201 Ченстохова, Республіка Польща

За допомогою програми HyperChem 7.5 проведено квантово-хімічні числення ефективності утворення ланцюгових та кільцеподібних кластерів сірки, що містять 2-10 атомів. Показано, що енергетично вигідними є ланцюги сірки, що мають 5 і більше атомів, а також кільця з 6 та 8 атомів сірки. Ключові слова: сірка, ab initio обрахунки.

ЦЕПЕ- И КОЛЬЦЕОБРАЗНЫЕ СЕРНЫЕ КЛАСТЕРЫ: МОДЕЛИРОВАНИЕ С ПОМОЩЬЮ ПРОГРАММЫ HYPERCHEM

В. Бойко1,2, M. Хиля3, O. Шпотюк1

1 Львовский научно-исследовательский институт материалов Научно-производственное предприятие "Карат " ул. Стрыйская, 202, 79031 Львов, Украина 2Национальный университет "Львовская политехника " ул. С. Бандеры, 12, 79013 Львов, Украина 3Институт физики, Университет им. Яна Длугоша ал. Армии Краевой, 13/15, 42201 Ченстохова, Республика Польша

С помощью программы HyperChem 7.5 проведены квантово-химические расчеты эффективности образования цепеобразных и кольцеобразных кластеров серы, которые содержат 2-10 атомов. Показано, что энергетически выгодными являются цепи серы, которые имеют 5 и больше атомов, а также кольца с 6 и 8 атомов серы.

Ключевые слова: сера, ab initio расчет.

Стаття надійшла до редколегії 04.06.2008 Прийнята до друку 25.03.2009

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V Boyko, M Hyla, O Shpotyuk - Chain- and ring-like sulphur clusters modeling within hyperchem program