Theoretical study on the [Si, C, P, S] potential energy surface

Chemical Physics 348 (2008) 113–121

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Theoretical study on the [Si, C, P, S] potential energy surface Fei Li a,b, Feng-Hua Zhang b, Hui-Ling Liu a, Guang-Tao Yu c, Xu-Ri Huang a,*, Chia-Chung Sun a a b c

State Key Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun 130023, People’s Republic of China School of Chemistry and Materials Science, Liaoning ShiHua University, FuShun, 113001 LiaoNing, People’s Republic of China Department of Molecular and Material Sciences, Faculty of Engineering Sciences, Kyushu University, 6-1 Kasuga-Park, Fukuoka 816-8580, Japan

a r t i c l e

i n f o

Article history: Received 22 May 2007 Accepted 25 February 2008 Available online 5 March 2008 Keywords: Potential energy surface Theoretical study Structure Stability [Si, C, P, S]

a b s t r a c t The structures, energetics, spectral parameters and stability of the doublet [Si, C, P, S] radical are explored at the density functional theory and ab initio levels. Sixteen isomers connected by 23 interconversion transition states are located on the PES. The structures of the stable isomers and their relevant transition states are further optimized at the QCISD/6-311G(d) level followed by CCSD(T)/6-311+G(2df) single-point energy calculations. At the QCISD/6-311G(d) level, the lowest-lying isomer is a bent SSiCP 1 (0.0 kcal/ mol) with considerable isomerization barriers (the lowest barrier is 12.6 kcal/mol). In addition, the bent isomer SiCSP 5 (57.3 kcal/mol) and the cyclic species S-cCSiP 6 (2.7 kcal/mol) also possess considerable isomerization barriers (more than 10.0 kcal/mol). The valence bond structures of the three isomers 1, 5 and 6 are analyzed. The calculated results are compared with those of analogous molecules C2PS and [Si, C, N, O]. Implications in laboratory and interstellar space are also discussed. Ó 2008 Elsevier B.V. All rights reserved.

1. Introduction Silicon, phosphorus and sulfur chemistry have received considerable attention from various fields. One particular field is their possible roles in astrophysical chemistry. Up to now, many silicon, nitrogen-, phosphorus- or sulfur-containing molecules, such as SiCn (n = 1–8), CnS (n = 1–9), HSiCN, SiP, SiS, CS, SO, CN and CP [1–7], have been detected either in the dense molecular clouds or circumstellar shells. The discoveries of these molecules in space have drawn attention to the rich cosmic chemistry of heteroatom, and led to the inclusion of such molecules into the chemical models of dense molecular clouds. Moreover, extensive experimental and theoretical investigations have been performed on the SiS, SiO, SO, PS and larger SiCN, SiCn, CnS, CnP species [8–15], which have been expected to be carriers of some interstellar bands. Here, we optimistically expect that the mixed [Si, C, P, S] species may be of astrophysical interest and will be detected in the interstellar medium. Efficient theoretical investigations and spectroscopic characterizations of the [Si, C, P, S] radical require the support of calculation work to provide accurate frequencies of the rotational spectrums in the radio band. In addition, compounds containing Si-element have also attracted continuous attention due to their applications in the microelectronic technology. It is well known that binary silicon carbides are used frequently in the microelectronic and photoelectronic apparatus [16]. Phosphorus and sulfur

* Corresponding author. Tel.: +86 43188498951; fax: +86 43188945942. E-mail address: [email protected] (X.-R. Huang). 0301-0104/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2008.02.057

are usually used as minute dopants. During P- and S-doped SiC vaporization process, the smaller [Si, C, P, S] species may be generated. Understanding the structures, bonding properties and stability of the [Si, C, P, S] species may be helpful for future identification of new Si-, C-, P- and S-containing species either in the laboratory or space and instructive for elucidation of the formation mechanism of the P- and S-doped SiCn clusters. In view of the potential importance of [Si, C, P, S] series, in this paper, we will study the tetra-atomic [Si, C, P, S] radical which is the isoelectronic species of the [Si, C, N, O] radical. Very recently, our theoretical investigations on the [Si, C, N, O] radical revealed that five doublet isomers are stable with respect to the separated reactants [17]. Muenow and Margrave concluded the existence of neutral isomer OSiCN and its cation OSiCN+ by means of Knudsen-cell mass spectrometry [15]. Shen et al. probed the cationic silicon isocyanate SiNCO+ in ion–surface collisions with fluorinated monolayer [18]. Srinivas et al. explored the [Si, C, N, O]+ cation via tandem mass spectrometry and produced the SiNCO and SiNCO+ [19]. Our calculated results of the [Si, C, N, O] isomers are in good agreement with the mass spectrometry experiments [15]. Therefore, it is highly possible that there will be various [Si, C, P, S] species which are stable with respect to the separated reactants attract experimental and astrophysical interest. For the [Si, C, P, S] radical, to our knowledge, has not been the subject of any theoretical study up to now. Because of the rather limited knowledge of the neutral [Si, C, P, S] radical, we decide to perform a detailed theoretical study on its potential energy surfaces (PES). The following problems will be resolved: (1) Is the lowest-lying isomer of [Si, C, P, S] similar to the [Si, C, N, O]? (2) Are there any other chainlike and

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cyclic isomers that are stable with respect to the separated reactants? (3) What is the bonding nature of the stable isomers? (4) What are the similarities and discrepancies compared with C2PS [20], [Si, C, N, O]? Surely, a detailed theoretical study on the [Si, C, P, S] radical will promote our understanding of the structural, energetic and bonding changes among the 19-valence-electron series XX0 PS (X, X0 = C, Si). Because the diatomic fragments SiP, CS, SiS, CP, SiC and PS have been discovered in the interstellar space, their direct addition may possibly lead to the formation of several [Si, C, P, S] isomers. Therefore, the discussion about the possible formation strategies of the stable isomers in the laboratory and space is also a purpose of the present paper. 2. Theoretical computational methods All computations are carried out using the GAUSSIAN 98 [21] program package. Density functional theory (DFT) methods have now been widely applied to various molecular systems and perform exceptionally well for molecular structures with much reduced computational effort than traditional ab initio methods [22]. Besides efficiency, DFT methods also present good accuracy, such as, density functional theory (Becke3LYP/6-31G*) has been used to predict energies for the stepwise mechanisms of the Diels–Alder reaction, predicted barrier heights and heats of reaction are in good agreement with experimental values with the stepwise barrier predicted to be the higher by 2.3–7.7 kcal/mol [23]. In this paper, the whole potential energy surface is initially surveyed at the 6-311G(d)B3LYP level, which includes Becke’s three-parameter-exchange functionals and non-local Lee–Yang–Parr correlation functional. The optimized geometries and harmonic vibrational frequencies of the local minima and transition states are obtained at the B3LYP/6-311G(d) level. To confirm whether the obtained transition states connect the right isomers, the intrinsic reaction coordinate (IRC) calculations are performed at the B3LYP/6-311G(d) level. To get better results for relevant species, we used the quadratic configuration interaction method with single and double substitutions (QCISD) for geometries and frequencies and the coupled cluster method with single, double and non-iterative triple substitutions (CCSD(T)) for energies, respectively. Both methods represent a higher-level treatment of electron correlation beyond MP4 and can usually provide greater accuracy [24]. The basis set ranges from 6-311G(d) for geometry and frequency calculations to 6-311G(2d) and 6-311G(2df) for single-point energy calculations. The zeropoint vibrational energies (ZPVE) at the 6-311G(d)-B3LYP and QCISD levels are included in the final relative energy consideration. For conciseness, the levels CCSD(T)/6-311G(2d)//B3LYP/6311G(d)+ZPVE and CCSD(T)/6-311G(2df)//QCISD/6-311G(d)+ZPVE are simplified as CCSD(T)//B3LYP and CCSD(T)//QCISD. 3. Results and discussion To include the isomeric forms of [Si, C, P, S] as many as possible, we initially considered three types of isomers, i.e., the linear or chainlike species, cyclic species and cage-like species. For conciseness, the results are arranged as follows. The geometries of the optimized [Si, C, P, S] isomers and the transition states are shown in Figs. 1 and 2, respectively. The geometries of optimized fragments of the [Si, C, P, S] are illustrated in Fig. 3. The schematic potential energy surface (PES) of the [Si, C, P, S] is presented in Fig. 4. The dissociation curve of the isomer SSiCP 1 is exhibited in Fig. 5. The valence bond structures of the stable isomers 1, 5 and 6 are shown in Fig. 6. The spectral parameters (harmonic frequencies, infrared intensities, dipole moments and rotational constants) of the stable isomers are listed in Table 1. The relative energies of all the isomers and transition states of the [Si, C, P, S], at the CCSD(T)//B3LYP level, are collected

in Table 2. The relative energies of various dissociation fragments of the [Si, C, P, S] are laid out in Table 3. 3.1. [Si, C, P, S] isomers Sixteen isomers (m) and 23 interconversion transition states (TSm/n) are located on the doublet potential energy surface (PES) at the B3LYP/6-311G(d) level. Among them, five isomers with 2A0 electronic state have a bent chainlike structure belonging to Cs symmetry, namely, SSiCP 1 (0.0, 0.0), SiSCP 2 (17.8), SPCSi 3 (31.7), SiCPS 4 (34.0) and PSCSi 5 (57.2, 57.3). The first and the second values in the parentheses are the relative energies (in kcal/ mol) of a isomer with reference to the isomer 1 (0.0, 0.0) at the CCSD(T)//B3LYP and CCSD(T)//QCISD levels, respectively. The present DFT/B3LYP/6-311G(d) method predicts that the lowest-lying isomer is the bent isomer SSiCP 1 (0.0, 0.0) on the PES, which is different from the [Si, C, N,O]. Among the [Si, C, N, O] isomers, the linear SiNCO can be viewed as the global minimum isomer [17]. For the cyclic isomers, five three-member ring isomers can be located on the PES. They are S-cCSiP 6 (4.7, 2.7), P-cCSiS 7 (8.1), S-cSiPC 8 (21.9), Si-cCSP 9 (31.0) and C-cSiPS 10 (86.4). Among the remaining six species, isomers cSiPCS 11 (14.0), cSSiCP 12 (26.1), cPSiCS 13 (28.6), cSSiCP 14 (28.8) and cPSiCS 16 (57.9) have a four-member ring structure, and possess SiC, SiP, PC, SC and SiS cross-bonding, respectively. Different from the cyclic isomers, the isomer cage-CSiSP 15 (31.4) can be viewed as an interesting cage-like species. Except for the isomers 10, 12, 15 and 16 belonging to C1 point group, the remaining all cyclic isomers are of Cs symmetry. In the case of electronic state, the isomers 6, 7, 8 and 14 have 2A0 electronic state, on the contrary, isomers 9, 11 and 13 have 2A00 electronic state. 3.2. [Si, C, P, S] isomerization and dissociation To discuss the stability of an isomer separated from other species, one needs to consider all possible isomerization and dissociation pathways. The lowest isomerization or dissociation barrier usually governs whether an isomer are stable with respect to the separated reactants. In general, an isomer separated from other species by a higher barrier should have higher stability. For simplicity, the details of the obtained 23 transition states are omitted. From the isomerization processes of the isomers depicted on the PES (shown in Fig. 4), we can see that some isomers can easily convert to the stable isomers through low isomerization barriers. These isomers are expected to be of little importance in the investigation. Two low-lying isomers 1, 6 and another high-lying species 5 attract our interest due to their relative higher conversion barriers (12.8 [12.6] for 1 ? 7, 15.5 [14.1] for 6 ? 11 and 12.0 [10.6] kcal/mol for 5 ? 9) which are stable with respect to the separated reactants. Such isomerization barriers are enough to ensure that isomers 1, 5 and 6 can exist in the low temperature conditions of the laboratory or interstellar space (such as in the dense interstellar clouds). Therefore, existence of the stable isomers 1, 5 and 6 that we predicted are promising. Note that the italic values in the square brackets are obtained at the CCSD(T)//QCISD level. In addition to the species what have discussed, the existence of the remaining isomers is less possible due to their higher energy or smaller isomerization barriers. As shown in Fig. 4, at the CCSD(T)// B3LYP level, the lowest isomerization barriers of the remaining species 2, 3, 4, 7, 8, 9, 10, 11, 12, 13, 14, 15 and 16 are 6.2 (2 ? 7), 5.2 (3 ? 4), 2.9 (4 ? 3), 4.7 (7 ? 1), 5.3 (8 ? 1), 0.3 (9 ? 14), 9.0 (10 ? 12), 6.2 (11 ? 6), 5.0 (12 ? 1), 4.7 (13 ? 6), 2.5 (14 ? 9), 6.9 (15 ? 12), 0.3 (16 ? 13) kcal/mol, respectively. For these remaining isomers, their least isomerization barriers are smaller than the 10.0 kcal/mol and may be of little interest as observable species either in the laboratory and space.

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Fig. 1. Optimized geometries of the [Si, C, P, S] isomers at the B3LYP/6-311G(d) level. Bond lengths and angles are in angstroms and degrees, respectively. The italic values are calculated at the QCISD/6-311G(d) level. The 41, 45 and 46 are the corresponding quartet isomers for the isomers 1, 5 and 6.

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Fig. 2. Optimized geometries of the [Si, C, P, S] transition states at the B3LYP/6-311G(d) level. Bond lengths and angles are in angstroms and degrees, respectively. The italic values are at the QCISD/6-311G(d) level. The ‘‘*” is used for distinguishing the transition states correlation the same two isomers.

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Fig. 3. The optimized dissociation fragments of the [Si, C, P, S] at the B3LYP/6-311G(d) level. Bond lengths and angles are in angstroms and degrees, respectively.

3.3. Properties of the stable [Si, C, P, S] isomers From what have discussed above, we know that the isomers 1, 5 and 6 are stable with respect to the separated reactants and more possible to be detected in the interstellar space. In this section, based on the results at B3LYP level, their properties of valence bond structure will be analyzed. For the lowest-lying isomer SSiCP 1, it has 2A0 electronic state. Its SSi bond length (1.9809 Å) is slightly longer than the S@Si bond length (1.9562 Å in H2SiS) and shorter than the S–Si (2.1676 Å). The internal SiC bond length (1.8580 Å) is close to the Si–C (1.8853 Å in H3SiCH3). The terminal CP bond length (1.5580 Å) is closer to the C„P bond length (1.5392 Å in HC„P) than to C@P bond length (1.6704 Å in H2C@PH). Based on the bond lengths and the spin density distribution (0.330, 0.559, 0.029 and 0.081 e for S, Si, C and P, respectively), the bent species 1 can be described as the following conjugated forms (shown in Fig. 6): The symbols ‘‘” and ‘‘j” denote the single electron and lone-pair electron, respectively. The resonance structures are also supported by the natural bond orbital (NBO) analyses. The unpaired single electron is mainly localized on the Si atom. From the analyses above, the conjugated form (1) should be view as the main form of the resonance structures and contributes a lot to the stability of isomer 1. Seen from the dissociation fragments and dissociation curve (Fig. 5) of the isomer SSiCP 1, it can be viewed as the direct combination between singlet SSi molecule and doublet CP radical. The chainlike isomer PSCSi 5 has 2A0 electronic states. Its PS bond length (2.0952 Å) is longer than the double P@S bond length (1.9501 Å in HP@S) and shorter than single P–S bond length (2.1669 Å in H2PASH). The internal SC bond length (1.6394 Å) is close to the typical S@C bond length (1.6149 Å in H2C@S). The terminal SiC bond length (1.6883 Å) is slightly shorter than Si@C bond (1.7068 Å in H2Si@CH2) and longer than Si„C bond (1.6473 Å in HSi„CH). The calculated spin density distribution (0.260, 0.223, 0.135, and 1.618 e for Si, C, S, and P, respectively) indicates that the unpaired single electron is mainly localized on the P atom. Then, species 5 may be best viewed as the following cumulenic form (shown in Fig. 6): The above resonance forms are also supported by the natural bond orbital (NBO) analyses.

The three-member ring isomer 6 also has the 2A0 state. Its SiP bond length (2.1853 Å) is longer than the Si@P bond length (2.0807 Å in H2SiPH) and shorter than the Si–P bond length (2.2820 Å in H3SiPH2). Its SiC bond length (1.9380 Å) is slight longer than the typical Si–C bond length (1.8853 Å in H3SiCH3). The CS bond length (1.6185 Å) is nearly equal to the C@S bond length (1.6149 Å in H2CS). The bond lengths and the spin density distribution (0.209, 0.072, 0.109, and 0.609 e for Si, P, C, and S, respectively) indicate that the isomer 6 can be mainly described as the following forms (shown in Fig. 6). The resonance structures are confirmed by the natural bond orbital (NBO) analyses. From the analyses above, the structure (1) should be view as the main form of the resonance form and contributes a lot to the stability of isomer 6. Seen from the dissociation fragments and transition states (TS6/18), the isomer 6 can be regarded as the product of direct addition between singlet CS molecule and doublet SiP radical. 3.4. Comparison with the analogues C2PS and [Si, C, N, O] It is interesting to compare [Si, C, P, S] with its isovalent analogues C2PS [20] and [Si, C, N, O] [17–19] which have been experimentally or theoretically studied. For C2PS and [Si, C, P, S], they all have the linear or chainlike isomers which are stable with respect to the separated reactants. The linear PCCS and bent SSiCP 1 are located as the lowest-lying isomers on the PESs of C2PS and [Si, C, P, S], respectively. In addition to the isomer SSiCP1, [Si, C, P, S] has a stable three-member ring structure isomer S-cCSiP 6, which is different from C2PS that has no cyclic isomer are stable with respect to the separated reactants. Obviously, one of C atom in C2PS is substituted by a Si atom, the cyclic structure isomer becomes increasingly important and stable, which can be attributed to the fact that the second-row element Si has higher preference to form r-bond than the first-row element C. For [Si, C, N, O] containing N and O atoms, besides two linear SiNCO and SiCNO, three bent OSiCN, OSiNC and SiOCN isomers are also thermodynamically and kinetically stable species. However, different from the inexistence of the cyclic cSiNCO and cSiCNO, the analogous four-member ring structure isomers cSiPCS 11 and cSiCPS 12 can be located on

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Fig. 4. Schematic potential energy surface of [Si, C, P, S] at the CCSD(T)/6-311G(2d)//B3LYP/6-311G(d)+ZPVE level. The relative values in italic and parentheses are at the CCSD(T)/6-311G(2d)//MP2/6-311G(d)+ZPVE and CCSD(T)/6-311+G(2df)//QCISD/6-311G(d)+ZPVE level, respectively.

Fig. 5. Dissociation curve of the isomer SSiCP 1 at B3LYP/6-311G(d) level. The dotted line denotes the total energy of SiS (1R+) and CP (2R+) at B3LYP/6-311G(d) level.

the PES of [Si, C, P, S], which can be ascribed the fact that the P and S atoms have less preference to form p-bond than the corresponding N and O atoms, respectively. 3.5. Interstellar and laboratory implications The isomers 1, 5 and 6 are predicted to be observable in the laboratory or interstellar space. Seen from Table 3, two sets of disso-

ciation fragments SiS (1R+) + CP (2R+) and SiP(2R+) + CS (1R+) attract us much attention because of their relative lower energy than the other dissociation fragments. Intuitively, the diatomic + diatomic consociation reactions of the radical-molecule CP/SiS and SiP/CS pairs may easily lead to the formation of isomers SSiCP 1 and ScCSiP 6 under the laboratory and interstellar space conditions. As shown in Fig. 4, at the CCSD(T)//MP2 level, the fragments SiP(2R+) + CS (1R+) are connected to form S-cCSiP 6 with a barrier (13.3 kcal/mol) via transition state TS6/18. Therefore, the formation of S-cCSiP 6 may occur by means of such an association reaction under particular laboratory or interstellar conditions. Note that TS6/18 is located at MP2/6-311G(d) level, since it can not be obtained at the B3LYP/6-311G(d) level. On the other hand, the fragments SiS (1R+) and CP (2R +) can also associate to form the isomer SSiCP 1 directly with no barrier (shown in Fig. 5), especially in some dark interstellar dense clouds with ultralow temperature and much collisional occasion. Therefore, the observation of isomer SSiCP 1 and S-cCSiP 6 in the interstellar space is promising. It is well known that the interstellar medium is composed primarily of three types of large-scale structures which are often called ‘clouds’. These are diffuse clouds, translucent clouds (semitransparent clouds), and dense clouds (cold clouds; molecular clouds) [25]. The nomenclature is based on an increasingly denser medium rising from 101 to 104 atoms cm3 as the temperature drops simultaneously from 120 to about 10 K. The interstellar molecules, radicals, and ions detected so far are not distributed homogeneously but are confined to distinct environments. In the diffuse clouds with the temperature of 100–120 K [26], the atomic C, Si and S is expected to be ionized, and the N and O should exist in their atomic form. The diatomic and triatomic species such as CS, CN, HCN and C2H have been detected unambiguously also. In the

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Table 1 Harmonic vibrational frequencies (cm1), infrared intensities (km/mol) (in parentheses), dipole moment (D) and rotational constants (GHz) of the stable [Si, C, P, S] isomers at the B3LYP/6-311G(d) and QCISD/6-311G(d) levels Species

Frequencies (infrared intensity)

Dipole moment

Rotational constant

SSiCP 1 SSiCP 1a PSCSi 5 PSCSi 5a S-cCSiP 6 S-cCSiP 6a

92(1), 183(5), 299(11), 97(1), 182(5), 298(11), 85(0), 195(8), 276(34), 91(2), 204(8), 297(43), 188(1), 351(8), 404(5), 192(1), 351(9), 411(3),

2.9993 2.7993 0.5221 1.0043 1.2189 0.8520

21.70957, 21.31830, 12.68037, 11.22765, 7.19010, 7.26890,

a

468(25), 681(63), 1433(17) 467(45), 702(63), 1325(15) 410(4), 560(2), 1316(198) 428(0), 695(115), 1527(891) 511(38), 595(2), 1157(107) 565(35), 623(14), 1126(68)

1.29098, 1.28780, 1.53969, 1.59655, 2.54266, 2.55360,

1.21852 1.21444 1.37298 1.39779 1.87840 1.88973

At the QCISD/6-311G(d) level.

Table 2 Relative energies (kcal/mol) of the [Si, C, P, S] isomers and transition states at the B3LYP/6-311G(d) and single-point CCSD(T)/6-311G(2d) levels Species a

SSiCP 1 SiSCP 2 SPCSi 3 SPCS 4 PSCSi 5 S-cCSiP 6 P-cCSiS 7 S-cSiPC 8 Si-cCSP 9 C-cSiPS 10 cSiSCP 11 cSSiPC 12 cSiCSP 13 cSiSPC 14 cCSiSP 15 cSiPSC 16 SiS (1R+) + CP (2R+) 17e SiP(2R+) + CS (1R+) 18e TS1/7 TS1/8 TS1/11 TS1/11* TS1/12 TS2/7 TS3/4 TS4/9 TS5/9 TS5/14 TS6/11 TS6/13 TS6/18 TS7/11 TS7/14 TS7/15 TS9/14 TS10/12 TS11/15 TS12/14 TS12/15 TS13/15 TS13/16 SSiCP 41f PSCSi 45f S-cCSiP 46f

State

B3LYPb

MZPVE B3LYPb

CCSD(T)c//B3LYPb

Total 1

2

0.0 19.1 27.5 30.4 55.1 1.1 7.7 23.2 29.9 88.8 16.0 30.1 30.6 29.5 35.8 62.3 56.1 72.4 12.0 28.7 45.9 43.5 33.9 23.8 34.4 40.3 66.9 98.5 20.2 34.0 91.9 21.4 32.5 50.0 30.6 95.5 58.6 41.6 42.6 45.9 63.5 49.5 63.1 46.9

0.0 0.1 0.2 0.3 0.4 0.1 0.1 0.0 0.5 1.3 0.0 0.3 0.3 0.6 0.3 0.7 1.6 1.7 0.7 0.8 1.4 1.2 0.8 0.5 0.9 1.0 1.1 1.7 0.8 0.8 1.5 0.8 0.7 1.1 0.7 1.6 1.2 1.1 0.9 0.8 1.2 0.4 0.6 0.6

0.0 17.8 31.9 34.3 57.6 4.6 8.2 21.9 31.4 87.7 14.0 26.4 28.9 29.3 31.7 58.6 51.3 66.7 13.5 28.1 43.7 40.3 31.9 24.5 37.8 43.5 70.3 97.6 20.9 34.1 76.5 22.7 33.4 47.9 31.9 97.0 53.2 40.5 39.2 44.9 59.4 53.8 64.1 50.5

0.0 17.8 31.7 34.0 57.2 4.7 8.1 21.9 31.0 86.4 14.0 26.1 28.6 28.8 31.4 57.9 49.7 65.0 12.8 27.3 42.3 39.1 31.1 24.1 36.9 42.5 69.2 95.9 20.2 33.3 75.0 21.9 32.7 46.9 31.1 95.4 52.0 39.4 38.3 44.2 58.2 53.4 63.5 49.9

0

A A0 A0 2 0 A 2 0 A 2 0 A 2 0 A 2 0 A 2 00 A 2 2

2

A00

2

A00 A0

2

2

A0

2

A0

2

A0 A0

2

2 2

A0 A0

2

A0

2

A00

4

A00 A0 4 0 A

4

QCISDb

MZPVE QCISDb

CCSD(T)d//QCISDb

Total 2

0.0

0.0

0.0

0.0

58.2 5.4

0.2 0.3

57.1 2.4

57.3 2.7

For the stable isomers, the relative energies are also included at CCSD(T)//QCISD level. The ‘‘*” is used for distinguishing the transition state correlation of the same two isomers. a The total energies of reference isomer 1 at the B3LYP/6-311G(d) level is 1067.1608544 au, at the CCSD(T)/6-311G(2d)//B3LYP/6-311G(d) level is 1065.57435090 au, at the QCISD/6-311G(d) level is 1065.4973704 au, at the CCSD(T)/6-311G(2df)//QCISD/6-311G(d) level is  1065.6526597 au. The ZPVE at the B3LYP, QCISD levels are 4.51321, 4.39126 kcal/mol, respectively. b The basis set is 6-311G(d) for B3LYP and QCISD. c The basis set is 6-311G(2d) for CCSD(T)//B3LYP. d The basis set is 6-311+G(2df) for CCSD(T)//QCISD. e The 17, 18 are the dissociation fragments SiS (1R+) + CP(2R+), SiP(2R+) + CS(1R+), respectively. f The 41, 45 and 46 are the corresponding quartet isomers for the isomers 1, 5 and 6.

Translucent clouds with the temperatures of 50–100 K [27], small diatomic CH, CS, CN and CO together with larger species C2H, H2CO have been found. The dense clouds are also referred to as cold

clouds, which temperature is of only 10–15 K [28]. The species in the dense clouds are carbon-rich, linear and cyclic molecules with up to 13 atoms. So we expect that the three species 1, 5 and 6

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Table 3 Relative energies (kcal/mol) of dissociation fragments of the [Si, C, P, S] isomers at the B3LYP/6-311G(d) and single-point CCSD(T)/6-311G(2d) levels Speciesa 2

1

PCS( P) + Si( D) cPCS(2A00 ) + Si(1D) PCS(2P) + Si(3P) cPCS(2A00 ) + Si(3P) cPSiC(2A0 ) + S(1D) SiCP(2P) + S(1D) cPSiC(2A0 ) + S(3P) SiCP(2P) + S(3P) SiPC(2A0 ) + S(3P) SiCS(1R) + P(4S) cSiCS(1A0 ) + P(4S) CSiS(1R) + P(4S) SiCS(3R) + P(4S) CSiS(3R) + P(4S) SiP(2R+) + CS(1R+) SiP(2R+) + CS(1R+)d SiS (1R+) + CP(2R+) SiS (3P) + CP(2R+) SiC(1R+) + PS(2P) SiC(3P) + PS(2P)

B3LYPb

DZPVE B3LYPb

CCSD(T)c//B3LYPb

Total

101.2 145.8 75.2 119.8 134.5 120.1 96.0 145.5 81.6 93.6 105.6 158.4 78.1 134.4 72.4 71.7 56.1 131.7 146.8 120.1

0.8 1.9 0.8 1.9 1.4 1.3 1.4 2.3 1.3 1.1 1.8 2.2 1.1 2.3 1.7 2.9 1.6 1.9 1.9 2.1

100.8 138.5 76.7 114.4 124.9 111.8 91.8 141.0 78.7 85.1 92.9 147.1 73.9 125.7 66.7 66.1 51.3 128.3 133.5 118.3

100.0 136.7 75.9 112.6 123.5 110.4 90.4 138.7 77.3 84.0 91.1 144.9 72.8 123.4 65.0 63.2 49.7 126.5 131.6 116.2

a The isomer 1 is the reference species for the dissociation fragments, and the total energy of isomer 1 at CCSD(T)//B3LYP level is listed in Table 2. The symbols in the parentheses of the column denote the electronic states. b The basis set is 6-311G(d) for B3LYP. c The basis set is 6-311G(2d) for CCSD(T). d The italic value are relative energies of dissociation fragments SiP(2R+) + CS(1R+) at CCSD(T)/6-311G(2d)//MP2/6-311G(d)+ZPVE level.

Moreover, the isomer 1 has a large dipole moment of 2.7993 D, which is also helpful for the future microwave detection. Finally, in order to provide a guide for the experimentalists, the CCSD(T)/ 6-311+G(2df) single-point energy calculations of the three stable isomers and their relevant transition states have also been done using the QCISD/6-311G(d) geometries. It is worthy of note that for the three stable isomers (1, 5 and 6) and their relevant transition states (TS1/7, TS5/9 and TS6/11), the calculated results including the relative energies (shown in Table 2) and isomerization barriers (shown in Fig. 3) at the B3LYP/6-311G(d) level are in excellent agreement with those at the higher QCISD/6-311G(d) level within 2 kcal/mol, which indicates the CCSD(T)//B3LYP method is adequate for calculation of the structures, spectroscopies and energies of [Si, C, P, S] isomers. Therefore, the predicted three stable isomers are expected to be promising for their future identification either in the laboratory or in interstellar space. In addition, we also investigated the quartet species 41, 45 and 46 (number 4 means quartet state) corresponding to the stable doublet isomers 1, 5 and 6, respectively. The geometrical structures of obtained singlet isomers are also shown in Fig. 1. The computed results, at the CCSD(T)//B3LYP level, showed that quartet isomers 41 (53.4 kcal/ mol), 45 (63.5 kcal/mol) and 46 (49.9 kcal/mol) are higher in energy than the corresponding doublet species with doublet-quartet energy gap of 53.4, 6.2 and 45.2 kcal/mol, respectively. Thus the quartet [Si, C, P, S] isomers were not considered further. 4. Conclusions The detailed doublet potential energy surface of the [Si, C, P, S] is theoretically investigated at the density functional theory and ab initio levels. At the CCSD(T)//QCISD level, the lowest-lying isomer is the bent isomer SSiCP 1 (0.0 kcal/mol). In addition, another bent isomer PSCSi 5 (57.3 kcal/mol) and the three-member ring S-cCSiP 6 (2.7 kcal/mol) are stable with respect to the separated reactants. As a result, the three isomers 1, 5 and 6 may be produced or detected in the laboratory and interstellar space. The similarities and discrepancies among PC2S, [Si, C, N, O] and [Si, C, P, S] are compared. The possible formation strategies and the implications of the stable isomers in the laboratory and space are also discussed in detail. The results are expected to be useful for the future laboratory and interstellar identification of various [Si, C, P, S] isomers. Acknowledgements This work is supported by the National Nature Science Foundation of China (Nos. 20333050 and 20643004), Excellent Young Foundation of Jilin Province, and Technology Development Project of Jilin Province (20050906-6). G.-T. Yu thanks the Japan Society for the Promotion of Science for financial support. References

Fig. 6. The valence bond structures of the stable isomers 1, 5 and 6.

which are stable with respect to the separated reactants also could be detected in the particular interstellar medium, such as in the dense clouds. In order to help experimentalists to identify the stable isomers of [Si, C, P, S] in the laboratory, higher calculations at the QCISD/6-311G(d) level have been done on the vibrational frequencies, dipole moments, and rotational constants (shown in Table 1) for the three stable isomers 1, 5 and 6. At the QCISD/6311G(d) level, the dominant frequencies of the three stable isomers 1, 5 and 6 are 702, 1527 and 1126 cm1, with the corresponding infrared intensities 63, 891 and 68 km/mol, respectively. They are very helpful for spectrum research of [Si, C, P, S] isomers.

[1] R.I. Kaiser, Chem. Rev. 102 (2002) 1309. [2] M.C. McCarthy, A.J. Apponi, C.A. Gottlieb, P. Thaddeus, Astrophys. J. 538 (2000) 766. [3] V.D. Gordon, M.C. Mccarthy, A.J. Apponi, P. Thaddeus, Astrophys. J. Suppl. Ser. 134 (2001) 311. [4] M. Agúndez, J. Cernicharo, Astrophys. J. 650 (2006) 374. [5] M. Guelin, J. Cernicharo, G. Pauber, B.E. Turner, Astron. Astrophys. 230 (1990) L9. [6] F.R. Ornellas, C.M. Andreazza, A.A. De Almeida, Astrophys. J. 538 (2000) 675. [7] M.E. Sanz, M.C. McCarthy, P. Thaddeus, Astrophys. J. 577 (2002) L71. [8] M.E. Sanz, M.C. McCarthy, P. Thaddeus, J. Chem. Phys. 119 (2003) 11715. [9] M. Ohishi, S.Y. Amamoto, S. Awito, K. Kawaguchi, Astrophys. J. 329 (1988) 511. [10] X.D. Ding, S.L. Wang, C.M.L. Rittby, W.R.M. Graham, J. Phys. Chem. A 104 (2000) 3712. [11] I. Pérez-Juste, A.M. Graña, L. Carballeira, R.A. Mosquera, J. Chem. Phys. 121 (2004) 10447. [12] A. Largo, C. Barrientos, X. Lopez, J.M. Ugalde, J. Phys. Chem. 98 (1994) 3985. [13] E. del Rˇ´o, C. Barrientos, A. Largo, J. Phys. Chem. 100 (1996) 585.

F. Li et al. / Chemical Physics 348 (2008) 113–121 [14] G.T. Yu, Y.H. Ding, X.R. Huang, C.C. Sun, J. Phys. Chem. A 109 (2005) 1594. [15] D.W. Muenow, J.L. Margrave, J. Phys. Chem. 74 (1970) 2577. [16] J. Furthmüller, F. Bechstedt, H. Hüsken, B. Schröter, W. Richter, Phys. Rev. B 58 (1998) 13712. [17] G.T. Yu, X.R. Huang, Y.H. Ding, C.C. Sun, J. Comput. Chem. 27 (2006) 749. [18] J.W. Shen, V. Grill, C. Evans, R.G. Cooks, J. Mass Spectrom. 34 (1999) 354. [19] R. Srinivas, S. Vivekananda, D. Schröder, H. Schwarz, Chem. Phys. Lett. 316 (2000) 243. [20] G.T. Yu, X.R. Huang, Y.H. Ding, H.T. Bai, C.C. Sun, J. Mol. Struct. (THEOCHEM) 759 (2006) 61. [21] M.J. Frisch, G.W. Trucks, H.B. Schlegel, et al., Gaussian 98, Revision A9, Gaussian, Inc., Pittsburgh, PA, 1998.

121

[22] W. Koch, M.C. Holthausen, A Chemist’s Guide to Density Functional Theory, second ed., Wiley-VCH, Weinheim, 2001. [23] E. Goldstein, Brett Beno, K.N. Houk, J. Am. Chem. Soc. 118 (1996) 6036. [24] J.B. Foresman, . Frisch, Exploring Chemistry with Electronic Structure Methods, second ed., Guassian, Inc., Pittsburgh, PA, 2000. [25] E.F. Van Dishoeck, in: T.W. Hartquist, D.A. Williams (Eds.), The Molecular Astrophysics of Stars and Galaxies, Oxford Science Publications, Oxford, 1998, p. 53. [26] W.B. Somerville, I.A. Crawford, J. Chem. Soc. Faraday Trans. 89 (1993) 2261. [27] B.E. Turner, Astrophys. J. 542 (2000) 837. [28] S.B. Charnley, P. Ehrenfreund, Y.J. Kuan, Spectrochim. Acta A 57 (2001) 685.