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Accurate ab initio-based analytical potential energy function for S2 (â1Δg) via extrapolation to the complete basis set limit Zhang Lu-Lu, Gao Shou-Bao, Meng Qing-Tian, Song Yu-Zhi Citation:Chin. Phys. B ,2015, 24(1): 013101. doi: 10.1088/1674-1056/24/1/013101

Journal homepage: http://cpb.iphy.ac.cn; http://iopscience.iop.org/cpb What follows is a list of articles you may be interested in

Potential energy curves and spectroscopic properties of X2Σ+ and A2Π states of 13C14N Liao Jian-Wen, Yang Chuan-Lu Chin. Phys. B , 2014, 23(7): 073401. doi: 10.1088/1674-1056/23/7/073401

Potential energy curve study on the 3Π electronic states of GaX (X=F, Cl, and Br) molecules Cao Yun-Bin, Yang Chuan-Lu, Wang Mei-Shan, Ma Xiao-Guang Chin. Phys. B , 2013, 22(12): 123401. doi: 10.1088/1674-1056/22/12/123401

A full-dimensional analytical potential energy surface for the F+CH4→HF+CH3 reaction Yang Chuan-Lu, Wang Mei-Shan, Liu Wen-Wang, Zhang Zhi-Hong, Ma Xiao-Guang Chin. Phys. B , 2013, 22(6): 063102. doi: 10.1088/1674-1056/22/6/063102

The analytical potential energy function of flue gas SO2(X1A1) Wu Dong-Lan,Xie An-Dong,Yu Xiao-Guang,Wan Hui-Jun Chin. Phys. B , 2012, 21(4): 043103. doi: 10.1088/1674-1056/21/4/043103

Accurate potential energy function and spectroscopic study of the X2Σ+, A2П and B2Σ+ states of the CP radical Liu Yu-Fang, Jia Yi Chin. Phys. B , 2011, 20(3): 033106. doi: 10.1088/1674-1056/20/3/033106 ---------------------------------------------------------------------------------------------------------------------

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蔡建伟 Cai Jian-Wei

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郭红丽 Guo Hong-Li

Chin. Phys. B Vol. 24, No. 1 (2015) 013101

Accurate ab initio-based analytical potential energy function for S2(˜a1∆g) via extrapolation to the complete basis set limit∗ Zhang Lu-Lu(张路路), Gao Shou-Bao(高守宝), Meng Qing-Tian(孟庆田), and Song Yu-Zhi(宋玉志)† College of Physics and Electronics, Shandong Normal University, Jinan 250014, China (Received 11 July 2014; revised manuscript received 8 August 2014; published online 9 December 2014)

The potential energy curves (PECs) of the first electronic excited state of S2 (˜a1 ∆g ) are calculated employing a multi-reference configuration interaction method with the Davidson correction in combination with a series of correlationconsistent basis sets from Dunning: aug-cc-pVXZ (X = T, Q, 5, 6). In order to obtain PECs with high accuracy, PECs calculated with aug-cc-pV(Q, 5)Z basis sets are extrapolated to the complete basis set limit. The resulting PECs are then fitted to the analytical potential energy function (APEF) using the extended Hartree–Fock approximate correlation energy method. By utilizing the fitted APEF, accurate and reliable spectroscopic parameters are obtained, which are consistent with both experimental and theoretical results. By solving the Schr¨odinger equation numerically with the APEFs obtained at the AV6Z and the extrapolated AV(Q, 5)Z level of theory, we calculate the complete set of vibrational levels, classical turning points, inertial rotation and centrifugal distortion constants.

Keywords: multi-reference configuration interaction method (MRCI), analytical potential energy functions, vibrational levels, spectroscopic parameters PACS: 31.15.A–, 34.20.Cf, 31.50.Df, 33.20.–t

DOI: 10.1088/1674-1056/24/1/013101

1. Introduction It has long been recognized that reduced sulfur-bearing species play an important role in the Earth’s atmosphere, in biochemistry, and in combustion chemistry. [1,2] Amongst the various reduced sulfur-bearing species, thiosulfeno radical HS2 , [3,4] hydrogen disulfide H2 S2 , [5] thiozone S3 , [6,7] etc. have aroused considerable interest. Diatomic sulfur S2 , one component of these species, has also been investigated by many groups. Graham [8] was the first to observe the tran3 − sition of the S2 B3 ∑− u –X ∑g state, and his work was followed by many attempts to interpret this heavily perturbed band system. The ground state X3 ∑− g of S2 was well characterized by a combination of electron paramagnetic resonance and microwaves. [9,10] Employing a combination of cavity ring-down spectroscopy and model calculations, Wheeler [11] et al. investigated the predissociation of the B3 ∑− u state and the B–X band system of S2 over the range of excited state vibrational levels 10 < v < 22. [12] Some of the accurate spectroscopic parameters and molecular constants reported in the literature prior to 1979 were summarized by Huber and Herzberg. [13] Out of a vast body of theoretical work, by carrying out the ab initio calculations using self-consistent field (SCF) and configuration interaction (CI) with double zeta quality augmented with polarization functions, Swope et al. [14] studied the spectroscopic properties of thirteen low-lying electronic states of S2 . Large scale CI calculations were carried out by Theodorakopoulos and Peyerimhoff [15] to inves-

1 1 + tigate the properties of the X3 ∑− g , a ∆g , and b ∑g states of S2 . Employing the B3LYP functional density theory, Mawhinney and Goddard [16] determined the spectroscopic parameters of these states. Denis [17] calculated the equilibrium geometry and the harmonic vibrational frequency of groundstate S2 using the coupled cluster theory. Utilizing the global potential energy surface (PES) of HS2 (X A00 ) state, Song et al. [3] obtained more accurate spectroscopic parameters of ground-state S2 . Most recently, Xing et al. [18] calculated the potential energy curves (PECs) of the ground and some excited states. It is known that S2 (˜a1 ∆g ) is involved in many reaction processes of sulfur-containing species, such as S(1 D) + S2 (1 ∆g ), [9] H2 S + S(3 P) → H2 +S2 (1 ∆g ), [5] H(2 S) + ˜ 2 Π), [19] etc. However, less effort S2 (˜a1 ∆g ) → S(3 P) + SH(X has been put into accurately determining the analytical potential energy function (APEF) of S2 (˜a1 ∆g ). So we are motivated to carry out more accurate theoretical investigations of S2 (˜a1 ∆g ). It could serve as a reference for future studies on the above reactions and as a building block of the global PES for such molecular systems as HS2 , H2 S2 , S3 , etc. In the present work, by utilizing the multi-reference configuration interaction including the Davidson correction (MRCI(Q)) method, [20] the PECs of the S2 (˜a1 ∆g ) radical are calculated with a series of correlation-consistent basis sets from Dunning et al., [21,22] i.e., aug-cc-pVXZ (X = T, Q, 5, 6), which are hereinafter denoted as AVXZ. The uniform singletand triplet-pair extrapolation (USTE) protocol [23] is employed to extrapolate the PECs calculated at AV(Q, 5)Z to the com-

∗ Project

supported by the National Natural Science Foundation of China (Grant Nos. 11304185 and 11074151). author. E-mail: [email protected] © 2015 Chinese Physical Society and IOP Publishing Ltd http://iopscience.iop.org/cpb　 　http://cpb.iphy.ac.cn † Corresponding

013101-1

Chin. Phys. B Vol. 24, No. 1 (2015) 013101 plete basis set (CBS) limit. All the PECs are then fitted to APEFs by using the extended Hartree–Fock approximate correlation energy method (EHFACE). [24] By numerically solving the radial Schr¨odinger equation of the nuclear motion, the complete vibrational levels, classical turning points, inertial rotation and centrifugal distortion constants are calculated when the rotational quantum number J equals zero. The present results provide more accurate and complete spectroscopic information about S2 (˜a1 ∆g ). The paper is organized as follows. Section 2 describes the theoretical methods, including ab initio calculations, the procedure utilized to extrapolate the calculated energies and the APEF formalism. The results and discussion are presented in Section 3. While Section 4 gives our concluding remarks.

2. Theoretical methods

where the subscript X indicates that the energy has been calculated in the AVXZ basis set, while the superscripts CAS and dc stand for the complete-active space and the dynamical correlation energies, respectively. The X = Q, 5 are adopted in the present work and denoted as USTE(Q, 5). The CAS energies, which are uncorrelated in the sense of lacking dynamical correlation, are extrapolated to the CBS limit by adopting the two-point extrapolation protocol proposed by Karton and Martin [31] EXCAS = E∞CAS + B/X α ,

where α = 5.34 is an effective decay exponent and E∞CAS is the energy when X → ∞. The USTE protocol [23,32] has been successfully applied to extrapolate the dc energies in MRCI(Q) calculations, which is written as EXdc = E∞dc +

2.1. Ab initio calculations All electronic structure calculations have been carried out at the MRCI(Q) level [20] using the full valence completeactive-space self-consistent field (CASSCF) [25] wave function as the reference, which has recently been applied to many diatomic molecules. [26–28] The AVXZ (X = T, Q, 5, 6) basis sets of Dunning [21,22] have been employed, and the calculations are carried out employing the MOLPRO 2012 package. [29] In the calculation, C2v point group symmetry is adopted, which holds four irreducible representations, namely, A1, B1, B2, and A2. For S2 (˜a1 ∆g ), four a1, two b1, and two b2 symmetry molecular orbitals (MOs) are determined as the active space, corresponding to the 3s3p shells of the sulfur atom in the CASSCF and MRCI(Q) calculation. This procedure involves 12 correlated electrons in eight active orbitals (4a1+ 2b1+2b2). For each basis set, the calculations of S2 (˜a1 ∆g ) PECs are performed for the internuclear separation ranging from 1.2a0 to 20a0 . Note that all the ab initio energies calculated at AVXZ (X = T, Q, 5, 6) basis sets are gathered in Table 1 of the Supplementary Material (SM). The core effects have been neglected by closing the core orbitals in the CASSCF and not correlating them in the MRCI(Q) calculation. A major reason for adopting the frozen core approximation lies in the fact that the raw ab initio energies calculated with relatively modest cost (AV(Q, 5)Z) are subsequently extrapolated to the CBS limit, denoted as CBS/AV(Q, 5)Z. The extrapolation is carried out via extrapolation of the electron correlation energy to the CBS limit plus extrapolation to the CBS limit of the CASSCF energy. 2.2. Extrapolation to the CBS limit The MRCI(Q) electronic energy can be treated in split form, which is written as [23,30] EX = EXCAS + EXdc ,

(2)

A3 3

(X + α)

+

A5 (X + α)5

,

(3)

where A5 is determined by the auxiliary relation 5/4

A5 = A5 (0) + cA3 .

(4)

Here A5 (0) = 0.0037685459, c = −1.17847713, and α = −3/8 are the universal-type parameters. [23,29] Equation (3) is thus transformed into an (E∞ , A3 ) two-parameter rule, which is actually used for the practical procedure of extrapolation. The USTE extrapolation scheme has been shown to yield more accurate energies even when the extrapolation is carried out with the cheapest AV(D, T)Z pair. [32] Thus, it is utilized here to extrapolate the dc energies to the CBS limit for the title system. 2.3. APEF of S2 (˜a1 ∆g ) The diatomic PECs of S2 (˜a1 ∆g ), which show the correct behavior at both the asymptotic limits R → 0 and R → ∞, have been modeled using the EHFACE model, [24] which takes the following form: V = VEHF (R) +Vdc (R),

(5)

where VEHF (R) and Vdc (R) denote the extended Hartree–Fock (EHF) and the dynamical correlation parts of the potential energy. The latter term is modeled by Vdc (R) = −

∑

Cn χn (R) R−n ,

(6)

n=6,8,10

with the damping functions for the dispersion coefficients assuming the form 
n χn (R) = 1 − exp −An R/ρ − Bn R2 /ρ 2 , (7) where An and Bn are auxiliary functions and defined as

(1) 013101-2

An = α0 n−α1 ,

(8)

Bn = β0 exp (−β1 n) ,

(9)

Chin. Phys. B Vol. 24, No. 1 (2015) 013101 with α0 , β0 , α1 , and β1 being universal dimensionless parameters for all isotropic interactions: α0 = 16.36606, β0 = 17.19338, α1 = 0.70172, β1 = 0.09574. Moreover,

2 1/2 2 1/2  is the ρ/a0 = 5.5 + 1.25R0 , R0 = 2 rA + rB

2

2 [33] LeRoy parameter, rA and rB are the expectation values of squared radii for the outermost electron in atoms A and B, respectively. The EHF-type energy term in Eq. (5) is written as ! n D i VEHF (R) = − 1 + ∑ ai r exp (γr) , (10) R i=1

Re , and γi are obtained from the least-square fitting procedure. We have tried n = 3 to n = 9 for the total numbers of coefficients ai with the purpose of getting a satisfactory result. By comparing the spectroscopic constants with the experimental and other theoretical data, the best results are obtained with n = 7. All parameters of APEFs for S2 (˜a1 ∆g ) in Eqs. (6) and (10) are collected in Table 1, while the ab initio and the fitted CBS/USTE(Q, 5) PECs are displayed in Fig. 2. As can be seen, the modeled potential accurately mimics the ab initio energies, with the maximum error being smaller than 0.05 kcal/mol.

where γ = γ0 [1 + γ1 tanh (γ2 r)], with r = R − Re , is the displacement from the equilibrium diatomic geometry; D, ai (i = 1, . . . , n), and γi (i = 0, 1, 2) are adjustable parameters to be obtained from a least-square fitting procedure.

S2

V/Eh

0

3. Results and discussion

USTE(Q,5) AV6Z

0 -0.137 V/Eh

V/Eh

-0.03

-0.09

-0.141 -0.143

-0.12 -0.15 2.0

-0.139

4.0

6.0 R/a0

3.5 3.6 3.7 3.8 R/a0

8.0

10.0

Fig. 1. Comparison of the PECs of S2 (˜a1 ∆g ) calculated at AV6Z and extrapolated to the CBS limit using AV(Q, 5)Z results.

The EHFACE model is then employed to obtain the APEFs for S2 (˜a1 ∆g ) by least-square fitting the PECs calculated using AVXZ (X = T, Q, 5, 6). The APEF is also obtained by fitting the PECs extrapolated to the CBS limit using the result calculated from AV(Q, 5)Z basis sets, hereinafter denoted as CBS/USTE(Q, 5) APEF. The parameters ai , D,

Err/kcalSmol-1

We compare in Fig. 1 the ab initio PECs of S2 (˜a1 ∆g ) calculated at AV6Z and extrapolated to the CBS limit using AV(Q, 5)Z results. It can be seen that both PECs show a smooth and converged behavior. The difference between these two PECs is small, with the well depths of the global minimum differing only ∼ 0.001Eh . The AV6Z is considered an expensive basis set, with higher computational cost than AVQZ and AV5Z. With the extrapolation using the USTE(Q, 5) scheme, the accurate CBS PEC can be obtained at a much lower computational cost. Note that this extrapolation procedure was also successfully employed by Liu et al. [34] recently to obtain an accurate PEC of CO(X1 Σ+ ), with results comparing favorably with the experimental ones.

-0.06

-0.08 -0.12

3.1. The potential energy function

0.03

-0.04

0.05 0 -0.05 2

4

6 R/a0

8

10

Fig. 2. The extrapolated CBS/USTE(Q, 5) PECs for S2 (˜a1 ∆g ). The circles indicate the ab initio energies, while the line is from the fitted APEF. The differences between them are charted in the bottom panel. Table 1. Fitted parameters of S2 (˜a1 ∆g ) APEFs in Eqs. (6) and (10). Basis set Re /a0 D/Eh a1 /a−1 0 a2 /a−2 0 a3 /a−3 0 a4 /a−4 0 a5 /a−5 0 a6 /a−6 0 a7 /a−7 0 γ0 /a−1 0 γ1 /a−1 0 γ2 /𝑎−1 0 C6 /Eh a−6 0 C8 /Eh a−8 0 C10 /Eh a−10 0 ∆ERMSD /kal · mol−1

AVTZ 3.65054 0.39440 1.23239 –0.11708 0.58250 –0.17925 0.16671 –0.09951 0.027782 0.82511 4.15409 0.14044 120.2491 3581.574 139745.4 0.02201

AVQZ 3.62319 0.41949 1.70342 0.46088 0.45736 0.05444 0.03317 –0.04654 0.01826 1.30369 1.66477 0.15422 117.8233 3509.326 136926.4 0.02079

AV5Z 3.60897 0.43231 1.38442 0.03153 0.43332 –0.08250 0.08731 –0.06044 0.01797 0.98878 4.64026 0.08179 115.9064 3452.232 134698.7 0.01860

AV6Z USTE(Q, 5) 3.60484 3.60071 0.43639 0.44014 1.52880 1.64029 0.21175 0.40683 0.40330 0.46036 –0.01765 0.03532 0.058693 0.05489 –0.05487 –0.05496 0.01835 0.02016 1.13506 1.24722 4.08810 1.90732 0.07346 0.14832 114.6994 114.5670 3416.279 3412.335 133295.9 133142.0 0.018300 0.01764

To evaluate the fitting quality of the fitted PECs, we calculate the root-mean square derivation (∆ERMSD ) using the following equation: v ( ) u u1 N ∆ERMSD = t (11) ∑ [VAPEF (i) −Vab (i)]2 , N i=1 where VAPEF (i) and Vab (i) are the i-th energies from fitting and from the ab initio calculation, respectively; N

013101-3

Chin. Phys. B Vol. 24, No. 1 (2015) 013101 is the number of points employed in the fitting procedure (N = 79). The values of ∆ERMSD are also gathered in Table 1. This table shows the ∆ERMSD for APEFs obtained from fitting the ab initio PECs of MRCI(Q)/AVTZ, MRCI(Q)/AVQZ, MRCI(Q)/AV5Z, MRCI(Q)/AV6Z, and the extrapolated CBS/USTE(Q, 5) are 0.02201 kcal/mol, 0.2079 kcal/mol, 0.01860 kcal/mol, 0.01830 kcal/mol, and 0.01764 kcal/mol, respectively. The ∆ERMSD shows a decreasing trend as the size of the basis set increases, and the CBS/USTE(Q, 5) APEF gives the smallest RMSD, which shows that the fitting process is of a high quality. 3.2. Spectroscopic constants Based on the APEFs obtained by fitting the raw MRCI(Q)/AVTZ, MRCI(Q)/AVQZ, MRCI(Q)/AV5Z, MRCI(Q)/AV6Z, and the extrapolated CBS/USTE(Q, 5) PECs, we calculate the spectroscopic constants of S2 (˜a1 ∆g ). Some other theoretical and experimental studies have published spectroscopic constants of S2 (˜a1 ∆g ). Among them, Swope et al. [14] calculated Re , ωe , Be , and αe from the SCF and CI calculations. Compared with the experimental value, their vibrational frequency is too large. By carrying out the MRCI(Q) level of theory calculation with a series of Dunning’s basis set, Peterson et al. [6] calculated Re , ωe and ωe χe . Xing et al. [18] calculated the PECs of the ground state and some excited states, and gave more complete spectroscopic constants of S2 (˜a1 ∆g ). The values of De , Re , ωe , Be , αe , and ωe χe are collected in Table 2 together with the other theoretical and experimental data [13] for convenient comparison. [6,14,18] As we can see from the table, the dissociation energy increases monotonically as the basis set increases from AVTZ to AV6Z, and the largest value is obtained at CBS/USTE(Q, 5) APEF, differing 0.0012Eh from that at the AV6Z APEF. The equilibrium bond length is calculated from CBS/USTE(Q, 5) APEF to be 3.6007a0 , which is only 0.0127a0 longer than the experimental value, [13] and 0.0035a0 longer than the most recent value obtained by Xing et al., [18] showing a high accuracy. The vibrational frequency is calculated to be 700.81 cm−1 , which differs from the experimental [13] and the theoretical [18] values by 1.54 cm−1 and 1.13 cm−1 , respectively. The spectroscopic constant Be from CBS/USTE(Q, 5) APEF is smaller than that of Ref. [18], which must be due to the fact that Be is inversely proportional to Re . However, the spectroscopic constants αe and ωe χe can be affected by Be , ωe , and the force constants (quadratic f2 , cubic f3 , and quartic f4 ). All of these parameters can cause the values of αe and ωe χe to be larger than those of Refs. [6] and [18]. Comparing the results from the present CBS/USTE (Q, 5) APEF with those of AV6Z, the deviations of De , Re , ωe , Be , αe , and ωe χe are 0.852%, 0.11%, 0.23%, 0.24%, 0.52%, and 0.38%, respectively. The

spin–orbital coupling effect on the diatomic PEC and nonadiabatic reaction dynamics were investigated and reported in Refs. [35] and [36], as it is known that the spin–orbital coupling effect is big when crossing exists or the avoidance of crossing among the PECs. Although the spin–orbital coupling may affect the diatomic PECs and the spectroscopic constants, the spin–orbital coupling effect is not included in the current work, since we do not find the crossing or avoided crossing between the a˜ 1 ∆g state and the ground state or the higher excited states. Table 2. Spectroscopic constants compared with experimental and others’ theoretical data for the S2 (˜a1 ∆g ) molecule. The dissociation energies are in Eh , equilibrium bondlength in a0 , while Be , αe , and ωe χe are in cm−1 . De AVTZ 0.128767 AVQZ 0.136479 AV5Z 0.140352 AV6Z 0.141464 CBS/USTE(Q, 5) 0.142679 Theory [6] – Theory [14] – Theory [18] 0.141963 Experiment [13] –

Re 3.6505 3.6232 3.6090 3.6048 3.6007 3.6070 3.605 3.5972 3.588

ωe 674.90 690.51 696.49 699.18 700.81 697.0 746 699.68 702.35

Be 0.2826 0.2869 0.2891 0.2898 0.2905 – 0.2897 0.2911 0.2926

αe 0.00197 0.00194 0.00194 0.00194 0.00193 – 0.0014 0.00168 0.00173

ωe χe 4.029 3.979 3.937 3.936 3.921 3.07 – 3.102 3.09

It can be concluded from the above discussion that the present spectroscopic constants of the S2 (˜a1 ∆g ) electronic state calculated from the CBS/USTE(Q, 5) APEF are in better agreement with the experiments and other theoretical results [6,13,14,18] than those from the AVXZ (X = T, Q, 5, 6) APEFs. It is worth noting that the computational cost of the CBS/USTE(Q, 5) scheme is much lower than that of AV6Z, while it provides more accurate results. 3.3. Vibrational manifolds By solving the radial Schr¨odinger equation of the nuclear motion with the program Level 7.5, [37] we obtain the vibrational energy levels. The radial Schr¨odinger equation of the nuclear motion is written as   h¯ 2 d 2 h¯ 2 − + J(J + 1) +V (r) ψν,J (r) 2µ dr2 2µr2 = Eν,J ψν,J (r) , (12) where ψν,J (r) and Eν,J are the eigenfunctions and eigenvalues h¯ 2 of the potential 2µr 2 J (J + 1) +V (r), respectively, and V (r) is the rotationless APEF, r is the internuclear distance of diatom S2 , µ is the reduced mass of the molecule, and ν and J are the vibrational and the rotational quantum numbers, respectively. For a given vibrational level, the rotational sublevels can be written as

013101-4

Eν,J = G (ν) + Bν [J (J + 1)] + Dν [J (J + 1)]2 + Hν [J (J + 1)]3 + Lν [J (J + 1)]4 + Mν [J (J + 1)]5 + Nν [J (J + 1)]6 + Oν [J (J + 1)]7 ,

(13)

Chin. Phys. B Vol. 24, No. 1 (2015) 013101 where G (ν) is the vibrational level, B (ν) is the inertial rotation constant, and Dν , Hν , Lν , Mν , Nν , and Oν are the centrifugal distortion constants, respectively. By solving Eq. (12) numerically, we obtain the complete set of vibrational states for S2 (˜a1 ∆g ) when the rotational quantum number J equals 0. Due to the length limitation, we tabulate the results of only the first 21 vibrational states, while the complete set of vibrational states can be found in Tables 2 and 3 of SM. For each vibrational state, one vibrational level G (ν) and its classical turning points, one inertial rotation constant B (ν), and six centrifugal distortion constants Dν , Hν , Lν , Mν , Nν , and Oν are obtained. Table 3 presents the vibrational

levels G (ν), the classical turning points Rmin and Rmax , and the inertial rotation constants B (ν) calculated from both the CBS/USTE(Q, 5) and AV6Z APEF. As we can see from Table 3, the CBS/USTE(Q, 5) APEF predicts slightly bigger vibrational levels G (ν) than AV6Z APEF does. The difference is only 0.257 cm−1 when ν = 0 and the difference becomes bigger as the vibrational number ν increases, with the largest difference being found to be 18.891 cm−1 when ν = 20. The maximal difference for the inertial rotation constants B (ν) is found at ν = 20 with the value of 1.93×10−4 cm−1 . Moreover, the classical turning points differ at a magnitude of 10−3 a0 , showing good accordance with each other.

Table 3. Vibrational levels G (ν) (in cm−1 ) , classical turning points (in a0 ), and rotational constant Bν (in cm−1 ) of the first 21 vibrational states for S2 (˜a1 ∆g ) when J = 0, predicted by the CBS/USTE(Q, 5) and AV6Z APEFs. ν 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

G (ν) 185.172 554.265 921.599 1287.176 1650.999 2013.068 2373.387 2731.955 3088.775 3443.849 3797.177 4148.762 4498.605 4846.708 5193.07 5537.694 5880.581 6221.731 6561.144 6898.822 7234.765

CBS/USTE(Q, 5) Rmin Rmax 3.52782 3.67880 3.47753 3.73954 3.44432 3.78325 3.41815 3.81998 3.39609 3.85265 3.37683 3.88258 3.3596 3.91052 3.34395 3.93694 3.32957 3.96214 3.31624 3.98635 3.30379 4.00973 3.2921 4.03241 3.28107 4.05448 3.27061 4.07603 3.26067 4.09713 3.2512 4.11781 3.24213 4.13814 3.23345 4.15815 3.22511 4.17787 3.21709 4.19734 3.20936 4.21657

AV6Z Bν 0.081213 0.080967 0.080721 0.080474 0.080227 0.079980 0.079732 0.079483 0.079235 0.078986 0.078736 0.078486 0.078236 0.077986 0.077735 0.077484 0.077232 0.076980 0.076728 0.076475 0.076222

G (ν) 184.815 553.046 919.521 1284.238 1647.198 2008.401 2367.848 2725.539 3081.474 3435.653 3788.078 4138.749 4487.665 4834.828 5180.236 5523.892 5865.795 6205.944 6544.341 6880.984 7215.874

Rmin 3.53187 3.48152 3.44827 3.42208 3.40000 3.38071 3.36347 3.34781 3.33342 3.32007 3.30761 3.29591 3.28487 3.27441 3.26447 3.25498 3.24592 3.23723 3.22889 3.22086 3.21313

Rmax 3.68302 3.74384 3.78761 3.82438 3.85709 3.88707 3.91505 3.94151 3.96676 3.99101 4.01444 4.03717 4.05929 4.08089 4.10204 4.12278 4.14316 4.16323 4.18301 4.20254 4.22183

Bν 0.081027 0.080781 0.080535 0.080289 0.080042 0.079795 0.079547 0.079299 0.079050 0.078800 0.078551 0.078301 0.078050 0.077799 0.077547 0.077296 0.077043 0.076790 0.076537 0.076283 0.076029

Table 4. Centrifugal distortion constants (in cm−1 ) of the first 21 vibrational states for S2 (˜a1 ∆g ) when J = 0, calculated from the CBS/USTE(Q, 5) APEF. ν 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Dν /10−8 1.56665 1.57004 1.57340 1.57674 1.58007 1.58337 1.58667 1.58995 1.59323 1.59650 1.59978 1.60306 1.60635 1.60965 1.61298 1.61633 1.61971 1.62313 1.62659 1.63010 1.63367

Hν /10−16 –8.95691 –9.27506 –9.59090 –9.90520 –10.21875 –10.53241 –10.84707 –11.16364 –11.48311 –11.80646 –12.13474 –12.46900 –12.81037 –13.15996 –13.51895 –13.88854 –14.26994 –14.66442 –15.07326 –15.49778 –15.93931

Lν /10−22 –8.25129 –8.25552 –8.26979 –8.29530 –8.33329 –8.38504 –8.45185 –8.53505 –8.63602 –8.75613 –8.89678 –9.05942 –9.24549 –9.45647 –9.69389 –9.95922 –10.25408 –10.57999 –10.93858 –11.33159 –11.76061

013101-5

Mν /10−28 –5.08739 –5.14787 –5.22525 –5.32102 –5.43681 –5.57420 –5.73479 –5.9201 –6.13196 –6.37168 –6.64096 –6.94164 –7.27516 –7.64324 –8.04798 –8.49025 –8.97336 –9.49803 –10.06606 –10.6814 –11.34443

Nν /10−34 –2.36233 –2.51306 –2.68695 –2.88650 –3.11267 –3.36701 –3.65089 –3.96602 –4.31302 –4.69446 –5.11172 –5.56539 –6.05834 –6.59358 –7.16731 –7.79045 –8.45635 –9.17441 –9.94908 –10.77300 –11.66060

Oν /10−40 –1.75398 –1.94317 –2.14477 –2.37081 –2.60739 –2.85517 –3.10489 –3.36851 –3.57035 –3.79589 –4.01575 –4.11601 –4.19887 –4.28826 –3.95498 –4.00788 –3.24847 –2.62293 –2.37387 –0.82122 0.34910

Chin. Phys. B Vol. 24, No. 1 (2015) 013101 Table 5. Centrifugal distortion constants (in cm−1 ) of the first 21 vibrational states for S2 (˜a1 ∆g ) when J = 0, calculated from AV6Z APEF. ν 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Dν /10−8 1.56317 1.56659 1.57001 1.57343 1.57685 1.58028 1.58371 1.58716 1.59061 1.59408 1.59756 1.60107 1.60459 1.60814 1.61172 1.61534 1.61899 1.62269 1.62643 1.63023 1.63408

Hν /10−16 –8.9723800 –9.3326478 –9.6905871 –10.046775 –10.401835 –10.756432 –11.111272 –11.467106 –11.824726 –12.184964 –12.548700 –12.916852 –13.29038 –13.670289 –14.057624 –14.453472 –14.858963 –15.275267 –15.703598 –16.145214 –16.601412

Lν /10−22 –8.28434 –8.35264 –8.42828 –8.51225 –8.60561 –8.70946 –8.82495 –8.95330 –9.09577 –9.25366 –9.42834 –9.62120 –9.83371 –10.06735 –10.32372 –10.60436 –10.91100 –11.24530 –11.60900 –12.00401 –12.43214

The other six centrifugal distortion constants Dν , Hν , Lν , Mν , Nν , and Oν obtained from the CBS/USTE(Q, 5) and AV6Z APEF are tabulated in Tables 4 and 5, respectively, with the difference between them being small. Unfortunately, as far as we know, there is no experimental or theoretical work reported on the vibrational levels, classical turning points, inertial rotation and centrifugal distortion constants. Thus, a direct comparison cannot be made between them. However, according to the high-quality fitting of the APEF and the excellent agreement between the present spectroscopic parameters and the available results reported in the literature, [6,13,14,18] we have reason to believe that the results collected in Tables 4 and 5 are accurate and reliable. Furthermore, although the CBS/USTE(Q, 5) scheme is less costly, the APEF obtained from this scheme can give results as good as those at the AV6Z level. Thus the CBS/USTE(Q, 5) APEF can describe the interaction potential energy of S2 (˜a1 ∆g ) well.

Mν /10−28 –5.45150 –5.52570 –5.61347 –5.71621 –5.83548 –5.97287 –6.13002 –6.30854 –6.51022 –6.73689 –6.99031 –7.27239 –7.58493 –7.92979 –8.30985 –8.72587 –9.18162 –9.67824 –10.21825 –10.80488 –11.44002

The PECs of the a˜ 1 ∆g electronic state of the S2 molecule have been calculated using the CASSCF as the reference wave function followed by the MRCI(Q) approach in combination with a series of correlation-consistent AVXZ (X = T, Q, 5, 6) basis sets. The USTE(Q, 5) scheme is employed to extrapolate the PEC to the CBS limit. The PECs so obtained are subsequently fitted to APEFs using the EHFACE model. Based on the APEFs of S2 (˜a1 ∆g ), the spectroscopic constants De , Re , ωe , Be , αe , and ωe χe are calculated. In comparison with the available experimental data, the results obtained from the CBS/USTE(Q, 5) and AV6Z APEF exhibit high accuracy.

Oν /10−40 –2.09230 –2.26506 –2.44633 –2.64588 –2.85515 –3.07270 –3.29388 –3.52844 –3.75602 –3.96240 –4.10439 –4.19250 –4.27008 –4.42659 –4.08569 –4.17647 –3.53648 –3.03344 –2.77913 –1.57803 –0.70514

Thus, they are used to perform the calculations of vibrational manifolds. By numerically solving the radial Schr¨odinger equation of the nuclear motion, the complete set of vibrational states have been obtained for the first time. For each vibrational state, one vibrational level and its corresponding classical turning points, one inertial rotation constant and six centrifugal distortion constants are also produced. As a whole, the present results provide a more accurate and complete investigations of the spectroscopic parameters and vibrational manifolds of the S2 (˜a1 ∆g ) molecule.

References [1] [2] [3] [4] [5] [6] [7]

4. Conclusions

Nν /10−34 –2.86599 –3.01006 –3.17299 –3.35755 –3.56515 –3.79766 –4.05691 –4.34502 –4.66371 –5.01533 –5.40049 –5.82277 –6.28464 –6.78922 –7.33465 –7.93090 –8.57278 –9.26948 –10.02695 –10.83568 –11.71439

[8] [9] [10] [11] [12] [13]

[14] [15] [16] [17]

013101-6

Huxtable R J 1986 Biochemistry of Sulphur (New York: Plenum Press) Denis P A 2005 Chem. Phys. Lett. 402 289 Song Y Z and Varandas A J C 2011 J. Phys. Chem. A 115 5274 Denis P A 2006 Chem. Phys. Lett. 422 434 Zhou C L, Sendt K and Haynes B S 2008 J. Phys. Chem. A 112 3239 Peterson K A, Lyons J R and Francisco J S 2006 J. Chem. Phys. 125 084314 McCarthy M C, Thorwirth S, Gottlieb C A and Thaddeus P 2004 J. Am. Chem. Soc. 126 4096 Graham J I 1910 Proc. R. Soc. London Ser. A 84 311 Wayne F D, Davies P B and Thrush B A 1974 Mol. Phys. 28 989 Pickett H M and Boyd T L 1979 J. Mol. Spectrosc. 75 53 Wheeler M D, Newman S M and Orr-Ewinga A J 1998 J. Chem. Phys. 108 6594 Wheeler M D, Newman S M, Orr-Ewing A J and Ashfold M N R 1998 J. Chem. Soc. Faraday Trans. 94 337 Huber K P, Herzberg G 1979 Constants of Diatomic Molecules, Molecular Spectra and Molecular Structure Vol. IV (Van Nostrand: Princeton) Swope WC, Lee Y P and Schaefer III H F 1979 J. Chem. Phys. 70 947 Theodorakopoulos G, Peyerimhoff S D and Buenker R J 1981 Chem. Phys. Lett. 81 413 Mawhinney R C and Goddard J D 2003 Inorg. Chem. 42 6323 Denis P A 2004 J. Phys. Chem. A 108 11092

Chin. Phys. B Vol. 24, No. 1 (2015) 013101 [18] Xing W, Shi D H, Sun J F, Liu H and Zhu Z L 2013 Mol. Phys. 111 673 [19] Li A Y, Xie D Q, Dawes R, Jasper A W, Ma J Y and Guo H 2010 J. Chem. Phys. 133 144306 [20] Werner H J and Knowles P J 1988 J. Chem. Phys. 89 5803 [21] Dunning T H 1989 J. Chem. Phys. 90 1007 [22] Woon D and Dunning T H 1993 J. Chem. Phys. 98 1358 [23] Varandas A J C 2007 J. Chem. Phys. 126 244105 [24] Varandas A J C and Silva J D 1992 J. Chem. Soc., Faraday Trans. 88 941 [25] Knowles P J and Werner H J 1985 Chem. Phys. Lett. 115 259 [26] Liao J W and Yang C L 2014 Chin. Phys. B 23 073401 [27] Cao Y B, Yang C L, Wang M S and Ma X G 2013 Chin. Phys. B 22 123401 [28] Li R, Wei C L, Sun Q X, Sun E P, Jin M X, Xu H F and Yan B 2013 Chin. Phys. B 22 123103

[29] Werner H J, Knowles P J, Knizia G, Manby F R, Sch¨utz M and others, MOLPRO, version 2012.1, a package of ab initio programs; see http://www.molpro.net [30] Song Y Z and Varandas A J C 2009 J. Chem. Phys. 130 134317 [31] Karton A and Martin J M L 2006 Theor. Chem. Acc. 115 330 [32] Varandas A J C 2000 J. Chem. Phys. 113 8880 [33] Le Roy R J 1973 Spec. Period. Rep. Chem. Soc. Mol. Spectrosc. 1 113 [34] Liu Y F, Jia Y, Shi D H and Sun J F 2011 J. Quant. Spectrosc. Radiat. Transfer 112 2296 [35] Zhai H S, Zhang X M and Liu Y F 2013 Commun. Comput. Chem. 1 351 [36] Chu T S, Zhang Y and Han K L 2006 Int. Rev. Phys. Chem. 25 201 [37] Le Roy R J 2002 LEVEL 7.5: A Computer Program for Solving the radial Schr¨odinger Equation for Bound and Quasibound levels, University of Waterloo Chemical Physics Report CP-655 (2002), available from http://leroy.uwaterloo.can/

013101-7

Chinese Physics B Volume 24

Number 1

January 2015

TOPICAL REVIEW — Magnetism, magnetic materials, and interdisciplinary research 014704

Surface modification of magnetic nanoparticles in biomedicine Chu Xin, Yu Jing and Hou Yang-Long

017505

MnFe(PGe) compounds: Preparation, structural evolution, and magnetocaloric effects Yue Ming, Zhang Hong-Guo, Liu Dan-Min and Zhang Jiu-Xing

017506

Dynamics of magnetic skyrmions Liu Ye-Hua and Li You-Quan TOPICAL REVIEW — Ultrafast intense laser science

013301

Population inversion in fluorescing fragments of super-excited molecules inside an air filament See Leang Chin and Xu Huai-Liang

014208

Femtosecond filamentation induced fluorescence technique for atmospheric sensing Yuan Shuai, Chin See Leang and Zeng He-Ping

015201

Absorption of ultrashort intense lasers in laser–solid interactions Sheng Zheng-Ming, Weng Su-Ming, Yu Lu-Le, Wang Wei-Min, Cui Yun-Qian, Chen Min and Zhang Jie

015204

Studies of collisionless shockwaves using high-power laser pulses in laboratories Yuan Da-Wei and Li Yu-Tong

015205

Developments in laser wakefield accelerators: From single-stage to two-stage Li Wen-Tao, Wang Wen-Tao, Liu Jian-Sheng, Wang Cheng, Zhang Zhi-Jun, Qi Rong, Yu Chang-Hai, Li Ru-

018201

Xin and Xu Zhi-Zhan Ultrafast solvation dynamics at internal sites of staphylococcal nuclease investigated by site-directed mutagenesis Gao Guang-Yu, Li Yu, Wang Wei, Wang Shu-Feng, Zhong Dong-Ping and Gong Qi-Huang

018704

Trends in ultrashort and ultrahigh power laser pulses based on optical parametric chirped pulse amplification Xu Lu, Yu Liang-Hong, Chu Yu-Xi, Gan Ze-Biao, Liang Xiao-Yan, Li Ru-Xin and Xu Zhi-Zhan REVIEW

010601

Progress on accurate measurement of the Planck constant: Watt balance and counting atoms Li Shi-Song, Zhang Zhong-Hua, Zhao Wei, Li Zheng-Kun and Huang Song-Ling RAPID COMMUNICATION

017404

Variational Monte Carlo study of the nematic state in iron-pnictide superconductors with a five-orbital model Zheng Xiao-Jun, Huang Zhong-Bing and Zou Liang-Jian (Continued on the Bookbinding Inside Back Cover)

018102

High-crystalline GaSb epitaxial films grown on GaAs(001) substrates by low-pressure metal–organic chemical vapor deposition Wang Lian-Kai, Liu Ren-Jun, L¨u You, Yang Hao-Yu, Li Guo-Xing, Zhang Yuan-Tao and Zhang Bao-Lin GENERAL

010201

c3 ) Cluster algebra structure on the finite dimensional representations of affine quantum group 𝑈q (𝐴 Yang Yan-Min, Ma Hai-Tao, Lin Bing-Sheng and Zheng Zhu-Jun

010202

Exact solutions and residual symmetries of the Ablowitz–Kaup–Newell–Segur system Liu Ping, Zeng Bao-Qing, Yang Jian-Rong and Ren Bo

010203

Residual symmetry reductions and interaction solutions of the (2+1)-dimensional Burgers equation Liu Xi-Zhong, Yu Jun, Ren Bo and Yang Jian-Rong

010204

Hybrid natural element method for viscoelasticity problems Zhou Yan-Kai, Ma Yong-Qi, Dong Yi and Feng Wei

010301

A new optical field generated as an output of the displaced Fock state in an amplitude dissipative channel Xu Xue-Fen and Fan Hong-Yi

010302

Efficient error estimation in quantum key distribution Li Mo, Patcharapong Treeviriyanupab, Zhang Chun-Mei, Yin Zhen-Qiang, Chen Wei and Han Zheng-Fu

010303

Disordered quantum walks in two-dimensional lattices Zhang Rong, Xu Yun-Qiu and Xue Peng

010304

Coherent spin dynamics in spin-imbalanced ferromagnetic spinor condensates Qiu Hai-Bo and Wu Li-Wei

010501

Neural adaptive chaotic control with constrained input using state and output feedback Gao Shi-Gen, Dong Hai-Rong, Sun Xu-Bin and Ning Bin

010502

Predictive control of a chaotic permanent magnet synchronous generator in a wind turbine system Manal Messadi, Adel Mellit, Karim Kemih and Malek Ghanes

010503

Robust output feedback cruise control for high-speed train movement with uncertain parameters Li Shu-Kai, Yang Li-Xing and Li Ke-Ping

010602

Design and test of the microwave cavity in an optically-pumped Rubidium beam frequency standard Liu Chang and Wang Yan-Hui

010701

Thermal efficiency of the principal greenhouse gases A. Y. Galashev and O. R. Rakhmanova ATOMIC AND MOLECULAR PHYSICS

013101

Accurate ab initio-based analytical potential energy function for S2 (˜a1 ∆g ) via extrapolation to the complete basis set limit Zhang Lu-Lu, Gao Shou-Bao, Meng Qing-Tian and Song Yu-Zhi

013201

Precision frequency measurement of 1 S0 –3 P1 intercombination lines of Sr isotopes Liu Hui, Gao Feng, Wang Ye-Bing, Tian Xiao, Ren Jie, Lu Ben-Quan, Xu Qin-Fang, Xie Yu-Lin and Chang Hong (Continued on the Bookbinding Inside Back Cover)

013202

Non-linear spectral splitting of Rydberg sodium in external fields Gao Wei, Yang Hai-Feng, Cheng Hong, Zhang Shan-Shan, Liu Dan-Feng and Liu Hong-Ping

013203

Lifetimes of Rydberg states of Eu atoms Jing Hua, Ye Shi-Wei and Dai Chang-Jian

013204

Control of electron localization in the dissociation of H+ 2 and its isotopes with a THz pulse Jia Zheng-Mao, Zeng Zhi-Nan, Li Ru-Xin, Xu Zhi-Zhan and Deng Yun-Pei

013302

Effect of pump-1 laser on Autler Townes splitting in photoelectron spectrum of K2 molecule Guo Wei, Lu Xing-Qiang, Wang Xin-Lin and Yao Hong-Bin

013401

Electron correlation in fast ion-impact single ionization of helium atoms E. Ghanbari-Adivi and S. Eskandari ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS

014101

Experimental demonstration of an invisible cloak with irregular shape by using tensor transmission line metamaterials Liu Guo-Chang, Li Chao and Fang Guang-You

014201

Broadband perfect polarization conversion metasurfaces Chen Hong-Ya, Wang Jia-Fu, Ma Hua, Qu Shao-Bo, Zhang Jie-Qiu, Xu Zhuo and Zhang An-Xue

014202

Wide-band circular polarization-keeping reflection mediated by metasurface Li Yong-Feng, Zhang Jie-Qiu, Qu Shao-Bo, Wang Jia-Fu, Zheng Lin, Zhou Hang, Xu Zhuo and Zhang An-Xue

014203

s-parameterized Weyl transformation and the corresponding quantization scheme Wang Ji-Suo, Meng Xiang-Guo and Fan Hong-Yi

014204

Role of incoherent pumping and Er3+ ion concentration on subluminal and superluminal light propagation in Er3+ -doped YAG crystal Seyyed Hossein Asadpour and H. Rahimpour Soleimani

014205

Macroscopic effects in electromagnetically-induced transparency in a Doppler-broadened system Pei Li-Ya, Niu Jin-Yan, Wang Ru-Quan, Qu Yi-Zhi, Wu Ling-An, Fu Pan-Ming and Zuo Zhan-Chun

014206

A quartz-enhanced photoacoustic spectroscopy sensor for measurement of water vapor concentration in the air Gong Ping, Xie Liang, Qi Xiao-Qiong, Wang Rui, Wang Hui, Chang Ming-Chao, Yang Hui-Xia, Sun Fei and Li Guan-Peng

014207

A 1.7-ps pulse mode-locked Yb3+ :Sc2 SiO5 laser with a reflective graphene oxide saturable absorber Ge Ping-Guang, Su Li-Ming, Liu Jie, Zheng Li-He, Su Liang-Bi, Xu Jun and Wang Yong-Gang

014209

Three-wavelength generation from cascaded wavelength conversion in monolithic periodically poled lithium niobate Xiao Kun, Zhang Jing, Chen Bao-Qin, Zhang Qiu-Lin, Zhang Dong-Xiang, Feng Bao-Hua and Zhang Jing-

014210

Yuan Fluctuations of optical phase of diffracted light for Raman–Nath diffraction in acousto–optic effect Weng Cun-Cheng and Zhang Xiao-Man (Continued on the Bookbinding Inside Back Cover)

014211

Backward Raman amplification in plasmas with chirped wideband pump and seed pulses Wu Zhao-Hui, Wei Xiao-Feng, Zuo Yan-Lei, Liu Lan-Qin, Zhang Zhi-Meng, Li Ming, Zhou Yu-Liang and Su Jing-Qin

014212

Picosecond pulses compression at 1053-nm center wavelength by using a gas-filled hollow-core fiber compressor Huang Zhi-Yuan, Wang Ding, Leng Yu-Xin and Dai Ye

014213

Crosstalk elimination in multi-view autostereoscopic display based on polarized lenticular lens array Wang Zhi-Yuan and Hou Chun-Ping

014214

All-fiber optical modulator based on no-core fiber and magnetic fluid as cladding Chen Yao-Fei, Han Qun and Liu Tie-Gen

014301

Sound field prediction of ultrasonic lithotripsy in water with spheroidal beam equations Zhang Lue, Wang Xiang-Da, Liu Xiao-Zhou and Gong Xiu-Fen

014302

Reception pattern influence on magnetoacoustic tomography with magnetic induction Sun Xiao-Dong, Wang Xin, Zhou Yu-Qi, Ma Qing-Yu and Zhang Dong

014401

Near-field radiative heat transfer in mesoporous alumina Li Jing, Feng Yan-Hui, Zhang Xin-Xin, Huang Cong-Liang and Wang Ge

014501

Stability and Hopf bifurcation of a nonlinear electromechanical coupling system with time delay feedback Liu Shuang, Zhao Shuang-Shuang, Wang Zhao-Long and Li Hai-Bin

014601

A measurement method for distinguishing the real contact area of rough surfaces of transparent solids using improved Otsu technique Song Bao-Jiang, Yan Shao-Ze and Xiang Wu-Wei-Kai

014701

Critical deflagration waves leading to detonation onset under different boundary conditions Lin Wei, Zhou Jin, Fan Xiao-Hua and Lin Zhi-Yong

014702

Partial slip effect on non-aligned stagnation point nanofluid over a stretching convective surface

014703

S. Nadeem, Rashid Mehmood and Noreen Sher Akbar Lattice Boltzmann simulation of liquid vapor system by incorporating a surface tension term Song Bao-Wei, Ren Feng, Hu Hai-Bao and Huang Qiao-Gao PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES

015101

Thermodynamic study of fluid in terms of equation of state containing physical parameters

015202

S. B. Khasare Cylindrical effects in weakly nonlinear Rayleigh Taylor instability Liu Wan-Hai, Ma Wen-Fang and Wang Xu-Lin

015203

Tunable terahertz plasmon in grating-gate coupled graphene with a resonant cavity Yan Bo, Yang Xin-Xin, Fang Jing-Yue, Huang Yong-Dan, Qin Hua and Qin Shi-Qiao CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

016101

Growth of PbS nanoclusters on specific sites of programmed oligodeoxynucleotides Lu Ying, Teng Cui-Juan, Li Ying, Wang Hui, Xu Chun-Hua, Hu Shu-Xin and Li Ming (Continued on the Bookbinding Inside Back Cover)

016102

Mechanism of single-event transient pulse quenching between dummy gate isolated logic nodes Chen Jian-Jun, Chi Ya-Qing and Liang Bin

016201

Electron–acoustic phonon interaction and mobility in stressed rectangular silicon nanowires

016202

Zhu Lin-Li Giant magnetic moment at open ends of multiwalled carbon nanotubes Wang Gang, Chen Min-Jiang, Yu Fang, Xue Lei-Jiang, Deng Ya, Zhang Jian, Qi Xiao-Ying, Gao Yan, Chu Wei-Guo, Liu Guang-Tong, Yang Hai-Fang, Gu Chang-Zhi and Sun Lian-Feng

016401

Effect of far-field flow on a columnar crystal in the convective undercooled melt Ji Xiao-Jian, Chen Ming-Wen, Xu Xiao-Hua and Wang Zi-Dong CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES

017101

Tb doping induced enhancement of anomalous Hall effect in NiFe films Zhu Jia-Peng, Ma Li, Zhou Shi-Ming, Miao Jun and Jiang Yong

017301

Tight-binding electron–phonon coupling and band renormalization in graphene Zhang De-Sheng, Kang Guang-Zhen and Li Jun

017302

Influence of compressive strain on the incorporation of indium in InGaN and InAlN ternary alloys Zhao Yi, Zhang Jin-Cheng, Xue Jun-Shuai, Zhou Xiao-Wei, Xu Sheng-Rui and Hao Yue

017303

Degradation mechanism of enhancement-mode AlGaN/GaN HEMTs using fluorine ion implantation under the on-state gate overdrive stress Sun Wei-Wei, Zheng Xue-Feng, Fan Shuang, Wang Chong, Du Ming, Zhang Kai, Chen Wei-Wei, Cao YanRong, Mao Wei, Ma Xiao-Hua, Zhang Jin-Cheng and Hao Yue

017304

Fano-type resonances induced by a boson mode in Andreev conductance

017305

J. Bara´nski and T. Doma´nski Different charging behaviors between electrons and holes in Si nanocrystals embedded in SiNx matrix by the influence of near-interface oxide traps Fang Zhong-Hui, Jiang Xiao-Fan, Chen Kun-Ji, Wang Yue-Fei, Li Wei and Xu Jun

017401

Applicability of the vortex-glass model for the single crystal Tl0.4 K0.41 Fe1.71 Se2 Yu Yi, Wang Chun-Chang, Wang Hong, Li Qiu-Ju, Zhang Chang-Jin, Pi Li and Zhang Yu-Heng

017402

Field-dependent resistive transitions in YBa2 Cu3 O7−δ thin films: Influence of the pseudogap on vortex dynamics S H Naqib and R S Islam

017403

Effects of pressure and/or magnetism on superconductivity of δ-MoN single crystal Miao Bo-Tong, Wang Shan-Min, Kong Pan-Pan, Jin Mei-Ling, Feng Shao-Min, Zhang Si-Jia, Hao Ai-Min, Yu Xiao-Hui, Jin Chang-Qing and Zhao Yu-Sheng

017501

Electronic, optical properties, surface energies and work functions of Ag8 SnS6 : First-principles method Lu Chun-Lin, Zhang Lin, Zhang Yun-Wang, Liu Shen-Ye and Mei Yang

017502

Effect of CoSi2 buffer layer on structure and magnetic properties of Co films grown on Si (001) substrate Hu Bo, He Wei, Ye Jun, Tang Jin, Syed Sheraz Ahmad, Zhang Xiang-Qun and Cheng Zhao-Hua (Continued on the Bookbinding Inside Back Cover)

017503

High-pressure synthesis, characterization, and equation of state of double perovskite Sr2 CoFeO6 Pan Yue-Wu, Zhu Pin-Wen and Wang Xin

017504

Fine-grained NdFeB magnets prepared by low temperature pre-sintering and subsequent hot pressing Ju Jin-Yun, Tang Xu, Chen Ren-Jie, Wang Jin-Zhi, Yin Wen-Zong, Lee Don and Yan A-Ru

017701

Ferroelectricity in hexagonal YFeO3 film at room temperature Zhang Run-Lan, Chen Chang-Le, Zhang Yun-Jie, Xing Hui, Dong Xiang-Lei and Jin Ke-Xin

017801

Temperature-dependent Raman spectroscopic study of bismuth borate Bi2 ZnOB2 O6 Zhang Ji, Zhang De-Ming, Zhang Qing-Li and Yin Shao-Tang

017802

Ordered silicon nanorod arrays with controllable geometry and robust hydrophobicity Wang Zi-Wen, Cai Jia-Qi, Wu Yi-Zhi, Wang Hui-Jie and Xu Xiao-Liang INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY

018101

Fluctuations of electrical and mechanical properties of diamond induced by interstitial hydrogen Zhuang Chun-Qiang and Liu Lei

018103

Measurement of micro weld joint position based on magneto-optical imaging Gao Xiang-Dong and Chen Zi-Qin

018501

GaSb p-channel metal-oxide-semiconductor field-effect transistor and its temperature dependent characteristics Zhao Lian-Feng, Tan Zhen, Wang Jing and Xu Jun

018502

Preparation of graphene on Cu foils by ion implantation with negative carbon clusters Li Hui, Shang Yan-Xia, Zhang Zao-Di, Wang Ze-Song, Zhang Rui and Fu De-Jun

018503

Excellent acetone sensing properties of porous ZnO Liu Chang-Bai, Liu Xing-Yi and Wang Sheng-Lei

018701

Mechanisms of ultrasonic modulation of multiply scattered incoherent light based on diffusion theory

018702

Zhu Li-Li and Li Hui PET image reconstruction with a system matrix containing point spread function derived from single photon incidence response Fan Xin, Wang Hai-Peng, Yun Ming-Kai, Sun Xiao-Li, Cao Xue-Xiang, Liu Shuang-Quan, Chai Pei, Li DaoWu, Liu Bao-Dong, Wang Lu and Wei Long

018703

Detecting overlapping communities in networks via dominant label propagation Sun He-Li, Huang Jian-Bin, Tian Yong-Qiang, Song Qin-Bao and Liu Huai-Liang

018801

Novel pressure and displacement sensors based on carbon nanotubes Kh. S. Karimov, Khaulah Sulaiman, Zubair Ahmad, Khakim M. Akhmedov and A. Mateen