Relationships between dipole moments of diatomic molecules. Department of Physics, Ocean University of China, Qingdao, Shandong , China 2

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Electronic Supplementary Material (ESI) for Physical Chemistry Chemical Physics. This journal is the Owner Societies 2015 Supplementary Data Relationships between dipole moments of diatomic molecules Shilin Hou 1,2 and Peter F. Bernath 2,* 1 Department of Physics, Ocean University of China, Qingdao, Shandong 266100, China 2 Department of Chemistry and Biochemistry, Old Dominion University, Norfolk, VA 23529, USA * Corresponding author. Email: pbernath@odu.edu Contents Figure S1-S10. Results for each alkali halide molecule from all possible schemes. Page 2- Page 11 Figure S11 Results for GeX (X=O,S,Se,Te). Page 12 Figure S12. Results for the ground states of PbX (X=O,S,Se,Te) Page 13 Figure S13. Results for general molecules from different molecule sets. Page 14 Figure S14. A collection of some results some general molecules from (Δn A,Δn B ) (1,1) schemes. Table S2. Predicted dipole moments from Eqns (3) and (5) for dozens of general molecules. Page 15 Page 16-page 18 Table S3. Dipole moments (in D) for some ground-state molecules. CCSD data are calculated using Gaussian 09 package. Page 19-page 20 Table S4. Data adopted for predicted dipole moments using Eqn (5) for GaCl, InBr, SrCl, SrS, CuCl, and CuBr ground state molecules. Page 21 1 P age

Figure S1. LiF & LiCl. The ( n A, n B )=(4,2) result from Eqn (5) for LiCl, and similar results from nine of the LiF schemes are unphysical. 2 P age

Figure S2. LiBr & LiI 3 P age

Figure S3. KF & NaF. The results from Eqn (5) for ( n A, n B ) = (2,3), (3,2), and (3,3) schemes are unphysical. 4 P age

Figure S4. KCl & NaCl 5 P age

Figure S5. KBr & NaBr 6 P age

Figure S6. KI & NaI 7 P age

Figure S7. CsF & RbF 8 P age

Figure S8. CsCl & RbCl 9 P age

Figure S9. RbBr and CsBr. 10 P age

Figure S10. CsI & RbI 11 P age

Figure S11. Results for GeX(X=O,S,Se,Te). The results for GeTe from Eqn (5) are unphysical. 12 P age

Figure S12. Results for the ground states of PbX (X=O, S, Se, Te). 13 P age

Figure S13. Results for general molecules from different molecule sets. The results for BrCl and GeTe are unphysical. This figure also shows that molecules in the same set with larger polar charges have relative smaller errors. 14 P age

Figure S14. A collection of some results some general molecules from (Δn A,Δn B ) (1,1) schemes. AgF and AgCl can be seemed as exceptions, since H and Ag are not in the same group (but they have kind of similarity in electron configurations and electronegativities). 15 P age

Table S2. Predicted dipole moments from Eqns (3) and (5) for dozens of general molecules. Ref.17 Ref.17 Ref.13 Dipole Dipole (charge=q) (charge=1e) Mole Re/Å Dipole/D q(in e) Eqn(3) (Eqn(3)) % a Eqn(5) (Eqn(5)) % b {AB,AX,BY,XY} (Δn A,Δn B ) SnS 2.20898 3.18 0.780 3.2213 0.0413 1.30 3.1770-0.0030-0.09 SnO PbO SnS PbS (1,1) PbO 1.9218359 4.64 0.970 4.7175 0.0775 1.67 4.6377-0.0023-0.05 SnO PbO SnS PbS (1,1) SnO 1.83251 4.32 0.975 4.2292-0.0908-2.10 4.3226 0.0026 0.06 SnO PbO SnS PbS (1,1) PbS 2.2868898 3.59 0.803 3.5498-0.0402-1.12 3.5925 0.0025 0.07 SnO PbO SnS PbS (1,1) SnO 1.83251 4.32 0.975 4.4224 0.1024 2.37 4.1652-0.1548-3.58 GeO SnO GeS SnS (1,1) SnS 2.20898 3.18 0.780 3.1317-0.0483-1.52 3.3469 0.1669 5.25 GeO SnO GeS SnS (1,1) GeO 1.62464 3.2823 0.887 3.1749-0.1074-3.27 3.5007 0.2184 6.65 GeO SnO GeS SnS (1,1) GeS 2.0120982 2 0.637 2.0369 0.0369 1.84 1.6745-0.3255-16.27 GeO SnO GeS SnS (1,1) GeO 1.62464 3.2823 0.887 3.3133 0.0310 0.94 3.2125-0.0698-2.13 SiO GeO SiS GeS (1,1) SiO 1.50975 3.0982 0.891 3.0620-0.0362-1.17 3.1760 0.0778 2.51 SiO GeO SiS GeS (1,1) GeS 2.0120982 2 0.637 1.9890-0.0110-0.55 2.0896 0.0896 4.48 SiO GeO SiS GeS (1,1) SiS 1.92926 1.73 0.605 1.7407 0.0107 0.62 1.6158-0.1142-6.60 SiO GeO SiS GeS (1,1) SnO 1.83251 4.32 0.975 4.4522 0.1322 3.06 4.1167-0.2033-4.71 SiO SnO SiS SnS (2,1) SnS 2.20898 3.18 0.780 3.1173-0.0627-1.97 3.3964 0.2164 6.80 SiO SnO SiS SnS (2,1) SiO 1.50975 3.0982 0.891 2.9357-0.1625-5.25 3.4177 0.3195 10.31 SiO SnO SiS SnS (2,1) SiS 1.92926 1.73 0.605 1.7766 0.0466 2.69 1.1678-0.5622-32.50 SiO SnO SiS SnS (2,1) PbO 1.9218359 4.64 0.970 4.8308 0.1908 4.11 4.4578-0.1822-3.93 SiO PbO SiS PbS (3,1) PbS 2.2868898 3.59 0.803 3.4890-0.1010-2.81 3.7790 0.1890 5.26 SiO PbO SiS PbS (3,1) SiO 1.50975 3.0982 0.891 2.8217-0.2765-8.93 3.4218 0.3236 10.44 SiO PbO SiS PbS (3,1) SiS 1.92926 1.73 0.605 1.8071 0.0771 4.46 1.1585-0.5715-33.04 SiO PbO SiS PbS (3,1) PbO 1.9218359 4.64 0.970 4.8053 0.1653 3.56 4.5006-0.1394-3.00 GeO PbO GeS PbS (2,1) 16 P age

PbS 2.2868898 3.59 0.803 3.5029-0.0871-2.43 3.7361 0.1461 4.07 GeO PbO GeS PbS (2,1) GeO 1.62464 3.2823 0.887 3.0788-0.2035-6.20 3.5043 0.2220 6.76 GeO PbO GeS PbS (2,1) GeS 2.0120982 2 0.637 2.0683 0.0683 3.42 1.6683-0.3317-16.58 GeO PbO GeS PbS (2,1) PbO 1.9218359 4.64 0.970 4.9433 0.3033 6.54 4.4194-0.2206-4.75 GeO PbO GeSe PbSe (2,2) PbSe 2.4022637 3.28 0.751 3.1498-0.1302-3.97 3.5153 0.2353 7.17 GeO PbO GeSe PbSe (2,2) GeO 1.62464 3.2823 0.887 2.8919-0.3904-11.89 3.6245 0.3422 10.43 GeO PbO GeSe PbSe (2,2) GeSe 2.1346561 1.65 0.567 1.7401 0.0901 5.46 0.9610-0.6890-41.76 GeO PbO GeSe PbSe (2,2) PbO 1.9218359 4.64 0.970 5.0607 0.4207 9.07 4.2193-0.4207-9.07 GeO PbO GeTe PbTe (2,3) PbTe 2.595006 2.73 0.662 2.6068-0.1232-4.51 3.1958 0.4658 17.06 GeO PbO GeTe PbTe (2,3) GeO 1.62464 3.2823 0.887 2.7182-0.5641-17.19 3.8964 0.6141 18.71 GeO PbO GeTe PbTe (2,3) GeTe 2.3401928 1.06 0.435 1.1225 0.0625 5.89 Unphysical - GeO PbO GeTe PbTe (2,3) PbS 2.2868898 3.59 0.803 3.6634 0.0734 2.04 3.5042-0.0858-2.39 GeS PbS GeSe PbSe (2,1) PbSe 2.4022637 3.28 0.751 3.2204-0.0596-1.82 3.3672 0.0872 2.66 GeS PbS GeSe PbSe (2,1) GeS 2.0120982 2 0.637 1.9392-0.0608-3.04 2.1661 0.1661 8.31 GeS PbS GeSe PbSe (2,1) GeSe 2.1346561 1.65 0.567 1.6923 0.0423 2.56 1.4388-0.2112-12.80 GeS PbS GeSe PbSe (2,1) PbS 2.2868898 3.59 0.803 3.7263 0.1363 3.80 3.2904-0.2996-8.35 GeS PbS GeTe PbTe (2,2) PbTe 2.595006 2.73 0.662 2.6546-0.0754-2.76 3.0446 0.3146 11.52 GeS PbS GeTe PbTe (2,2) GeS 2.0120982 2 0.637 1.8845-0.1155-5.78 2.5185 0.5185 25.93 GeS PbS GeTe PbTe (2,2) GeTe 2.3401928 1.06 0.435 1.0990 0.0390 3.68 Unphysical - GeS PbS GeTe PbTe (2,2) PbSe 2.4022637 3.28 0.751 3.3312 0.0512 1.56 3.0619-0.2181-6.65 GeSe GeTe PbSe PbTe (2,1) PbTe 2.595006 2.73 0.662 2.6951-0.0349-1.28 2.9552 0.2252 8.25 GeSe GeTe PbSe PbTe (2,1) GeSe 2.1346561 1.65 0.567 1.6122-0.0378-2.29 2.0685 0.4185 25.36 GeSe GeTe PbSe PbTe (2,1) GeTe 2.3401928 1.06 0.435 1.0784 0.0184 1.73 Unphysical - GeSe GeTe PbSe PbTe (2,1) InF 1.9854 3.4 0.738 3.3700-0.0300-0.88 3.2110-0.1890-5.56 InF TlF InCl TlCl (1,1) TlCl 2.48483 4.54299 0.766 4.5223-0.0207-0.46 4.4318-0.1112-2.45 InF TlF InCl TlCl (1,1) 17 P age

TlF 2.08439 4.2282 0.799 4.2595 0.0313 0.74 4.3667 0.1385 3.27 InF TlF InCl TlCl (1,1) InCl 2.40117 3.79 0.713 3.8092 0.0192 0.51 3.9239 0.1339 3.53 InF TlF InCl TlCl (1,1) IF 1.90976 1.948 0.593 2.0677 0.1197 6.14 1.8519-0.0961-4.93 BrF IF BrCl ICl (1,1) ICl 2.32088 1.24 0.447 1.1872-0.0528-4.26 1.3557 0.1157 9.33 BrF IF BrCl ICl (1,1) BrF 1.75894 1.422 0.510 1.3174-0.1046-7.36 1.5551 0.1331 9.36 BrF IF BrCl ICl (1,1) BrCl 2.13607 0.519 0.295 0.5439 0.0249 4.81 Unphysical - BrF IF BrCl ICl (1,1) LiRb 3.46615 * 4 0.441 4.1071 0.1071 2.68 3.7428-0.2572-6.43 LiK LiRb NaK NaRb (1,1) LiK 3.27 3.45 0.407 3.3520-0.0980-2.84 3.7435 0.2935 8.51 LiK LiRb NaK NaRb (1,1) NaRb 3.6435 # 3.1 0.376 3.0288-0.0712-2.30 3.3918 0.2918 9.41 LiK LiRb NaK NaRb (1,1) NaK 3.49958 2.693 0.354 2.7581 0.0651 2.42 2.2978-0.3952-14.68 LiK LiRb NaK NaRb (1,1) AgF 1.983203 6.22 0.975 6.6473 0.4273 6.87 6.5777 0.3577 5.75 HF HCl AgF AgCl AgCl 2.280819 6.08 0.923 5.7555-0.3245-5.34 5.7433-0.3367-5.54 HF HCl AgF AgCl HCl 1.2745717 1.1086 0.441 1.2605 0.1519 13.70 2.8900 1.7814 160.69 HF HCl AgF AgCl HF 0.91682 1.82653 0.610 1.2284-0.5981-32.75 Unphysical - HF HCl AgF AgCl a %=[Dipole(Eqn (3))-Diploe(exp.)]/Diploe(exp) 100%. b %=[Dipole(Eqn (5))-Diploe(exp.)]/Diploe(exp) 100% * M. Ivanova, A. Stein, A. Pashov, H. Knöckel, and E. Tiemann, The X 1 Σ + state of LiRb studied by Fourier-transform spectroscopy, J. Chem. Phys. 134, 024321 (9pp) (2011) # S. Kasahara, T. Ebi, M. Tanimura, H. Ikoma, K. Matsubara, M. Baba, and H. Kato, High-resolution laser spectroscopy of the X 1 Σ + and (1) 3 Σ + states of 23 Na 85 Rb molecule, J. Chem. Phys. 105, 1341-1347 (1996) 18 P age

Table S3. Dipole moments (in D) for some ground-state molecules. CCSD data are calculated using Gaussian 09 package. 18 All experimental data involved in Eqn (5) are from Ref. 17. AB Exp. 17 CCSD/ 6-311++G(3df) /D a Eqn (5) /D b Scheme (Δn A,Δn B ) LiCl 7.12887 7.2326 0.10 6.9604-0.17 {LiBr+NaCl-NaBr} (1,1) NaCl 9.00117 9.2876 0.29 9.1133 0.11 {NaBr+LiCl-LiBr} (1,1) KCl 10.269 10.6485 0.38 10.2312-0.04 {KBr+RbCl-RbBr} (1,1) LiBr 7.268 7.4029 0.13 7.4184 0.15 {LiCl+NaBr-NaCl} (1,1) NaBr 9.1183 9.4559 0.34 9.0126-0.11 {NaCl+LiBr-LiCl} (1,1) KBr 10.628 11.0439 0.42 10.6624 0.03 {KCl+RbBr-RbCl} (1,1) BrF 1.422 1.4405 0.02 1.5551 0.13 {BrCl+IF-ICl} (1,1) NaK 2.693 2.7862 0.09 2.2978-0.40 {NaRb+LiK-LiRb} (1,1) LiK 3.45 3.8859 0.44 3.7435 0.29 {LiRb+NaK-NaRb} (1,1) SiS 1.73 1.7733 0.04 1.6158-0.11 {SiO+GeS-GeO} (1,1) SiO 3.0982 3.2492 0.15 3.1760 0.08 {SiS+GeO-GeS} (1,1) GeO 3.2823 3.5904 0.31 3.2125-0.07 {GeS+SiO-SiS} (1,1) GeS 2 2.223 0.22 2.0896 0.09 {GeO+SiS-SiO} (1,1) GeSe 1.65 1.8784 0.23 1.4388-0.21 {GeS+PbSe-PbS} (2,1) IF 1.948 1.8519-0.10 {ICl +BrF -BrCl} (1,1) ICl 1.24 1.3557 0.12 {IF +BrCl -BrF} (1,1) LiRb 4 3.7428-0.26 {LiK+NaRb-NaK} (1,1) NaRb 3.1 3.3918 0.29 {NaK+LiRb-LiK} (1,1) CsBr 10.82 10.7197-0.10 {CsCl+RbBr-RbCl} (1,1) RbBr 10.86 10.8277-0.03 {RbCl+KBr-KCl} (1,1) CsCl 10.387 10.4964 0.11 {CsBr +RbCl-RbBr} (1,1) RbCl 10.51 10.5452 0.04 {RbBr+KCl-KBr} (1,1) RbI 11.5 11.7775 0.28 {RbBr+CsI-CsBr} (1,1) CsI 11.69 11.4221-0.27 {CsBr+RbI-RbBr} (1,1) NaI 9.236 9.1165-0.12 {NaBr+LiI -LiBr} (1,1) KI 10.8 10.5912-0.21 {KBr+NaI -NaBr} (1,1) LiI 7.428 7.5934 0.17 {LiBr+NaI-NaBr} (1,1) InF 3.4 3.2110-0.19 {InCl +TlF -TlCl} (1,1) TlCl 4.54299 4.4318-0.11 {TlF +InCl -InF} (1,1) TlF 4.2282 4.3667 0.14 {TlCl +InF -InCl} (1,1) InCl 3.79 3.9239 0.13 {InF +TlCl -TlF} (1,1) SnS 3.18 3.1770-0.01 {SnO+PbS-PbO} (1,1) PbO 4.64 4.6377-0.01 {PbS+SnO-SnS} (1,1) 19 P age

SnO 4.32 4.3226 0.01 {SnS+PbO-PbS} (1,1) PbS 3.59 3.5925 0.01 {PbO+SnS-SnO} (1,1) PbSe 3.28 3.3672 0.09 {PbS+GeSe-GeS} (2,1) PbTe 2.73 2.9552 0.23 {PbSe+GeTe-GeSe} (2,1) Average c 0.23 0.14 a =Dipole(CCSD)-Diploe(exp). b =Dipole(Eqn (5))-Diploe(exp). c The mean absolute deviation. 20 P age

Table S4. Data adopted for predicted dipole moments using Eqn (5) for GaCl, InBr, SrCl, SrS, CuCl, and CuBr ground state molecules. All experimental data are from Ref. 17 except those indicated. The atomic charges are also presented for references. AB R e /Å µ d /D (Predicted) BY Re/Å µ d /D q(e) AX Re/Å µ d /D q(e) XY µ d /D Re/Å q(e) GaCl 2.20169 3.17469 InCl 2.40117 3.79 0.71 GaF 1.77437 2.45 0.76 InF 1.9854 3.4 0.74 InBr 2.54315 3.761849 Tl 81 Br 2.61817 4.49 0.75 InCl 2.40117 3.79 0.71 TlCl 2.48483 4.54299 0.77 SrCl 2.575848 a 3.847601 CaCl 2.43676 3.6 0.69 SrF 2.074685 3.4676 0.72 CaF 1.951639 3.07 0.69 SrS 2.441 b 11.54003 BaS 2.5074 10.86 1.32 SrO 1.91983 8.9 1.25 BaO 1.939712 7.954 1.22 CuCl 2.05118 5.658725 AgF 1.983203 6.22 0.97 CuF 1.744951 5.77 0.98 AgCl 2.280819 6.08 0.92 CuBr 2.17344 5.203706 AgCl 2.280819 6.08 0.92 CuCl 2.05118 5.74 c ~0.92 AgBr 2.393138 5.62 0.88 a From Ref. 19. b From Ref. 20. c. Theoretical data from Ref.13. 21 P age