Theoretical investigations on structure, electrostatic potentials and vibrational frequencies of diglyme and Li+–(diglyme) conformers

31 August 2001

Chemical Physics Letters 344 (2001) 527±535

www.elsevier.com/locate/cplett

Theoretical investigations on structure, electrostatic potentials and vibrational frequencies of diglyme and Li‡±…diglyme† conformers Shridhar P. Gejji *, Shridhar R. Gadre, Vishal J. Barge Department of Chemistry, University of Pune, Pune 411 007, India Received 21 May 2001; in ®nal form 5 July 2001

Abstract The trends for cation binding for several conformers of diglyme are predicted by mapping the topography of the molecular electrostatic potential (MESP) at the Hartree±Fock (HF) level. Di€erent Li‡ ±…diglyme† geometries derived by exploiting the MESP cooperative e€ects are used subsequently in ab initio computations. The binding energies for Li‡ with diglyme have been calculated in mono-, bi- and tridentate coordinations by employing the HF, second-order Mùller±Plesset (MP2) and the hybrid density functional methods. The calculated vibrational spectrum of Li‡ ±…diglyme† also points to a gauche conformation of diglyme in the complex. Ó 2001 Elsevier Science B.V. All rights reserved.

1. Introduction The oligomers of poly(ethylene oxide) represented by the formula H3 CO±…CH2 ±CH2 ±O†n ±CH3 complexed with the lithium salts like LiCF3 SO3 [1] or Li…CF3 SO2 †2 N [2,3] have been of great interest in the recent literature. These solid polymer electrolytes show high ionic conductivity facilitating their use in solid state batteries or electrochromic devices [4]. One of the key factors governing this ionic conductivity being cation± polymer interaction which in turn results in polymer segmental motion. With this view, the recent studies have focused on investigating the Li‡ ±…diglyme† complexes at molecular level using the ab initio quantum chemical methods. Confor-

*

Corresponding author. Fax: +91-020-565-1728. E-mail address: [email protected] (S.P. Gejji).

mational changes in diglyme as well as in PEO induced by lithium tri¯uoromethanesulfonate …LiCF3 SO3 † have been probed by Frech and Huang [5] using Raman scattering and infrared transmission spectroscopy. They concluded that for diglyme complexed with LiCF3 SO3 , new CH2 bending vibrations appear at higher frequencies, which increase in intensities with the increasing salt concentration. The elementary steps in lithium ion transport along a PEO chain have been modeled with the quantum chemical calculations in the recent literature [6]. Ab initio studies of the potential energy surface of diglyme [7] and further the cation migration between one- and two- and also two- and three-coordination sites in Li‡ ±…diglyme† complexes [8] have been reported. The barrier for the lithium cation migration from lower to higher coordination was predicted to be less than 2 kcal mol 1 as compared to 20± 30 kcal mol 1 when the cation transfers from

0009-2614/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 ( 0 1 ) 0 0 8 2 4 - 7

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higher to lower coordination. Very recently Curtiss and coworkers [9] have studied lithium ion migration in Li‡ ±…diglyme†2 and LiClO4 ±…diglyme† complexes and the binding energies of the Li‡ ±…diglyme† and Li‡ ±…diglyme†2 have been predicted to range from 44 to 121 kcal mol 1 . Ab initio molecular orbital calculations for Li‡ ±…diglyme†n (n ˆ 4 to 6) complexes reported by Lindgren and coworkers [10] suggest that the average coordination number for lithium in these complexes and in the PEO chain as well, is 5 when no counteranion is present. The anity of Li‡ towards anions such as CF3 SO3 , …CF3 SO2 †2 N and …CF3 SO2 †2 CH arises mainly due to the electrostatic e€ects and contributions from the charge-transfer interactions are less important [11]. Thus it felt worthwhile to probe the role of electrostatic potential as a tool for understanding the cation coordination in the Li‡ ±…diglyme† complexes. The scalar ®eld of the molecular electrostatic potential (MESP) has been widely used for studying a variety of intermolecular interactions [12±28]. The use of MESP as a harbinger to cation coordination with the tri¯ate CF3 SO3 ion has recently been demonstrated by Gejji et al. [29]. In a pursuit of these issues, we herein address the following questions: How can the topographical features of the MESP be utilized to predict the stabilities and binding energies in Li‡ ±…diglyme† complexes? Are the variations in the C±C±O±C±C framework of the all-trans diglyme conformer manifested in its vibrational spectrum? How is the vibrational spectrum of the gauche diglyme conformer altered on lithium cation coordination? The computational method has been outlined in the following section. 2. Computational method The equilibrium geometry of diglyme in the alltrans conformation was derived from the ab initio Hartree±Fock (HF) theory using the GA U S S I A N 94 program [30] by employing the internally stored 6-31G(d, p) basis set. Di€erent conformers of diglyme were generated by either a single C±C or C±O bond rotation or by simultaneous rotations around the central C±C as well as C±O bonds of

all-trans conformer. Geometry optimizations of these rotamers were performed and the vibrational frequencies were computed subsequently. Further the MESP for these conformers was generated using the ab initio HF wavefunction. The MESP, V …r†, at a point r due to a molecular system with nuclear charges fZA g located at fRA g and electron density q…r† is given by Z N X ZA q…r0 † d3 r0 V …r† ˆ ; …1† jr RA j jr r0 j Aˆ1 where N is the total number of nuclei in the molecule. The MESP comprises of the bare nuclear potential and electronic contributions represented by the ®rst and second terms of Eq. (1) respectively. The V …r† was calculated at the HF/631G(d, p) level of theory 1 and its topographical features [13±15] were studied to obtain the MESP critical points. At a critical point (CP), the ®rstorder partial derivatives of a function with respect to all its dependent variables vanish. A non-degenerate CP of MESP can be characterized according to its rank and signature as …3; 3†, …3; 1†, …3; ‡1† and …3; ‡3†. The …3; 3† CP refers to a (local) maximum while the …3; 1† and …3; ‡1† CPs correspond to a saddle point. Similarly, a CP of type …3; ‡3† stands for a local minimum. The lithium cation was then placed in the neighborhood of the deepest MESP minimum of the corresponding diglyme conformers and the structures of Li‡ ±…diglyme† were reoptimized. Out of 12 Li‡ ±…diglyme† conformers thus obtained, the HF optimizations ®nally converged to seven different local minima as characterized by a frequency run. These conformers were subsequently subjected to optimization with the second-order Mùller±Plesset (MP2) theory and the hybrid density functional method employing the Becke's three-parameter functional due to Lee, Yang and Parr (B3LYP) [32,33]. Vibrational frequencies were calculated with the HF and B3LYP methods only. The assignments to normal vibrations were carried out by visualizing the displacements of 1 UNIPROP, The molecular property calculation package developed at the Department of Chemistry, University of Pune, Pune (India). See [31].

S.P. Gejji et al. / Chemical Physics Letters 344 (2001) 527±535

529

Fig. 1. MESP isosurface of 36:4 kcal mol 1 for diglyme conformers obtained from the HF/6-31G(d, p) theory. Here mi and si denote the CPs, which are minima and saddles, respectively.

atoms around their equilibrium position through the program UN I V I S -2000. 2 The HF, B3LYP and MP2 interaction energies were obtained for these Li‡ ±…diglyme† complexes. In the following section, we present these results for diglyme and the Li‡ ±…diglyme† complexes. 3. Results and discussion The optimized geometries of di€erent diglyme conformers from the HF theory are displayed in 2 The package UN I V I S -2000 developed at the Department of Chemistry, University of Pune. See [19].

Fig. 1 along with the V ˆ 36:4 kcal mol 1 MESP iso-surface. The conformers are denoted as `g' for gauche or `t' as trans around the C±C, C±O, O±C and C±C bonds of the central C±C±O±C±C linkage, respectively. The g‡ and g denote gauche conformers around the C±C bonds in opposite directions. Thus the notation g±t±t±g denotes gauche conformation around the C±C bonds and trans for the C±O bonds. It may be noticed from Fig. 1 that the volume enclosed by the MESP iso-surface is relatively large for the conformers g‡ ±t±t±g (3a) and g ±g ±t±g (6a) than the others. The MESP minima …mi † and saddle points …si † have been reported in Table 1. For the 3a and 6a conformers

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S.P. Gejji et al. / Chemical Physics Letters 344 (2001) 527±535

Table 1 MESP values …kcal mol 1 † at the critical points (minima and saddles) in di€erent diglyme conformers CP

1a

2a

3a

4a

5a

6a

7a

1b

2b

m1 m2 m3 m4 m5 m6 s1 s2 s3 s4 s5

)51.77 )51.77 )47.70 )47.70 )51.77 )51.77 )51.52 )47.20 )51.52

)50.20 )61.50 )63.38

)65.26 )67.77 )65.26

)53.09 )53.08 )56.47

)48.32 )46.43 )65.26 )64.01

)64.63 )67.14 )63.37

)54.90 )54.90 )60.62 )63.31

)56.47 )55.85 )56.47 )55.85 )51.45

)10.67 )52.08

)54.60 )54.60

)53.02 )37.65

)45.18 )21.96 )53.34

)53.34 )52.08

)54.78 )36.40 )50.32

)54.78 )54.97 )54.97 )54.97 )54.97 )54.78 )54.78 )35.58 )54.78 )35.58 )54.78

)55.85 )35.77

Please refer to Fig. 1.

stronger cation binding has been predicted from the deepest MESP minima. The MESP minima therefore serve as the potent sites of cation coordination [29]. As pointed out in Section 2, the Li‡ ion was placed in the vicinity of the deepest minima and these geometries were subjected to subsequent optimization using HF followed by the B3LYP as well as MP2 methods. In Fig. 2, the HF optimized geometries of the Li‡ ±…diglyme† complexes with tri-, bi- and monodentate coordinations are depicted. The diglyme conformers 3a, 6a and 7a on Li‡ coordination engender tridentate T1 , T2 and T3 Li‡ ±…diglyme† complexes, whereas the 5a, 2a and 4a conformers yield the bidentate B1 , B2 and B3 complexes, respectively. It should be noted here that the diglyme conformers exhibiting deeper MESP minima provide a better initial geometry for the Li‡ ±…diglyme† complexes in subsequent ab initio optimizations reducing the computational time signi®cantly. The relative stabilization energies for the Li‡ ±…diglyme† complexes reported in Table 2 show that the energy di€erence of the T1 and T2 conformers is 1:88 kcal mol 1 for the HF method, which reduced further to 1:61 kcal mol 1 at the MP2 level which incorporates electron correlation e€ects. The calculated energy di€erence from the MP2 theory is in excellent agreement with the B3LYP predicted one. Selected geometrical parameters for the tri- and bidentate complexes are presented in Tables 3 and 4, respectively. As may be noticed from Table 3, the C±O bond lengths from the  longer than B3LYP and MP2 theories are 0.023 A

the corresponding HF ones. The bond angles as well as the dihedral angles from the HF theory agree well, within 4°, when compared to their B3LYP or MP2 counterparts. Similar conclusions may be drawn in the bidentate Li‡ ±…diglyme† complexes (Table 4). For the monodentate …M1 † complex in the HF theory, Li‡ lies in the O±C±C plane. This structure turns out to be a transition state. On the other hand B3LYP optimization of the same leads to a local minimum, wherein Li‡ lies 19° below the O±C±C plane. The binding energies …DE…Li‡ ±diglyme† † de®ned by DE…Li‡ ±diglyme† ˆ E…Li‡ ±diglyme†

…ELi‡ ‡ Ediglyme † ‡

…2†

for the tri-, bi- and monodentate Li ±…diglyme† complexes have been reported in Table 5 along with the corresponding ZPE corrected values in the parentheses. The B3LYP values generally show an improvement over the HF ones and compare well with the corresponding MP2 values for the low lying energy conformers. The binding energies follow the trend: tri > bi > mono. This is consistent with the inferences drawn from the MESP topography as discussed earlier. In what follows, we discuss the vibrational spectra of diglyme and Li‡ ±…diglyme† complex. The energy di€erence between the all-trans and the g‡ ±t±t±g diglyme conformers within the HF theory is 3:13 kcal mol 1 . For the MP2 and B3LYP framework this di€erence is reduced to 1:3 kcal mol 1 . The variation in the C±C±O±C±C backbone of the all-trans diglyme conformer manifests in the vibrational spectrum. It, therefore, may

S.P. Gejji et al. / Chemical Physics Letters 344 (2001) 527±535

531

Fig. 2. HF/6-31G(d, p) optimized geometries for Li‡ ±…diglyme† complexes.

be worthwhile to compare the predicted vibrational spectra of g‡ ±t±t±g and the all-trans diglyme conformer. The B3LYP vibrational frequencies in 827±1495 cm 1 region for the all-trans and the g‡ ±t±t±g conformer are displayed in Table 6 along

with those for the tridentate Li‡ ±…diglyme† complex. These are scaled by a factor of 0.9613 [34]. It should be noted here that the CH2 wagging vibrations in 827±852 cm 1 region of the g‡ ±t± t±g diglyme conformer and the tridentate

Table 2 Relative stabilization …kcal mol 1 † of the Li‡ ±…diglyme† complexes Method used

T1

HF

0.0

1.88 (1.92)

B3LYP

0.0

MP2 (full)

0.0

T2

T3

B1

B2

B3

M1

5.13 (5.06)

18.25 (17.79)

18.52 (17.96)

21.07 (20.26)

46.47 (44.55)

1.61 (1.65)

4.67 (4.62)

18.03 (17.53)

18.32 (17.74)

21.53 (20.62)

47.34 (45.44)

1.59

4.89

19.60

19.92

23.87

51.04

The ZPE corrected values are given in parentheses. The HF, B3LYP and MP2 energies (a.u.) for the T1 conformer are )467.29166, )470.13542 and )468.73903, respectively.

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Table 3 Geometrical parameters for the tridentate Li‡ ±…diglyme† complexes optimized at di€erent levels of theory using the 6-31G(d, p) basis set Geometrical Parameters

HF

B3LYP T2

T1

T3

T1

MP2 (full) T2

T3

d…O1 ±Li† d…O2 ±Li† d…C3 ±O2 † d…C2 ±C3 † \…C3 ±O2 ±C4 † \…C2 ±C3 ±O2 † \…Li±O2 ±C4 ±C5 †

1.937 1.933 1.939 1.923 1.920 1.927 1.919 1.932 1.922 1.918 1.935 1.927 1.413 1.417 1.417 1.436 1.441 1.441 1.513 1.519 1.519 1.518 1.524 1.524 117.8 118.1 121.5 116.6 116.7 119.8 106.5 110.2 110.3 106.4 110.6 111.0 41.7 45.6 28.0 42.4 47.2 26.3  and the bond angles …\† and dihedral angles …\† are in degrees. The bond lengths (d) are in A

T1

T2

T3

1.933 1.933 1.436 1.508 115.2 105.7 44.3

1.932 1.953 1.441 1.514 115.0 110.2 48.5

1.938 1.950 1.440 1.514 118.0 111.0 28.3

Table 4 Geometrical parameters for the bidentate Li‡ ±…diglyme† complexes optimized at di€erent levels of theory using the 6-31G(d, p) basis set Geometrical Parameters

HF

B3LYP

B1

B2

B3

B1

MP2 (full) B2

B3

d…O1 ±Li† d…O2 ±Li† d…C3 ±O2 † d…O2 ±C4 † d…C2 ±C3 † d…C4 ±C5 † \…C2 ±O2 ±C4 † \…C2 ±C3 ±O2 † \…O2 ±C4 ±C5 † \…Li±O2 ±C4 ±C5 †

1.874 1.874 1.876 1.865 1.865 1.870 1.867 1.869 1.880 1.857 1.861 1.869 1.429 1.428 1.420 1.454 1.452 1.442 1.429 1.429 1.427 1.453 1.451 1.446 1.512 1.513 1.513 1.515 1.517 1.518 1.512 1.511 1.515 1.517 1.516 1.523 116.3 117.6 114.8 114.9 116.0 114.1 108.0 107.7 108.2 107.8 107.6 107.8 111.7 113.0 108.6 112.7 113.3 108.1 108.7 83.7 38.3 125.6 75.0 39.5  The bond lengths (d) are in A and the bond angles …\† and dihedral angles …\† are in degrees.

B1

B2

B3

1.898 1.875 1.453 1.448 1.504 1.508 114.2 107.1 110.5 97.7

1.889 1.881 1.451 1.449 1.507 1.507 115.2 106.9 112.8 81.6

1.893 1.892 1.442 1.446 1.507 1.512 112.8 107.2 107.7 42.2

Table 5 Binding energies …DE† …kcal mol 1 † for the various tri-, bi- and monodentate Li‡ ±…diglyme† complexes Method used

T1

T2

T3

B1

B2

B3

M1

HF

)90.34 ()88.47) )92.63 ()89.39) )95.37

)90.02 ()88.05) )92.27 ()89.09) )93.41

)88.94 ()86.39) ) 90.84 ()88.14) )92.11

)71.51 ()69.06) )73.77 ()71.24) )75.05

)72.69 ()70.38) )74.64 ()72.25) )74.27

)70.05 ()68.20) )72.33 ()70.39) )70.57

)40.73 ()38.54) )44.06 ()42.81) )43.03

B3LYP MP2 (full)

The ZPE corrected values are given in parentheses.

Li‡ ± …diglyme† complex are strongly coupled. For the all-trans diglyme conformer, however, these relatively pure vibrations have been predicted to be at 804 and 813 cm 1 . The rotations around the C±C bonds in the all-trans diglyme conformer give rise to a new band at 850 cm 1 . Lindgren and coworkers [10] have analyzed the vibrational spectra of

H3 C±…O± CH2 ±CH2 †n ±OCH3 for 4 6 n 6 6, coordinating with Li‡ at the HF level using the lower 321G basis set. These authors have pointed out that such a vibration (850 cm 1 ) resembles the `breathing' mode of a PEO chain solvating a lithium cation, which adopts a `conformation similar to crown-ether'. Present studies reveal that 852 cm 1

S.P. Gejji et al. / Chemical Physics Letters 344 (2001) 527±535

533

Table 6 B3LYP scaled vibrational frequencies …cm 1 † for the all-trans (1a) and gauche (3a) diglyme conformers and the Li‡ ±…diglyme† complex …T1 † Assignment

1a

3a

T1

CH2 wag ‡ C±O str ‡ C±C str

827 (15) 830 (3)

802 (9) 810 (18)

CH2 wag ‡ CO±C bend ‡ C±O str ‡ C±C str C±C str ‡ CH2 wag C±O str C±C str ‡ C±O str C±O str ‡ C±C str C±C str C±C str ‡ C±O±C bend

852 (86) 925 (16)

848 (32) 921 (13)

1020 (7) 1058 (15)

981 (51) 991 (1)

CH2 wag

804 (0) 813 (0)

940 (86) 1006 (0) 1028 (0) 1078 (4)

C±O str

1124 (64) 1134 (2) 1137 (479)

1113 (295) 1129 (118) 1142 (15)

1042 (257) 1065 (296) 1098 (74)

CH3 rock ‡ C±O str

1184 (122)

1186 (49)

1176 (12)

1214 1224 1258 1265

(14) (25) (14) (19)

1210 (2) 1223 (24) 1240 (7) 1251 (6)

CH2 wag

1187 (0)

1198 (19) 1248 (0) 1249 (0) CH2 rock

1297 (60) 1328 (10) 1389 (4) 1416 (0)

1335 (94) 1361 (27) 1381 (0) 1410 (9)

1330 (39) 1358 (12) 1373 (0) 1401 (2)

CH2 scissor

1472 (12) 1486 (0) 1495 (0)

1448 (22)

1451 1454 1468 1473

1474 (1) 1475 (0)

(7) (3) (5) (4)

The ZPE corrected values are given in parentheses.

vibration occurs in the gauche diglyme conformer as well and further remains unaltered on Li‡ coordination. The C±C stretching vibrations at 1028 and 1078 cm 1 of the all-trans conformer show a red shift of 103 and 58 cm 1 , respectively, with reference to the gauche conformer. These are coupled with CH2 wagging and C±O stretchings. Further the 940 cm 1 vibration in the all-trans diglyme conformer is not present in the gauche conformer. Two intense bands assigned as C±O stretchings at 1113 and 1129 cm 1 have been noted for the gauche conformer. However, only a single, very intense vibration (C±O stretching of the central C±O±C

framework) is seen at 1137 cm 1 for the all-trans conformer. This has been correlated with the 1142 cm 1 weak band of the T1 conformer. The O±Li‡ stretching vibrations in the tridentate Li‡ ±…diglyme† complex are noticed at 469 and 568 cm 1 . From the measurements of the infrared and Raman spectra of diglyme and diglyme±LiCF3 SO3 , Frech and Huang [5] concluded that a relatively strong CH2 bending vibration of pure diglyme disappears on cation coordination. They also noted that new bands appear at higher frequencies, with varying intensities for di€erent salt concentrations. Assignments

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S.P. Gejji et al. / Chemical Physics Letters 344 (2001) 527±535

of the normal vibrations presented in [5] are qualitatively di€erent than what we present herewith. The near doublet at 1113 and 1129 cm 1 in the gauche diglyme conformer are assigned to C±O stretchings and on Li‡ coordination the separation of these two bands increases from 16 to 23 cm 1 . The 1129 cm 1 vibration becomes more intense on cation coordination. It may be inferred from Table 6 that the bands corresponding to CH2 wagging vibrations fall in the range 1211±1278 cm 1 , while the CH2 rocking vibrations are noted in 1327±1403 cm 1 . Frech and Huang [5], however, have assigned the CH2 rocking vibrations (coupled with C±O stretchings) in 850±932 cm 1 region. It should be noted here that the vibrational spectrum of the T1 complex overall resembles to the gauche diglyme than the all-trans conformer. This suggests that lithium cation binds preferably to the g‡ ±t±t±g diglyme conformer to form the lowest energy Li‡ ±…diglyme† complex, which has been predicted a priori through the MESP topography of the diglyme conformers.

4. Concluding remarks In summary, the MESP topography presents a systematic way for deriving the equilibrium geometries of the Li‡ ±…diglyme† complexes. The qualitative predictions of the binding energies through MESP are supported by the subsequent ab initio HF, B3LYP and MP2 computations. This approach may be extended further for analyzing the cation binding patterns of higher PEO oligomers (glymes) or other ¯exible molecules. Rotations around the C±C bonds in the all-trans diglyme conformer result in disappearance of the C±O stretching vibration at 940 cm 1 as seen in the gauche conformation. The normal vibrations in the gauche conformer, in general, have more strong coupling from the CH2 bending and C±O stretching internal coordinates as compared to the all-trans conformer. The separation of intense bands at 1113 and 1129 cm 1 (C±O stretching) in the gauche diglyme conformer increases from 16 to 23 cm 1 on coordination with Li‡ .

Acknowledgements SPG and SRG, respectively, acknowledge the support from the University Grants Commission [F. 12-37/97 (SR-I)], New Delhi, and Centre for Development of Advanced Computing (C-DAC), Pune. References [1] S.P. Gejji, K. Hermansson, J. Tegenfeldt, J. Lindgren, J. Phys. Chem. 97 (1993) 11402. [2] S.P. Gejji, C.H. Suresh, K. Babu, S.R. Gadre, J. Phys. Chem. A 103 (1999) 7474. [3] L. Rey, P. Johansson, J. Lindgren, J.C. Lassegues, J. Grondin, L. Servant, J. Phys. Chem. A 102 (1998) 3249. [4] M.B. Armand, Ann. Rev. Mater. Sci. 16 (1986) 245. [5] R. Frech, W. Huang, Macromolecules 28 (1995) 1246. [6] P. Johansson, J. Tegenfeldt, J. Lindgren, J. Phys. Chem. A 102 (1998) 4660. [7] A. Sutjianto, L.A. Curtiss, Chem. Phys. Lett. 264 (1997) 127. [8] A. Sutjianto, L.A. Curtiss, J. Phys. Chem. A 102 (1998) 968. [9] A.G. Baboul, P.C. Redfern, A. Sutjianto, L.A. Curtiss, J. Am. Chem. Soc. 121 (1999) 7220. [10] P. Johansson, J. Tegenfeldt, J. Lindgren, Polymer 40 (1999) 4399. [11] R. Arnaud, D. Benrabah, J.Y. Sanchez, J. Phys. Chem. 100 (1996) 10882. [12] S.R. Gadre, P.K. Bhadane, S.S. Pundlik, S.S. Pingale, in: J.A. Murray, K. Sen (Eds.), Molecular Electrostatic Potentials: Concepts and Applications, Elsevier, Amsterdam, 1996, p. 219. [13] S.R. Gadre, I.H. Shrivastava, J. Chem. Phys. 94 (1991) 4384. [14] S.R. Gadre, S.A. Kulkarni, I.H. Shrivastava, J. Chem. Phys. 96 (1992) 5253. [15] S.R. Gadre, C. K olmel, M. Ehrig, R. Ahlrichs, Z. Naturforsch 48a (1993) 145. [16] A.C. Legon, D.J. Millen, Chem. Soc. Rev. 16 (1987) 467. [17] C.E. Dykstra, J. Am. Chem. Soc. 111 (1989) 6168. [18] C. Alhabama, F.J. Luque, M. Orozco, J. Phys. Chem. 99 (1995) 3084. [19] A.C. Limaye, S.R. Gadre, Curr. Sci. (India) 80 (2001) 1296. [20] S.R. Gadre, R.N. Shirsat, Electrostatics of Atoms and Molecules, Universities Press, Hyderabad, India, 2000. [21] A.D. Buckingham, P.W. Fowler, J. Chem. Phys. 79 (1983) 6426. [22] A.D. Buckingham, P.W. Fowler, Can. J. Chem. 63 (1985) 2018. [23] P. Politzer, D.G. Trulhar (Eds.), Chemical Applications of Atomic and Molecular Electrostatic Potentials, Plenum Press, New York, 1981.

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