IC/96/10

United Nations Educational Scientific and Cultural Organizationand

International Atomic Energy Agency

INTERNATIONAL CENTRE FOR. THEORETICAL PHYSICS

STRUCTURES AND POTENTIAL ENERGY SURFACESOF LITHIUM ISOCYANIDE AND ITS ISOMERS1

Yubin Wang, Xingji Hong, Jun LiuInstitute of Modern Physics, Northwest University,Shaanxi, Xian 710069, People's Republic of China

and

Zhenyi Wen2

International Centre for Theoretical Physics, Trieste, Italy.

ABSTRACT

In this pa,per the optimized geometries for lithium isocyanide and its isomcrs arereported by MRCISD calculations. The order of stabilities is found to be LiNC > LiCN> LiCN(T). A Sorbie-Murrell potential energy surface of the tri-atomic system is studiedbased on approximately 500 MRCISD calculations. The three stable structures and twosaddle points are investigated along a minimum energy path on the PES. The local fittingto power functions are also studied and thus the harmonic vibrational frequencies can bedetermined for the three isomers.

MIRAMAR.E - TRIESTE

January 1996

'Submitted to Journal of Molecular Structure.2Permanent address: Institute of Modern Physics, Northwest University, Shaanxi, Xian

710069, People's Republic of China.

1 Introduction

The structure and relative stability of the triatomic molecule composed of Lithium, Ni-trogen and Carbon have been the object of many ab initio studies1"34'19. Although themolecule was considered to be highly ionic, the ab initio energy scanning searched outthroe stable structures, i.e. linear Li-N=C (A), L>C= N (B) and triangular LiCN(T)(C).However the theoretical prediction of geometries and relative stabilities for the three struc-tures spread even at post HF levels. For example for the triangular LiCN(T), the Li-Nbond length discrepancy was as large as 0.085 A and the bond angle difference came upto 13 degrees, which were much higher than generally expectatcd. Tho relative stabilitiesof the three isomers have not established for certainty. While SCF calculations concludethat the order of stabilities was (A) > (C) > (B), some calculations of high levels preferred(C) as the most stable structure'1'10. The highest level calculations so far supported theSCF results8, but employed the optimized geometries obtained by lower level calculations.One may suspect that those structures are still optimal at higher level calculations. Thepotential energy surface (PES) of LiNC in the region near- to the local minimum has alsobeen calculated by some authors. It was mainly based on the SCF or MP2 level and,therefore, not considered to be accurate. In addition, as we know, multireference meth-ods pay a dominant role in calculations of PES n , but have not been used in the work ofLiNC isomers. All those confusions oblige us to do further investigation for this system.

2 Computational Methods

The following two basis sets are used in ab initio calculations:(l) a TZ2P basis set, whichis Huzinaga-Dunning's (Ils7p)/[5s3p], augmented with two d functions on C (exponents1.097 and 0.318) and N (exponents 1.654 and 0.469); (2) a smaller basis set DZP, i.e.(9s5p)/[4s2p], augmented one d function on C (exponent 0.75) and on N (exponent 0.83).For the latter set, only SCF and single reference CI optimization are carried out. TheMELD program package13 is used in this work. For the first set all energy calculationsincluding optimization of geometric structures and single point calculations on PES, arecarried out at the MRCISD level. Considering the expense of calculations, the configura-tion selections based on the second order perturbation energy contribution are performed.We follow the approach suggested by Buenker12, i.e. calculating CI energies for two en-ergy threshold values Tl=10 f.t h and T2=20 ji h, then determining the extrapolationenergy corresponding to the threshold value zero. Suppose Eci(Tl) and EQI(T2) are theMRCISD energies with threshold T l and T2, AECI(tl) and /\ECi(t2) arc the sum ofcontributions of unselected configurations in Tl and T2, then

ECI(T2) - EcijTl)

In equation (1), Ea(0) is obviously an approximation to the true zero-threshold MR-CISD energy. But as Buenker has pointed out that the extrapolation energies correctedby Davidson's formula always gave rise to better estimations to the full CI energy thanthe true zero-threshold energies. Three Davidson-type corrections14 are used in this study,namely

Di = [ECi(0)~Eref](l~Cb) (2)

D2 = D1{2Cb-l)~1 (3)

D3 = A<V(l-2/A0 (4)

ETef is the lowest eigenvalue of the reference configuration subspace, C& is the squaresum of all CI coefficients (using the average value of the two Ct> corresponding to thetwo thresholds). D3 is usually referred to the Pople's correction15. Thus Ec.i(0) + D-t areestimated full CI energies. In this work reference configurations are chosen with respectto a threshold of Cj > 0.03, where d is the coefficient of i'th configuration in the CISDwave function. This choice results in 8 orbital products (13 reference configurations) forlinear LiNC and LiCN, and 13 orbital products (19 reference configurations) for angularLiCN(T), which are listed in Tables 1, 2 and 3. The value of EC? or Cb for the statesaround the equilibrium points falls in 0.91 - 0.92, and in lower values for points faraway the equilibrium. These values are smaller than the standard one recommendedby Buenker. Other calculations, such as fitting from the results of electronic structurecalculations to PES and determining vibrational frequencies, will be described in thefollowing subsections.

Table 1: Reference configurations used in LiNC

12345678where

6£>; lb]] lb?A

6D;lb2,;ib27b2

6L>;4&i7&i;16|

6D;16i76i;1624b26D;lb'i;4bl6D-Ab2

x;lbl

6X>;1614Ai;162762

6D = (l ~ 6ai)12

Table 2: Reference configurations used in LiCN

12345678where

6D; 162; 16|6D;162;463762

QD' 16i46i' 16o4&9

6D~ 16i76i; 16^462

(1 -4a 1 ) 8 5a 1 6a 2 ; 16 2 ;6D;162;462

6D; lbiAbi] 1627&2

6Z>;16i5&i;l&25&26D = (1^6a1)

12

lb2

Table 3: Reference configurations used in LiCN(T)

12345678910111213where

5D6a27a2;lb2

5D6a'27a2:4b2

5DQa27a2]4b7br)D4a,7a27a; 1646

7>D6a27a2; 7b'2

5D6a27a2;4bbb5Dla6a7a2;lb7b5D2a3a6a2;lb4b5Dla6a7a2; 1646

5£>6a27a2;562

5£>6a7a214a;56765D7a214a2;162

5D6a7a2Ha; 16765D - (1 - 5a)10

3 Geometry optimizations and relative stabilities

Structure optimizations of the three isomers are performed at SCF, CISD and MRCISDlevels for the chosen basis sets. For the MRCISD optimization, corrected energies bythe Davidson's formula £>2 (equation 3) were taken as the criteria. All bond lengths areaccurate within 0.002 A, and bond angle in the triangle structure within 0.5 deg. Theoptimized geometries arc summarized in Table 4, in which a line separates present resultsfrom some recent calculations reported in literatures.

In view of the table several general feathers may be noted. (1) Bond lengths ofMP2 calculations are consistently greater than corresponding values of SCF calculations,specially for the C-N bond. Comparing with the available experimental values17, MP2overestimated the C-N bond length, while SCF underestimated it. This is often the case.

4

However, both SCF and MP2 calculations give better prediction for the loosely Li-C or Li-N bond lengths. It seems that the optimized geometry of LiNC by MRCISD/TZ2P levelcalculations is more accurate. (2) The C-N bond length in the cyanide is always shorterthan the N-C bond in the isocyanide, while the lithium bond is longer in the former thanin the latter. This is true and in keeping with the conventional multiple bonding concept,because that the C-N bond in cyanide is believed to be triple bonding and the N-C inisocyanide double bonding, although the both compounds have the ionic characterization.(3) The optimized bond angle ZLi-N-C in LiCN(T) was found to be within 82-84 deg inmany reports (mostly by MP2 calculations), but there was a different value 95.21 deg atMRCISD level. Unfortunately the triangular structure of LiCN(T) has not been detectedexperimentally, thus at present it is not able to check ab initio calculations.

In order to compare relative stabilities of the isomers, we list absolute energies of thedifferent calculation levels in Table 5, and relative energies in Table 6. In these tablesunder the line of MRCISD. corrected energies by formulae (1), (2) and (3) were listed.All our calculations conclude that the linear isocyanide (A) is the most stable, which isin agreement with experimental data17. But the relative stability of the linear cyanide(B) and the triangular structure (C) depends on levels of calculations. At our highestlevel of calculation MRCISD/TZ2P, the linear cyanide (B) is a little more stable than thetriangular structure (C), while at the other levels a contrary situation is indicated. Theseresults can be more clearly seen from relative or isomerization energies with respect toisocyanide (A). Both the large basis set and the higher level of correlations have morepreference of cyanide (B) over the other isomers, especially the large correlation effect bythe multireference CI calculation leads isomer (B) having lower energy than isomer (C).It can be also noticed that the correlation effect is similar for isomer (C) and (A), butthe basis set extension slightly prefers (C) to (A). The least LiNC—• LiCN isomerizationenergy in the highest level of calculation is 0.27 kcal/mol, little less than the lower limit0.34 kcal/mol obtained by the experiment17. The small energy difference confirms againthe nonusual "polytopic bond" in the lithium cyanide molecule.

Table 4: Optimized bond lengths (in A) of LiNC isomers

optimizationlevel

Near HF :

rm SCF/6-31G*9

MP2/6-31+G*(2d)9

MP2/6-311G*6MP2/6-311+G*(2di)10

QCISD/CCTZ8SCF/D2P

SCF/TZ2PCISD/D2P

MRCISD/TZ2Pexpt.17

LiNC(A)Li-N1.7731.7871.7601.7821.7791.775

1.7861.7681.8011.7941.760

N-C1.1541.1631.1901.1891.1831.1971.1661.1531.1851.1691.168

LICN(B)Li-C1.9311.9491.9011.9181.9161.9191.9611.9351.9511.940

C-N1.1321.1471.1851.1841.1771.1911.1511.1401.1751.161

LiCN(T)(C)Li-C

2.0882.0882.6612.3552.2892.3002.277

Li-N

1111111

874 1872 1.775 1.841 1.824 1.816 1.833 1

C-N

194183197.166.154.185.174

Table 5: Calculated energies (in a.u.) of the stational structures

CalculationsSCF/DZPSCF/TZ2PCISD/D2P

MRCISD/TZ2P

LiNC(A)-99.79749-99.81943

-100.09424-100.18380-100.18902-100.18263

LiCN(B)-99.78790-99.81090-100.08881-100.18280-100.18859-100.18167

LiCN(C)-99.77923-99.89588

-100.08899-100.18031-100.18577-100.17919

Table 6: Relative energies (in kcal/mol) of the isomers

CalculationsSCF/DZPSCF/TZ2PCISD/DZP

MRCISD/TZ2P

LiNC(A)0.00.00.00.0

LiCN(B)6.025.353.410.620.270.60

LiCN(T)(C)3.282.233.292.192.042.16

4 Ab initio potential energy surface

In order to determine the ground state PES of the molecule, we performed extensiveMRCISD calculations for 504 different molecular geometries, which are located aroundthe three stable structures. The data of energies and geometries are then fitted into ananalytic form. In this work we adopt the many-body expansion suggested by Murrell etal.18. For a triatomic system, the potential function of this kind can be written as

A A,B

where VA, VAB and VABC are one-body, two-body and three-body contributions respec-tively. Similar to HCN18, the atom plus diatom dissociation limit for the ground state1 £ + of LiNC can be

+) (6a)

-) (66)

+) (6c)

Instead of (6a) there is an alternative channel.

in which the energy of CN~ is 3.514 ev lower than that of C7V(2£+) for their equilibriumstructures according to our calculation, but Li+^S) state lies 5.393 ev above Li(2S), thusonly the channel (6a) is considered in this work.

For the two-body potential V^\ we use the Extended Rydberg(ER) function

V® = -De(\ + £ akpk)exp{-alP) (7)

fc=i

where p is the deviation from the equilibrium bond length Re

Thus the diatomic potential function can be deduced by fitting the ab initio energyvalues. The parameters in three functions V^2) are shown in Table 7.

The three-body potential V^ is written as the product of a polynomial P and aso-called range function T,

V® = P(Si)T(Pi) (8)

where displacement coordinates p\ are defined with respect to the bond length of somereference structure R°,

The reference structure is determined from the three stable geometries and shown inFig. 1

7

Fig. 1 The reference structurei = 2.2039a.« R% = 4.0652o.« R% = 5.0692a.u

The range function has the formg

(9)

In equation (8), s{ are the optimized coordinates, which are obtained by a rotation ofthe displacement coordinates pi

S = I> (10)

where the rotation matrix Y is found as follows.

0.9999 0.0129 0.0088r = | -0.0048 0.7873 -0.6166 | (11)

-0.0149 0.6165 0.7872

The three-body polynomial P{si) can be written as

3 3 3 3

i= l

The least square procedure is used to fit the coefficients in eqn.(12) to ab initio energyvalues and the results are given in Table 7. The fitted potential function has a standarddeviation to the data points of 0.098 ev with the maximum error 0.32 ev.

Table 7: Many-body potential for the ground state of LiNC.

Two-body terms:Species Rfija.u

C-NLi-NLi-C

-0.29157 2.215 1.9362 0.0667 0.0-0.08142 3.562 1.2995 0.3726 0.1063-0.08717 3.565 1.1375 0.1212 0.0129

Three-body terms:7i7273

c2

Cu

-0.08240.9600

-0.36722.41803.66404.75690.04510.81810.00010.0715

cum 10~6

^22

CV2

C\Z

C-TA

cmC222

^333

Cll2

Cl22

0.00020.18860.01500.39300.00090.01990.00010.05970.00260.1847

Cll3

Ci33

C223

C233

C-12?,

C l U l

C2222

C33.33

C1112

C1122

0.03860.00220.00000.06330.56240.04020.00000.00000.02300.0061

C1222

Cni3

C1133

C1333

C2223

C2233

C2333

C1123

^1223

C1233

0.04421.07270.00120.05100.00000.09790.00020.00490.00071.1154

From the optimal function a two-dimensional PES can be obtained by keeping C-Nbond length at 2.201 a.u=1.165 A (the mean length of the C-N bond in LiNC and inLiCN). Energy contours of the PES are shown in Fig.2, in which the C and N atoms arelocated in horizontal axis and the origin is at the centre of the average CN bond. Thisfigure thus describes the motion of a lithium atom around the CN group.

In order to understand the orbit motion of Li atom around CN group more clearly,we transfer the potential function in RCN, RUN and RLic to that represented in Jacobicoordinates R and <&, which are explained in Fig.3.

v/a.u.

-15 5.5

Fig.2 Energy contours of the function in Table 7C-N bond length = 2.201 a.u

Contour 1 = -100.182 a.u. contour intervals = 0.001 a.u

Li

Fig.3 Jacobi coordinates R and $

Energy contours obtained from the new potential function V(R, $, RON) for the fixedRCN are shown in Fig.4. As is expected there are three minima and two saddle points onthe PES. A minimum energy path(the dished line) connecting the minima is generated bysearching valley points, i.e. for a given angle $, the coordinate R with the lowest energyis found out.

10

3.2 v~ f—~~i F 1 1 i r—~—i ••••^•T"&jfi 1 1 1 1 1 r

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 ISO 160 170 180

/deg

Fig.4 Potential energy surface of LiNC in the Jacobi coordinates <& and R,Contour 1 = -100.182 a.u, contour intervals — O.OOla.uThe dashed curve represents a minimum energy path

Fig.5 shows the energy change along the lowest energy path for the tri-atomic system.In this figure, a) gives the energy change with respect to the Jacobi coordinate $, whilecorresponding R values arc shown in b). Coordinates and energies of the five extremepoints on the lowest energy path are listed in Table 8.

11

-100.172-100.174

3-100.176-ffl-100.178m -100.18

-100.182-100.184

(a) Plot of Jacob coordinate Phi-Energy

20 40 60 80 100 120 140 160 180Phi/deg

(b) Plot of Jacob coordinete Phi-RT

0 20 40 60 80 100 120 140 160 180Phi/deg

Fig.5 The energy-Jacobi coordinate $ curve on the minimum energy path

Table 8: Coordinates and energies of extreme pointstype

minimumsaddle

minimumsaddle

minimum

$(deg)180.0128.3105.770.50.0

R(A)2.3162.0641.9002.1172.474

1.7331.7641.8313.3763.057

RMC(A)

2.8982.4682.1332.0001.892

E(a.u)-100.1836-100.1769-100.1783-100.1735-100.1778

A Efcm-1)0

1470116322171273

Since RCN is kept constant in this path, these extreme points are not real optimizedstructures. It is believed, however, that these structures are close to optimized ones, atleast for the three minima, which can be seen by comparing table 8 and 4. It is noticedthat the stability order for LiCN and LiCN(T) in this path is reversed. Although thisorder is consistent with many theoretical calculations, it comes, in fact, from the fittingerror of the PES. The height of barriers can also be measured from the figure and listed inthe last column in Table 8. But due to the accuracy limitation of the PES. it is difficultto judge the quantitative meaning of the data.

12

5 Vibrational Frequencies

To calculate vibrational frequencies of LiNC. LiCN and LiCN(T). The local fitting forthe three isomers should be performed. The ab initio energies of those points around thethree stational structures were separately fitted to quadratic, cubic and quartic powerfunctions of SPF internal coordinates pj,

thus their frequencies could be determined by transforming the SPF coordinates to normalones. This procedure was carried out by the program SURVIB20. The calculated harmonicfrequencies for LiNC are given in Tables 9, 10 and 11.

Table 9 Vibrational frequenciesfcm"1) of LiNC obtainedby the quadratic potential function

v3

1*7041022062

2711862059

37011012062

47011312066

57071302061

6707

no2063

76991552062

87071312062

^1, all points arc included in fitting; 2. points of deviation angleto linear being 5 are omitted; 3. points of deviation angle to linearbeing 30 arc omitted; 4. points of deviation angle to linear being40 are omitted; 5. points of deviation angle to linear being 5 and30 are omitted; C. points of deviation angle to linear being 5 and40 are omitted; 7. points of deviation angle to linear being 30 and40 are omitted; 8. points of deviation angle to linear being 5;30and 40 are omitted;

Table 10: Vibrational frequencies {cm l) of LiNC obtainedby the cubic potential function

i709982038

2719802031

3702972039

47041292048

57101282045

67111052044

77011542047

87081292046

13

Table 11: Vibrational frequencies (cm 'l) of LiNC obtainedby the quartic potential function

vu

15461571784

25911261763

35651751780

45062111801

55562231775

65431761782

75012581788

85952231771

Tables 9, 10 and 11 show that the powers of the force field and the choice of pointscause variations of calculated frequencies. It is noticed that the bending mode frequency utwill decrease if the points associated with small angles are omitted from fitting. Involvingpoints with larger angles(e.g. 40 degree) has the same trend, which means that the energyrising for points far away from equilibrium angle is smaller than is expected. It is obviousthat involving or omitting points with different angles only brings about a small variationof the stretching mode frequencies us and vu.

The effect of the expansion power is a little more complicated. Prom the quadraticfunction to the cubic one the symmetric stretch frequency vs is slightly increased; theasymmetric stretch frequency vu and bent one z/& are slightly decreased. As a whole,however, the variation of frequencies is not large. But the quartic force field leads to aconsiderable increase of u^ and decrease of the stretching modes ua and uu.

If we take the average of calculated frequencies and compare with the experimentalvalues (see Table 12) we find that as far as harmonic frequencies the quadratic and cubicpotential functions are better than the quartic function. However harmonic frequenciesare only the approximation to fundamental frequencies. The latter involve contributionsfrom anharmonic parts and it is the latter that should compare with observed frequencies.The quartic potential function has obviously many anharmonic terms which do not existin the quadratic and cubic functions. We have performed some trial calculations andresults are under preparation.

The fitted stational geometries are basically determined by the power of expansionseries. In general the increase of the power leads to the contraction of bond lengths andthe decrease of zeroth energies, which can be seen from Table 12. Comparing with theoptimized geometry the Li-N bond length is shorter and C-N bond slightly longer but isstill reasonable a,greement with the experiment. It is interesting to notice that the Li-Nbond length obtained by local fitting is more close to the experimental value while theC-N bond length obtained by direct optimization is more close to experimental one.

14

Table 12: Average vibrational frequencies (cm : ) , stational structures (Ji) and zerothenergies (cm'1) of LiNC

Vb

Vu

R-CN

Zerothenergy

Quadratic705118

20621.7781.1881485

Cubic708113

20421.7671.1801471

Quartic55019417811.7641.1811322

Exp.68116

12020801.7601.168

Similar calculations are also performed for the other two isomers, and the frequenciesare 662 cm,-1, 196 cm"1 and 2245 cm'1 for LiCN and 683 cnr1, 185 cm"1 and 2035 era'1

for LiCN(T).

6 Summary

Extensive ab initio calculations based on CISD and MRCISD were performed for lithiumisocyanide and its isomers. The optimized geometry of LiNC and the globe minimumof the triatomic system were found to be good agreement with the available experimen-tal results. But the linear LiCN was found to be a little more stable than the angularLiCN(T), which is different with most of reports. The energy differences between thethree isomers were such small that the isomerization between them should not be diffi-cult. A globe Sorbie-Murrell PES for the ground state of the system was determined byfitting MRCISD energies of more than 500 molecular geometries with a standard devi-ation of 0.098 ev. A approximate minimum energy path on the PES and five extremepoints(three minima and two saddle points) along the minimum energy path were found,which is assistant with some recent calculations.

Around the three stational structures local fittings were separately done by the powerseries expansion of the SPF coordinates. Based on the fitting the harmonic vibrationalfrequencies and the new equilibrium geometries were determined for the three isomers.The new geometries were very close to those by the direct optimization and reasonableagreement with the experiments. It was found that calculated frequencies depend on theorder of the fitting functions and choice of the fitting points.Lithium isocyanide is a interesting molecule. Unfortunately there arc only few experi-mental data. The vibrational frequencies of this molecule were measured twenty yearsago and could not considered to be reliable. Thus it is highly desirable to make furthermeasurements for its spectra and other properties.

15

7 Acknowledgments

One of the authors (Z.W) would like to thank the International Centre for TheoreticalPhysics, Trieste, for hospitality. This work was supported by the Natural Science Fundof China.

1G

References

[1] E. dementi, H. Kisteenmecher and H. Popkie, J. Chem. Phys. 58, 2460 (1973)

[2] P.P... Bunker and D.J. Howe, J. Mol. Spectrosc, 83, 288 (1980)

[3] R. Esser, J. Tennyson and P.E.S. Wormer, Chem. Phys. Lett,, 89, 223 (1982)

[4] P.R. Schleycr, A. Sawaryn, E.A. Read and P. Hobza, J. Comput. Chem.,7, 666 (1986)

[5] L.T. Redmon, G.D. Purvis III and R.J. Bartlett, J. Chem. Phys.,72, 986 (1980)

[6] L. Adamowich and C.L Frum, Chem. Phys. Lett., 157, 496 (1989)

[7] J. Tellinghutsen and C.S. Ewig, J. Chem. Phys., 911, 5476 (1989)

[8] A. Dorico, PR. Schleyer and P. Hobza, J. Comput. Chem.,15, 322 (1994)

[9] M. Spoliti, F. Ramando, F. Diomed-Camassei and L. Bencivenni, J. Mol. Structure,312, 41(1994)

[10] J. Makarenicz and Tae-Kyu Ha, J. Mol. Structure, 315, 149 (1994)

[11] M. Urban. I. Cernusak, V. Kello and J. Noga, in "Method in Computational Chem-istry1', ed. by S.Wilson. pll7. Plenum Press, New York and London, 1987

[12] B.J. Buenker, D.B. Knowlcs, S.N. Rai, G. Hirsch, K. Bhanuprakash and J.R. Alvarez-Collado, in "Quantum Chemistry: Basic Aspects, Actual Trends", p.181, ed. byCarbo, Elsevier, 1989

[13] In "MOTECC-90", p.553, ed. by Clementi, Kingston Science Publisher, 1990

[14] E.R. Davidson and D.W. Silver, Chem. Phys. Lett., 52, 403 (1977)

[15] J.A. Pople; R. Seeger and R. Krishnon, Int. J. Quant. Chem., Sl l , 149 (1977)

[16] Z.K. Ismail, R.H. Haugc and J.L. Malgrave, J. Chem. Phys., 57, 5137 (1972)

[17] J.J. van Vaale, W.L .Mcerta and A. Dymanus, Chem. Phys., 82, 385 (1983)

[18] J.N. Murrell, S. Curter. S.C. Farantos, P. Huxley and A..T.C. Verandas, MolecularPotential Energy Functions, John Wiley and Sons, 1984

[19] J. Makarenicz and Tae-Kyu Ha, Chem. Phys. Lett,, 232, 497 (1995)

[20] L.B. Harding and W.C. Ermler, J. Comput. Chem., 6, 13 (1985)

17