Structures and potential energy surfaces of lithium isocyanide and its isomers

THEO CHEM ELSEVIER

Journal of Molecular Structure (Theochem) 369 (1996) 173-182

Structures and potential energy surfaces of lithium isocyanide and its isomers Yubin Wang, Xingji Hong, Jun Liu, Zhenyi Wen* Instituteof Modern Physics, Northwest University, Shaanxi, Xian 710069, People’s Republic of China

Received 23 January 1996; accepted 29 February 1996

Abstract In this paper the optimized geometries for lithium isocyanide and its isomers are reported by MRCISD calculations. The order of stabilities is found to be LiNC > LiCN > LiCN(T). A Sorbie-Murrell potential energy surface of the k-atomic system is studied based on approximately 500 MRCISD calculations. The three stable structures and two saddle structures are searched out along a minimum energy path on the PES. The local fitting to power functions are also studied and thus the harmonic vibrational frequencies can be determined for the three isomers. Keywords:

Ab initio calculation;

Lithium isocyanide;

Potential energy surface

1. Introduction The structure and relative stability of the tri-atomic molecule composed of lithium, nitrogen and carbon have been the object of many ab initio studies [l-14,19]. Although the molecule was considered to be highly ionic, the ab initio energy scanning searched out three stable structures, i.e. linear Li-N-C (A), Li-=N (B) and triangular LiCNQ(C). However, the theoretical prediction of geometries and relative stabilities for the three structures spread even at post HF levels. For example, for the triangular LiCN(T), the Li-N bond length discrepancy was as large as 0.085 A and the bond angle difference came up to 13”, which was much higher than general expectation. The relative stabilities of the three isomers have not been established for certainty. While SCF calculations conclude that the order of stabilities was (A) > (C) > (B), some * Corresponding

author.

calculations of high levels preferred (C) as the most stable structure [4,10]. The highest level calculations so far supported the SCF results [8], but employed the optimized geometries obtained by lower level calculations. One may suspect that those structures are still optimal at higher level calculations. The potential energy surface (PES) of LiNC in the region near to the local minimum has also been 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, multi-reference methods play a dominant role in calculations of PES [ll], but have not been used in the work of LiNC isomers. All these uncertainties obliged us to further investigate this system.

2. Computational methods The following two basis sets were used in ab initio calculations: (1) a TZ2P basis set, which is

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Y Wang et aLlJournal of Molecular Structure (Theochem) 369 (I 996) 173-182

Huzinaga-Dunning’s (lls7p)/[5s3p], augmented with two d functions on C (exponents 1.097 and 0.318) and N (exponents 1.654 and 0.469); (2) a smaller basis set DZP, i.e. (9sSp)/[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 were carried out. The MELD program package [13] was used in this work. For the first set, all energy calculations including optimization of geometric structures and single point calculations on PES, were carried out at the MRCISD level. Considering the expense of calculations, the configuration selections based on the second order perturbation energy contribution were performed. We followed the approach suggested by Buenker [12], i.e. calculating CI energies for two energy threshold values Tl = 10 p h and T2 = 20 p h, then determining the extrapolation energy corresponding to the threshold value zero. Suppose E&l) and E&2) are the MRCISD energies with thresholds Tl and 72, A,!?c,(tl) and A/?&n) are the sum of contributions of unselected configurations in Tl and 12, then

EC*(o) =&I +

-%,W) -E&l) &Tl

- 62

‘=Tl

(1)

In Eq. (l), E&O) is obviously an approximation to the true zero-threshold MRCISD energy, but as Buenker has pointed out, the extrapolation energies corrected by Davidson’s formula always give rise to better estimations to the full CI energy than the true zero-threshold energies. Three Davidson-type corrections [14] were used in this study, namely Dl = [&I(O)

- Eref I(1 - cb)

(3)

L)z=&(2&1)-1

Table 1 Reference configurations 1 2 3 4 5 6 7 8 where

(2)

used in LiNC

60; lb:; lb: 60; lb:; 4b27b2 60; 46,7b,; lb: 60; lb,4bI; lb2462 60; lb,761; lb2462 60; lb;; 46: 60, 4b:; lb: 60; lb,46,; 162762 6D=(1=6a1)‘2

Table 2 Reference configurations 1 2 3 4 5 6 7 8 where

used in LiCN

60; lb:; lb: 60; lb:; 4b27bz 60; lb,46,; 1b24b2 60; lb,7b,; lbz4bz (1 = 4a1)*5a,6a:; lb:; lb: 60; lb:; 46: 6D; lb,4b,; lb27b2 60; lb15b,; 1b25b2 60 = (1 = 6a1)”

D3 =D&(l-2/N)

(4)

Eref is the lowest eigenvalue of the reference configuration subspace, Cb is the square sum of all CI coefficients (using the average value of the two Cb corresponding to the two thresholds). 03 is usually referred to as the Pople’s correction [15]. Thus E,(O) + D, are estimated full CI energies. In this work reference configurations are chosen with respect to a threshold of Ci 2 0.03, where Ci is the coefficient of ith configuration in the CISD wave function. This choice results in 8 orbital products (13 reference configurations) for linear LiNC and LiCN, and 13 orbital products (19 reference configurations) for angular LiCN(T), are listed in Tables 1-3. The value of CC: or Cb for the states around the equilibrium points falls in 0.91-0.92, and in lower values for points far away the equilibrium. These values are smaller than the standard one recommended by Buenker. Other calculations, such Table 3 Reference configurations 1 2 3 4 5 6 7 8 9 10 11 12 13 where

used in LiCN(T)

5D6a27a2; lb2 5D6a27a2; 4b2 5D6a27a2; 4b76 5D4a7ava; lb46 5D6a27a2; 7b2 5D6a 27a ‘; 4b5b 5Dla6a7a2; lb7b 5D2a3a6a2; lb4b 5Dla6a7a2; lb46 5D6a27a2; 5b2 5D6a7a214a; 5676 5D7a214a2; lb2 5D6a7az14a; lb7b 5D = (1 - 5a)”

175

Y. Wang et aLlJournal of Molecular Structure (Theochem) 369 (1996) 173-182

as fitting from the results of electronic structure calculations to PES and determining vibrational frequencies, will be described in the following sections.

3. Geometry optimizations and relative stabilities Structure optimizations of the three isomers were performed at SCF, CJSD and MRCISD levels for the chosen basis sets. For the MRCISD optimization, corrected energies by Davidson’s formula D2 (Eq. (3)) were taken as the criteria. All bond lengths are accurate within 0.002 A, and bond angles in the triangle structure within 0.5”. The optimized geometries are summarized in Table 4. A line separates present results from calculations reported in some recent literature. In view of the table several general points may be noted. 1. Bond lengths of MP2 calculations are consistently greater than corresponding values of SCF calculations, specially for the C-N bond. Comparing with the available experimental values [17], MP2 overestimated the C-N bond length, while SCF underestimated it. This is often the case. However, both of 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 MRCISDiTZ2P level calculations is more accurate. 2. The C-N bond length in the cyanide is always

shorter than the N-C bond in the isocyanide, while the lithium bond is longer in the former than in the latter. This is true and in keeping with the conventional multiple bonding concept, because the C-N bond in cyanide is believed to be triple bonded and the N-C in isocyanide double bonded, although both compounds have the ionic characterization. 3. The optimized bond angle LLi-N-C in LiCNQ was found to be within 82-84” in many reports (mostly by MP2 calculations), but there was a different value of 95.21” at the MRCISD level. the triangular structure of Unfortunately, LiCN(T) has not been detected experimentally, 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 the different calculation levels in Table 5, and relative energies in Table 6. In these tables, corrected energies from formulae (l), (2) and (3) were listed below MRCISD. All our calculations conclude that the linear isocyanide (A) is the most stable, which is agreement with experimental data [17], but the relative stability of the linear cyanide (B) and the triangular structure (C) depends on levels of calculations. At our highest level of calculation of MRCISD/‘TZ2P, the linear cyanide (B) is a little more stable than the triangular structure (C), while at the other levels a contrary situation is indicated. These results can be more clearly seen from relative or isomerization energies with

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

LiNC(A)

LiCN(B)

LiCN(T)(C)

Li-N

N-C

Li-C

C-N

Li-C

Li-N

C-N

Near HF [l] rm SCF/6-31G* [9] MP2/6-31 + G’(2d) [9] MP2/6-311G’ [6] MP2/6-311 + G’(2d,f) [lo] QCISD/C(JTZ [8]

1.773 1.787 1.760 1.782 1.779 1.775

1.154 1.163 1.190 1.189 1.183 1.197

1.931 1.949 1.901 1.918 1.916 1.919

1.132 1.147 1.185 1.184 1.177 1.191

2.088 2.088 2.661

1.874 1.872 1.775

1.194 1.183 1.197

SCF/D2P SCF/TZ2P CISD/DZP MRCISD/TZ2P Expt. [17]

1.786 1.768 1.801 1.794 1.760

1.166 1.153 1.185 1.169 1.168

1.961 1.935 1.951 1.940

1.151 1.140 1.175 1.161

2.355 2.289 2.300 2.277

1.841 1.824 1.816 1.833

1.166 1.154 1.185 1.174

176

Table 5 Calculated

of Molecular Structure (Theochem) 369 (1996) 173-182

Y. Wang et aLlJournal

can be written as energies (in au.) of the stational structures

Calculations SCF/DZP SCFfIZ2P CISD/D2P MRCISD/TZ2P

LiNC(A)

LiCN(B)

LiCN(C)

- 99.79749 - 99.81943 - 100.09424 - 100.18380 - 100.18902 - 100.18263

- 99.78790 - 99.81090 - 100.08881 - 100.18280 - 100.18859 - 100.18167

- 99.77923 - 99.89588 - 100.08899 - 100.18031 - 100.18577 - 100.17919

respect to isocyanide (A). Both the large basis set and the higher level of correlations have more preference of cyanide (B) over the other isomers, especially the large correlation effect by the multi-reference CI calculation which leads to isomer (B) having a lower energy than isomer (C). It can be also noticed that the correlation effect is similar for isomer (C) and (A), but the basis set extension slightly prefers (C) to (A). The least LiNC - LiCN isomerization energy in the highest level of calculation is 0.27 kcal mol-‘, a little less than the lower limit, 0.34 kcal mol-‘, obtained by the experiment [17]. The small energy difference confirms again the unusual “polytopic bond” in the lithium cyanide molecule.

v,,

= J VJ” + 2 vz + vzc A.8

where VA, V, and V,, are one-body, two-body and three-body contributions respectively. Similar to HCN [18], the atom plus diatom dissociation limit for the ground state ‘2 + of LiNC can be

LiNC(‘C+)-

Li(%) + CN(‘C’)

(a)

q4P) + LiN(3C-)

(b)

N(4S) + LiC(4Ct)

(c)

In order to determine the ground state PES of the molecule, we performed extensive MRCISD calculations for 504 different molecular geometries, which are located around the three stable structures. These data of energies and geometries are then fitted into an analytic form. In this work, we adopt the many-body expansion suggested by Sorbie and Murrell [181. For a tri-atomic system, the potential function of this kind

LiNC(‘C+)+Li+(iS)+CN-(‘C+) in which the energy of CN- is 3.514 eV lower than that of CN(2C’) for their equilibrium structures according to our calculation, but the Li’(‘S) state lies 5.393 eV above Li(*S), thus only the channel Eq. (6a) is considered in this work. For the two-body potential Vc2), we use the Extended Rydberg (ER) function

Calculations

LiNC(A)

LiCN(B)

LiCN(T)(C)

SCFIDZP SCF/TZ2P CISD/DZP MRCISDmZP

0.0 0.0 0.0 0.0

6.02 5.35 3.41 0.62 0.27 0.60

3.28 2.23 3.29 2.19 2.04 2.16

exp(-alp)

(7)

where p is the deviation from the equilibrium bond length R, p=RAB-R,

Thus the diatomic potential function can be deduced by fitting the ab initio energy values. The parameters in three functions V@)are shown in Table 7. The three-body potential I’(‘) is written as the product of a polynomial P and a so-called range function T, vC3)= P(s)T(p.) I 1

Table 6 Relative energies (in kcal mol-‘) of the isomers

(6)

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

Vc2)= -D,(l+k$lakpk)

4. Ab initio potential energy surface

(5)

(8)

where displacement coordinates pi are defined with respect to the bond length of some reference structure RP, pi =Ri-RP The reference structure is determined from the three stable geometries and shown in Fig. 1.

177

Y. Wang et aLlJournal of Molecular Structure (Theochem) 369 (1996) 173-182

Table 7 Many-body Two-body

potential for the ground state of LiNC terms:

Species

D, (au.) - 0.29157 - 0.08142 - 0.08717

C-N Li-N Li-C Three-body

R, (a.u.)

01 1.9362 1.2995 1.1375

2.215 3.562 3.565

a3

a2

0.0 0.1063 0.0129

0.0667 0.3726 0.1212

terms: - 0.0824 0.9600 - 0.3672 2.4180 3.6640 4.7569 0.0451 0.8181 0.0001 0.0715 10-b

YI Y2 73

RY &I R! cl c2 c3

c11 cl1111

0.0002 0.1886 0.0150 0.3930 0.0009 0.0199 0.0001 0.0597 0.0026 0.1847

c22 c33

Cl? Cl3 c23

Cl11 c222

c 333 Cl12 Cl22

Cl13 Cl33

c 223 c 233

Cl113

c ,222

0.0000

Cl133

c 1333 c 2223

cl111

0.0633 0.5624 0.0402

c2222

0.0000

c2333

c3333

0.0000

cl123

cl112

0.0230 0.0061

c 1233

c123

Cl122

The range function has the form

0.0386 0.0022

c2233

cl223

0.0442 1.0727 0.0012 0.0510 0.0000 0.0979 0.0002 0.0049 0.0007 1.1154

where the rotation matrix I’ is found as follows,

(9) In Eq. (8), si represents the optimized coordinates, which are obtained by a rotation of the displacement coordinates, pi s=rp

r-

0.9999

0.0129

0.0088

i - 0.0048

0.7873

- 0.6166 1

- 0.0149

0.6165

0.7872

(II)

The three-body polynomial P(sJ can be written as

(10)

(12) Li

N

C

Fig. 1. The reference structure: Ry - 2.2039 a.u.; Ri - 4.0652 au.; R i - 5.0692 a.u.

The least square procedure is used to fit the coefficients in Eq. (12) to ab initio energy values and the results are given in Table 7. The fitted potential function has a standard deviation to the data points of 0.098 eV with the maximum error 0.32 eV. From the optimal function a two-dimensional PES can be obtaiaed by keeping C-N bond length at 2.201 au = 1.165 A (the mean length of the C-N bond in LiNC and in LiCN). Energy contours of the PES are shown in Fig. 2, in which the C and N atoms are located in the horizontal axis and the origin is at the centre of the average CN bond. This figure thus describes the motion of a lithium atom around the CN group. In order to understand the orbit motion of the Li

178

Y. Wang et al./Joumal of Molecular Structure (Theochem) 369 (1996) 173-182

yhl

-0.5

00

0’5

3'5

4.;

x/am Fig. 2. Energy contours of the function in Table 7 (C-N bond length = 2.201 a.“.; contour 1 - - 100.182 a.u.; contour intervals - 0.001 ax.).

atom around the CN group more clearly, we transfer the potential function in Rm, RL~ and RLiC to that represented in Jacobi coordinates R and a’, which are explained in Fig. 3. Energy contours obtained from the new potential function V(R, 9, Rm) for the fixed R,-- are shown in Fig. 4. As is expected, there are three minima and two saddle points on the PES. A minimum energy path (the dashed line) connecting the minima is generated by searching valley points, i.e. for a given angle 4, the coordinate R with the lowest energy is found. Fig. 5 shows the energy change along the lowest energy path for the tri-atomic system. In this figure,

Li

(a) gives the energy change with respect to the Jacobi coordinate a, while corresponding R values are shown in (b). Coordinates and energies of the five extreme points on the lowest energy path are listed in Table 8. Since Ra is kept constant in this path, these extreme points are not real optimized structures. It is believed, however, that these structures are close to optimized ones, at least for the three minima, which can be seen by comparing Table 8 and Table 4. It is noticed that the stability order for LiCN and LiCN(T) in this path is reversed. Although this order is consistent with many theoretical calculations, it comes, in fact, from the fitting error of the PES. The heights of barriers can also be measured from the figure and these values are listed in the last column in Table 8, but due to the accuracy limitation of the PES, it is difficult to judge the quantitative meaning of the data.

5. Vibrational

C Fig. 3. Jacobi coordinates

N R and 0.

frequencies

To calculate vibrational frequencies of LiNC, LiCN and LiCN(T), the local fitting for the three isomers should be performed. The ab initio energies of those points around the three stational structures were

Y. Wang et al.lJotunal of Molecular Structure (Theochem)369 (1996) 173-182

”

IO

20

30

40

60

60

70

80

90

100

110

120

130

140

150

160

170

180

%eg Fig. 4. Potential energy surface of LiNC in the Jacobicoordinates @ and R (contour 1 = - 100.182 a.u.; contour intervals - 0.001 a.u.). The dashed curve represe& a minimum energy path.

separately fitted to quadratic, cubic and quartic power functions of SPF internal coordinates pi, PSPF = @

-RJIR

thus their frequencies could be determined by transforming the SPF coordinates to normal ones. This procedure was carried out by the program SURVIB [20]. The calculated harmonic frequencies for LiNC are given in Tables 9-11. Tables 9-11 show that the powers of the force field and the choice of points cause variations of calculated frequencies. It is noticed that the bending mode frequency Ybwill decrease if the points associated with small angles are omitted from the fitting. Involving points with larger angles (e.g. 40”) has the same trend, which means that the energy rising for points far away from the equilibrium angle is smaller than is expected. It is obvious that involving or omitting points with different angles only brings about a small variation of the stretching mode frequencies u, and v,.

The effect of the expansion power is a little more complicated. From the quadratic function to the cubic one, the symmetric stretch frequency v, is slightly increased, while both the asymmetric stretch -100.172I

0

(al plotof Jacob coordinate +-Energy ,

I

20

40

I c r

60

I

I

I

I

I

80 100 120 140 160 180 */deg

(b)Plot of Jacob coordinete@-R

_.

0

20

40

60

80 100 120 140 160 160 @/deg

Fig. 5. The energy-Jacob coordinate ip curve on the minimum energy path.

Y. Wang et al.IJournal of Molecular Structure (Theochem) 369 (1996) 173-182

180

Table 8 Coordinates

and energies of extreme points + (deg)

Type Minimum Saddle Minimum Saddle Minimum

Table 9 Vibrational

v, “b

Y..

R (A)

180.0 128.3 105.7 70.5 0.0

frequencies

2.316 2.064 1.900 2.117 2.474

0 R UN (A)

R Lit (A)

1.733 1.764 1.831 3.376 3.057

2.898 2.468 2.133 2.000 1.892

(cm-‘) of LiNC obtained by the quadratic

E (ax.) -

AE (cm-‘)

100.1836 100.1769 100.1783 100.1735 100.1778

-

0 1470 1163 2217 1273

potential function

1”

2

3

4

5

6

7

8

704 102 2062

711 86 2059

701 101 2062

701 131 2066

707 130 2061

707 110 2063

699 155 2062

707 131 2062

a 1, all points are included in fitting; 2, points of deviation angle to linear being 5 are omitted; 3, points of deviation angle to linear being 30 are omitted; 4, points deviationangle to linear being 40 are omitted; 5, points of deviation angle to linear being 5 and 30 are omitted; 6, points of deviation angle to linear being 5 and 40 are omitted; 7, points of deviation angle to linear being 30 and 40 are omitted; 8, points of deviation

of

angle to linear being 5, 30 and 40 are omitted;

Table 10 Vibrational

frequencies 1

v, yb

VU

Table 11 Vibrational

y, Yb y.

709 98 2038

frequencies

(cm-‘) of LiNC obtained by the cubic potential function 2

3

4

5

6

7

8

719 80 2031

702 97 2039

704 129 2048

710 128 2045

711 105 2044

701 154 2047

708 129 2046

(cm-‘) of LiNC obtained by the quartic potential function

1

2

3

4

5

6

7

8

546 157 1784

591 126 1763

56.5 175 1780

506 211 1801

556 223 1775

543 176 1782

501 258 1788

595 223 1771

frequency Y, and the bent one Vb are slightly decreased. As a whole, however, the variation of frequencies is not large. But the quartic force field leads to a considerable increase of vb and a decrease of the stretching modes v, and v,. If we take the average of calculated frequencies and compare them with the experimental values (see Table 12) we find that as far as harmonic frequencies,

the quadratic and cubic potential functions are better than the quartic function. However, harmonic frequencies are only the approximation of fundamental frequencies. The latter involve contributions from anharmonic parts and it is the latter that should be compared with observed frequencies. The quartic potential function has obviously many anharmonic terms which do not exist in the quadratic and cubic

Y. Wang et al.lJournal of Molecular Structure (Theochem) 369 (1996) 173-182

Table 12 Average vibrational frequencies (cm-‘), stational structures (A) and zeroth energies (cm-‘) of LiNC

y, Yh y, RbN R Z%h energy

Quadratic

Cubic

Quartic

Exp.

705 118 2062 1.778 1.188 1485

708 113 2042 1.767 1.180 1471

550 194 1781 1.764 1.181 1322

681 [16] 120 2080 1.760 1.168

functions. We have performed some trial calculations and results are under preparation. The fitted stational geometries are basically determined by the power of expansion series. In general, the increase of the power leads to the contraction of bond lengths and the decrease of zeroth energies, which can be seen from Table 12. Comparing with the optimized geometry the Li-N bond length is shorter and C-N bond slightly longer but is still reasonable agreement with the experiment. It is interesting to notice that the Li-N bond length obtained by local fitting is more close to the experimental value while the C-N bond length obtained by direct optimization is more close to experimental one. Similar calculations are also performed for the other two isomers, and the frequencies are 662, 196 and 2245 cm-’ for LiCN and 683,185 and 2035 cm-’ for LiCN(T).

6. Summary Extensive ab initio calculations based on CISD and MRCISD were performed for lithium isocyanide and its isomers. The optimized geometry of LiNC and the globe minimum of the tri-atomic system were found to be in good agreement with the available experimental results. The linear LiCN was found to be little more stable than the angular LiCN(T), which is different with most other reports. The energy differences between the three isomers were so small that the isomerization between them should not be difficult. A globe Sorbie-Murrell PES for the ground state of the system was determined by fitting MRCISD energies of more than 500 molecular geometries with a standard deviation of 0.098 eV. An approximate

181

minimum energy path on the PES and five extreme points (three minima and two saddle points) along the minimum energy path were found, which is consistent with some recent calculations. Around the three stational structures, local fittings were separately done by the power series expansion of the SPF coordinates. Based on the fitting of the harmonic vibrational frequencies and the new equilibrium, geometries were determined for the three isomers. The new geometries were very close to those found by the direct optimization and were in reasonable agreement with the experiments. It was found that the calculated frequencies depend on the order of the fitting functions and choice of the fitting points. Lithium isocyanide is an interesting molecule. Unfortunately there is little experimental data available. The vibrational frequencies of this molecule were measured 20 years ago and could not be considered reliable. Thus, it is highly desirable to make further measurements for its spectra and other properties.

Acknowledgements The author (Z.W.) would like to thank ICTP for the opportunity to visit Trieste. This work was supported by the Natural Science Fund of China.

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