Density functional and ab initio study of the free radical MgNC

THEO CHEM ELSEVIER

Journal of Molecular

Structure (Theochem)

422 (1998) 133- 141

Density functional and ab initio study of the free radical MgNC’ Martina Kieninger”, Kenneth Irving”, F. Rivas-Silvab, Alejandro Palmab’c, Oscar N. Venturaa’* “MTC-Lab,

Facultad de Quimica, C.C. 1157, 11800 Montevideo, Uruguay

‘Institute de Fisica (BUAP), A.P. J-48, Puebla 72570, Mexico ‘Institute National

de A.strofi.sica, Optica y Electrdnica

Received

17 September

(INAOEJ, A.P. 51 y 216, Puebla, Pue. 72000, Mexico

1996; accepted 28 February

1997

Abstract A new “non-terrestrial” molecule present in the envelope of the carbon star IRC + 10216 was described for the first time in 1986. Recently, this molecule was identified as the free radical MgNC, the first Mg-containing molecule in space. We present here the first density functional study performed on this radical, as well as on its isomer MgCN and the transition state connecting these species. It is shown that the optimum geometry obtained at the Becke3LYP/6-31 l+G(3df) level leads to the most exact rotational constants B, and B, calculated up to now. It is also shown that the energy differences between the three species are completely in agreement with the best ab initio calculations available. Furthermore, it is shown that the popular MP2 method fails for this system in the same way that has been demonstrated for other radicals. 0 1998 Elsevier Science B.V. Keywords:

MgCN; Density functional;

Free radicals; Extraterrestrial

1. Introduction In 1986, M. Guklin et al. [ 1] reported the discovery molecule in the envelope of a new “non-terrestrial” of the carbon star IRC + I02 16. The spectral pattern they reported was consistent with a linear or slightly bent molecular free radical. Guklin et al. [1] determined a rotational constant of 5966.82 MHz and considered several candidates that could be responsible for these spectral lines, such as HSiCC, HCCSi, HSCC, CCCL etc. It was only recently, however, that Kawaguchi et al. [2], on the basis of laboratory microwave spectroscopy, were able to assign the unidentified lines in the circumstellar envelope of IRC +

* Corresponding author. E-mail: [email protected] ’ Extended abstract published in TMMeC I (1997) 10.

chemistry

10216 to MgNC, the first magnesium-containing molecule identified in space. Several theoretical studies have been performed on MgNC. The first published study was done by Bauschlicher et al. [3] in 1985, at the SCF and SDCVTZ2P levels. They predicted that MgNC is more stable than MgCN and calculated the energy of dissociation in fragments Mg and CN. More recently, Ishii et al. [4,5] performed a ROHF/TZ2P optimization of MgNC, MgCN and the transition state between them. They calculated also a 3D potential energy surface around the global minimum MgNC at the SDCII TZ2P level, from which they derived a vibrationally averaged rotational constant B, of 5939.7 MHz using their own values of the equilibrium rotational constant B, and rotation-vibration interaction constants (Y. Following an alternative method recently proposed by Carter et al. [6], they obtained an even better

0166- 1280/97/$17.00 0 1998 Elsevier Science B.V. All rights reserved. PI/ SOl66-1280(97)OOlOl-2

134

M. Kieninger

et al.Nournal

qf Molecular

value of 5975.2 MHz, in good agreement with the experimental results of 5966.82 MHz [l] or 5966.8969 MHz [2]. In this paper, we report a density functional study of MgNC, MgCN and the transition state between these species. Our goal was to answer the question of whether DFT is able to give results as precise as the best ab initio methods available, for geometries, energies and spectroscopic properties. The results show that DFT methods, used in combination with extended basis sets, are as good as (and less expensive than) SDCI calculations in this respect. Moreover, it is shown that MP2 calculations fail in predicting MgNC as more stable than MgCN using the same extended basis sets as used with DFT, and give a barrier about 30% (2 kcal mol-‘) lower than the most reliable results.

2. Methods Both ab initio and density functional calculations were performed using the GAUSSIAN 94 program package [7]. Geometry optimizations were performed using four different basis sets [8]. The characteristics of these basis sets can be seen in Table 1. Moller-Plesset perturbation theory at second order (MP2) [9] was employed to perform the ab initio geometry optimizations. Three different combinations of functionals were employed for the DFT geometry optimizations. In one case, the combination of Slater exchange functional [IO] with the Vosko et al. [I l] correlation functional was used and is identified as SVWN in the following. This functional is a realization of the so-called “local spin-density approximation” (LSDA). It works in DFT in a similar way to Table I Structure of the basis sets employed

Uncontracted

6-3 lG(d)

Mg: C.N: Mg: C,N: Mg: C,N: Mg: C,N:

6-3 I I+G(3d) 6-31 I+G(3df)

(Theochem)

422 (1998) 133- 14 1

Hartree-Fock in conventional ab initio calculations, serving as a reference functional to gauge the improvements introduced by modifications of the exchange or correlation potentials. The results of this local density functional were compared with the “non-local” Becke3LYP functional, in which the exchange potential is formed as a combination of the Slater exchange, the exact Hartree-Fock exchange and the Becke 1988 correction [ 121, using coefficients determined semiempirically [ 131, while the correlation functional is that of Lee et al. [14]. This method will be called B3LYP in the following. Finally, a combination of the “non-local” Becke3 exchange potential with the local VWN correlation potential was also employed, and is identified as B3VWN in the rest of the paper. The reason for including this non-standard potential is to assess whether the improvements observed by the use of B3LYP are dependent on the exchange or the correlation functionals (since both are modified in passing from LSDA to B3LYP). Frequency calculations were performed as usual to verify the character of the minima and transition states located at the ab initio and density functional levels. To obtain a good ab initio estimation of the energy difference between the MgNC and MgCN species, we also employed the complete basis set (CBS) extrapolation methods developed recently by Petersson and co-workers [ 15- 181. The methods employed here are identified as CBS-4, CBS-Lq and CBS-Q. CBS-4 is a relatively inexpensive method which can be applied to about 12 non-hydrogen atoms. First, a geometry optimization is performed at the HF/321G(d) level, followed by a large basis set HartreeFock calculation with 6-3 1 l+G(3d2f,2dfp,p) (this notation implies one extra d and f functions on elements Na through Ar). The frequency calculation, for

in this work

Set

6-31 lG(2d)

Structure

(16slOpld) (lOs4pld) (17sllp2d) (I ls5p2d) (I 8s I2p3d) (I 2s6p3d) (18s12p3dlf) (12s6p3dlf)

Contracted I08

122 149

170

Mg: C,N: Mg: C.N: Mg: C.N: Mg: C,N:

[4s3pl d] [3s2pld] [5s4p2d]

49 77

[4s3p2d]

[6s5p3d] [%4p3d] [6s5p3dl l-j [5s4p3d I fj

104 125

M. Kirningrr

et nl.Nound

of Molednr

obtaining the zero-point energy, is also performed at the HF/3-21G(d) level (with the force constants corrected by an appropriate scale factor). The CBS extrapolation scheme is then applied to an MP2/631+G(d’,p’) basis set (the ’ implies that the polarization functions are taken from the 6-31 lG(d,p) basis set), using a frozen-core MP4(SDQ)/6-3 1G calculation for correcting for higher than second-order effect in correlation energy. The model includes a correction for spin contamination and a size-consistent higher order correction. CBS-Q uses a larger basis set at each level of theory. The calculation starts with a UHF geometry optimization, frequency calculation and MP2 correlation energy correction always using the 6-31G(d’) basis set. The CBS extrapolation is based on an MP2/6-3 1 l++G(3d2f,2df,2p) calculation. Higher order contributions are estimated with two calculations: MP4(SDQ)/6_31+G(d-(f),d,p) where the (f)” indicates that there arefpolarization functions on elements P to Ar, and QCISD(T)/6-3 l+G(d’). This model also includes corrections for zero-point energy, spin contamination and higher order effects. Finally, the process is similar for CBS-Lq, which is intermediate between CBS-4 and CBS-Q. An initial geometry optimization is performed at the UHF/3-2 1G(d) level, followed by a frequency calculation. Then, correlation energy is added at the UQCISD(T)/6_31G, UMP4SDQ/6-3 lG(d’) and UMP2/6-3 l+G(d’,p’) levels. The CBS extrapolation is performed in the same way as in CBS-4. A better description of these methods can be found in the original references. A recent paper has been published by Ochterski et al. [22] on the analysis of several different model chemistries (including CBS-4, CBS-Q and Pople’s G2 [23]). It is known that these methods give an average accuracy of between 2 and 1 kcal mall’ in the G2 set of molecules of Pople and co-workers [23]. An additional set of ab initio calculations was performed using the multi-reference configuration interaction (MRCI) method, as coded in the MOLCAS-3 molecular orbital package [ 191. MRCI single-point calculations were performed on the B3LYP optimum geometries with each of the different basis sets reported before. All electrons were correlated in these calculations and all references contributing more than 0.1 to the wavefunction were included. Davidson correction was included in the calculations to take into account the effect of quadruple excitations [20].

Structure (Throc~hrm) 422 (1998) 133-141

135

The equilibrium rotational constants B, reported later in this work were calculated in the standard way at the optimum equilibrium geometries within each basis set. The ground state rotational constants B,, were obtained from them using the formula

where the ol were taken from the work of Ishii et al. [4].

3. Results The geometries of MgCN, MgNC and the transition state were optimized at the MP2, SVWN, B3VWN and B3LYP levels. These data are available in Table 2. The total and relative energies of the three species, obtained with the different methods with which the geometry was optimized, are collected in Table 3. The energies, enthalpies and free energies obtained with the CB2 methods are shown in Table 4. The results obtained at the MRCI level using the optimum B?‘LYP geometries are reported in Table 5. Finally, Table 6 shows the rotational constants at equilibrium obtained with the different methods. Also the ground-state rotational constants are displayed, although these were obtained using our own equilibrium rotational constants and the rotation-vibration constants of Ishii et al. [4,5] (23.7, - 85.2 and 32.9 MHz respectively).

4. Discussion Taking into account the results presented in the tables, several aspects can be discussed. Mainly, these are: (a) the influence of the basis set on the precision of the DFT results as compared with conventional ab initio calculations, (b) the influence of the different type of exchange and correlation functionals on the accuracy of the DFT results, and (c) the relative accuracy of DFT calculations with respect to ab initio ones. In the following, we address each one of these facets of the problem. 4.1. Basis set completeness The influence of the basis set on the geometry can be observed in Table 2. Regrettably, only for MgNC

M. Kienbqer

136 Table

et ul./Journal

of Molecular Srrucrure (Throchemj

422 (1998)

133-141

2

Geometrical

structure

in A and angles Basis set

of rhe three species studied

in this work,

with the different

methods

of calculation

and basis sets employed.

Distances

are

are in degrees MgNC

M&N r(MgC)

r(CN)

r(MgN)

Transition

state

r(NC)

r(MgC)

r(CN)

0

MP2 6-3lG(d)

2.09

I.1684

I .963 I

I.1959

2.0679

I. 1870

106.69

6-3 I I G(2d)

2.0830

1.1645

I .9525

I.1841

2.0703

1.1789

103.63

6-31 I+G(3d)

2.0848

1.1665

I .9535

I. 1855

2.0746

I. I SOS

101.39

6-31 l+G(3df)

2.0749

1.1658

I.945

I.1830

2.0652

I.1783

102.66

SVWN 6-3 I G(d)

I .974l

I.1718

I .8744

I.1917

I .9473

I.1790

112.41

6-3 I I G(2d)

I.9618

I. 1596

I xi44

I.1794

I .9370

I.1661

114.42

6-31 I+G(3d)

I .95SS

I. 1598

I Xi02

I.1804

I .9347

I.1667

113.31

6-31 l+G(3df)

I .9564

I.1590

I .8476

I.1795

I .9329

I.1658

113.21

B3VWN 6-3lG(d)

2.0905

I.1663

I .9553

I, I830

2.0849

I.1747

102.6s

6-3 I I G(2d)

2.0855

1.1554

I .9474

I.1711

2.0804

I.1634

103.62

6-3 I I+G(3d)

2.0882

I.1563

I ,948 I

I.1718

2.0864

I.1648

101.34

6-31 l+G(3df)

2.0847

I.1554

I .9448

I. I708

2.0837

I.1636

101.72

B3LYP 6-3lG(d)

2.0866

I.1682

I.951

I. I 849

2.0777

I.1764

104.28

6-31 lG(2d)

2.08 I4

I, 1573

I .9427

1.1730

2.0750

I. I649

104.84

6-31 l+G(3d)

2.0848

I.1584

I .9442

I.1737

2.08 I3

1.1666

102.12

6-3 I I +G(3df)

2.0813

I. IS75

I .9408

1.1727

2.079 I

I.1655

102.32

I .9370

l.lSSO

2.09 IO

1.1360

I.9310

I.1540

2.0740

I.1430

108.5

1.9310

I.1540

18

I

I

Literature ROHFITZP ROHFlTZ2P ROHFiTZZP ROHF/QZ?P SDCIITZ2P

+

1.9310

I.1540

I .94so

1.1700

are accurate post-Hartree-Fock data available in the literature. We have calculated full MP2 data here, and one can observe that although the Mg-N bond at the MP2/6-31 l+G(3df) level is in agreement with the SDCI/TZ2P result, this is not true with respect to the NC bond. Also in the MP2 geometries, one observes the same behavior in both cases: a reduction of about 0.017 A for the MgC and MgN bonds in MgCN and MgNC, respectively. Both B3VWN and B3LYP show a smaller variation of the geometries with the basis set. In Table 3, one can observe the convergence of the isomerization energy and the barrier height for the reaction with the basis set. These parameters are much more sensible to the completeness of the basis set than the geometries. There is a variation of about 2 kcal mol-’ on the isomerization energies at all levels between the worst and best values. Again, one

observes that the effect of the basis set on the DFT results is smaller than in the MP2 ones. In fact, the MP2 results for the barrier height have a spread of about 3.6 kcal mol-‘, while in the most sensible case, the DFT results spread over a range of about 2.9 kcal mol-‘. Leaving aside the 6-3lG(d) basis set, which is obviously too small, the spread of results for MP2, MRCI (using the Ref. + Corr. + Davidson results presented in Table 5), SVWN, B3VWN and B3LYP respectively are, for the isomerization energy, 0.18, 0.10, 0.24, 0.26 and 0.27 kcal mol-‘, and for the barrier height, 0.66, 0.62, 0.91, 1.08 and 0.98 kcal mol-‘. Therefore, for the best basis sets, the convergence is even better for conventional ab initio methods than for DFT ones. These two contradictory observations imply that DFT methods behave better than conventional ab initio ones if a small basis set is used.

Table 3 Total energies (in hartrees) and relative energies (in kcal mol-‘)

with respect to MgCN of the three species studied in this work, with different

methods and basis sets Basis set

MgCN

MgNC

AE

TS

AE

MP? 6-3 I G(d)

- 292.215600

- 292.2 I2659

6-31 IG(2d)

- 292.440340

- 292.440387

6-31 I+G(3d)

- 292.462 I70

6-3 I I +G(3df)

- 292.492 177

6-3lG(d)

- 291.334181

6-31 IG(2d)

- 291.379913

6-3 I I +G(3d) 6-31 I+G(3dt-)

- 292.2 IO268

I.5

- 0.03

I .85

- 292.433308

4.44

- 292.46 1932

0.14

- 292.453799

5.1 I

- 292.49 I954

0.14

- 292.483824

5.1

- 291.330716

2.17

- 291.327122

4.43

- 29 I .378492

0.89

- 291.374038

3.69

- 291.384008

- 29 I .382340

I .05

- 291.377021

4.38

- 291.387517

- 291.386229

0.8 I

- 291.380337

4.5

6-3 I G(d)

- 294.00288 I

- 294.003343

5.23

- 294.046 I 8 I

- 294.049522

- 0.29 _ 2.10

- 293.995007

6-31 IG(2d)

- 294.038976

6.62

- 1.84

- 294.041523

6.25

- 1.99

- 294.044033

7.71 4.8

SVWN

1

B3\‘WN

6-3 6-3

I I +G(3d) I 1+G(3df)

- 294.050 I46

- 294.053075

- 294.053 144

- 294.0563

- 292.907509

II

B3LYP - 292.907856

- 0.21

- 292.900 I95

I I G(2d) 1I +G(3d)

- 292.95 I445

- 292.955035

- 2.25

- 292.944709

6.48

- 292.955929

- 292.959080

- 1.98

- 292.947662

7.17

6-3 I I +G(3df)

~ 292.958949

- 292.962360

- 2.14

- 292.95047 I

7.46

6-3 I G(d) 6-3 6-3

Literature SDCUTZ2P

- 2.57

7.47

SDCI + Q/TZ2P

- 1.46

6.2 I

Table 4 Components

of the CBS energies (in hartrees) calculated

isomers is also reported (in kcal mol.‘). the Influence

of the vibrational

Enthalpies

for the two stable minima

and free energies are calculated

motton on the energy difference

Property

CBS-4

E(ZPE)

0.007296

E(0 K)

- 292.358417

- 292.364812

Energy

- 292.354843

Enthalpy

- 292.353899

Free energy

- 292.382063

CBS-Q

MgNC 0.0067 I8

Differences A(E-ZPE)(O

K)

- 3.65

AE(0 K)

- 4.01

- 292.361009

AE14X

- 3.87

- 292.360065

AH?%%

- 3.87

- 292.388768

Ac-X+

- 4.21

E(ZPE)

0.007296

ACE-ZPE)(O K)

- 2.90

Et0 K)

- 292.380007

- 292.385208

AE(0 K)

- 3.26

Energy

- 292.376432

- 292.381405

AE2’)X

- 3.12

Enthalpy

- 292.375488

- 292.380461

AHlYX

- 3.12

Free energy

- 292.403652

- 392.409 I64

AG/4X

- 3.46

E(ZPE)

0.007040

O.OOh718

0.0065 IO

A(E-ZPE)(O

K)

between both

to have an indication

between the isomers

Method

CBS-Lq

MgCN

in this work. The CBS energy dtfference

at normal pressure and temperature

- 1.75

Et0 K)

- 292.34928 I

- 292352.593

A&O K)

_ 2.08

Energy

- 29234.5474

- 292.348573

AE?#

- 1.94

Enthalpy

- 292.344530

- 292.341628

AHL’)X

- 1.94

Free energy

- 292.373303

- 292.377140

AG‘ZUX

- 2.41

of

138

M. Kirnirtpr

et ctl./Jounutl

of Molecular

Structure (Theoc.hern) 422 (199X) I_?& 141

Table 5 Components of Lhe MRCI total energies (in hartrees) and relative energies with respect to MgCN (in kcal mol -I). calculated with different hasi\ sets for the three species studied in this work. ERW stands for the weight of the extra reference configurations that must be included in the MRCI. Correlation and Ref. + Corr. are the energies calculated at the MR-SDCI level without including and including the energy of the main reference configuration, respectively. Davidson stands for Davidson’s approximate correction for quadruple excitations Species

Basis set

MgCN

6-3 I G(d) 6-31 IG(2d) 6-31 I+G(3d) 6-3 I I +G(.?df) 6-3lG(d) 6-31 IG(2d) 6-31 l+G(3d) 6-31 l+G(3df) 6-3 I G(d) 6-3 I I G( 2d) 6-31 l+G(3d) 6-31 I+G(3df)

TS

MgNC

-

Reference

ERW

Correlation

Ref. + Corr.

Dawdson

Total

291.883865 29 I .93X738 291.941666 29 I .944880 29 I .874898 29 I .932606 29 I .934439 29 I .937392 29 I .904707 29 I .950687 29 1.953402 29 I .956967

0.100 0. IO2 0.103 0.103 0.098 0.102 0.104 0.104 0.099 0.101 0.102 0.103

- 0.22743.5 - 0.405653 - 0.4 18739 - 0.44 I SO6 - 0.230096 - 0.404967 - 0.4 I8229 -0.441116 - 0.217666 -0.399lll - 0.412293 - 0.4349 I I

-

- 0.02452 I - 0.045870 - 0.047997 - 0.050930 - 0.025006 - 0.04624 I - 0.04833 I - 0.05 1236 - 0.02392 I - 0.044926 - 0.047006 - 0.049773

-

Species

Basis set

Reference

Ref. + Corr.

Ref. + Con-. t Dawdson

MgCN

6-31G(d) 6-31 IG(2d) 6-3 I I tG(3d) 6-31 ItG(3df) 6-3 I G(d) 6-31 IG(2d) 6-3 I I tG(3d) 6-31 I+G(3df)

- 13.08 - 7.so - 7.36 - 7.58 18.71 II.35 I I .90 12.28

- 6.95 - 3.39 ~ 3.32 - 3.45 IO.91 7.67 8.17 8.39

- 6.57 - 2.80 - 2.70 - 2.72 10.22 6.85 7.35 7.47

TS

4.2. Influence of the type of exchange and correlation functionals The three types of DFT calculations performed here differ both in the exchange and correlation potentials. SVWN presents the simpler “local” density type

Table 6 Equilibrium

and ground state rotational

constants

(in MHz) computed

using data from Ref. [2] and calculated

B3LYP

R,

B,>

B,

5732.8 5810.6 5802.6 5844.7

5789.7 15867.5 S859.5 5901.6

5814.2 5885.1 5876.4 5893.7 B,=5939.7 B, =5975.2

Experimental

in this work

MgCN

MP2

B, =5882.8

292. I3582 I 292.39026 I 292.408402 292.4373 16 292.130000 292.3838 13 292.400999 292.429745 292.146394 292.394723 292.412702 292.441652

functional for exchange and correlation. This type of potential is unable to describe the subtle details of weak interactions. Consequently, it wrongly predicts that MgNC is less stable than MgCN and the barrier height is half of what it should be (Table 3). In both these aspects SVWN behaves similarly to MP2. When

MgNC

6-3 lG(d) 6-3 I lG(2d) 6-3 I I t G(3d) 6-3 I 1 t G(3dfl SDCUTZ2P [2]

292.1 II300 292.344391 292.360404 292.386386 292. IO4994 292.337572 292.352668 292.378508 292. I22373 292.349797 292.365696 292.39 I878

B, = 5966.9

MP2

587 I. I 5942.0 5933.3 5950.6 (Meth. I) (Meth. 2)

B3LYP

B,

B,

4993.9 5033.7 5022.6 5058.0

5012.1 5057.8 5043.5 5057.6

M. Kieningrr

et ai.Nournd

of Molecular

the exchange potential is modified to a hybrid functional where the local exchange of Slater, the gradient corrections of Becke and the exact Hartree-Fock exchange are mixed with appropriate coefficients, the results are consequently much better. Now MgNC is more stable than MgCN and the barrier height is nearer to the more exact value. Finally, substituting the VWN correlation energy functional with LYP, the results suffer a small alteration in the correct direction, both for the barrier height and the isomerization energy (see next section) but the change is not so dramatic as when the exchange functional was changed. There is also a noticeable effect on the geometries, as one can see in Table 2. The MgC and MgN bonds are shorter for the SVWN optimum geometries than with all the other methods. The change on the exchange functional elongates the MgC and MgN bonds, and contracts the CN bond length. The change in the correlation energy functional again does not provoke such a large shift as the modification of the exchange functional. 4.3. Accuracy

of DFT and ab initio calculations

The accuracy of both DFT and MP2 calculations can be addressed with respect to the calculations of Ishii et al. [4,5] and our own MRCI calculations reported in Table 5, and the CBS calculations in Table 4. With respect to the energies (Table 3 and Table 5) one sees that both MP2 and SVWN calculations predict incorrectly the relative stability of MgNC with respect to MgCN (+0.14 and +0.81 kcal mall’, respectively). The values obtained by Ishii et al. [4,5] at the SDCI levels, using a TZ2P basis set, with and without inclusion of quadruple excitations, are -2.57 and -1.46 kcal mol-‘, respectively, while our own calculations give -3.45 kcal mol-’ (without quadruples) and -2.72 kcal mall’ (including quadruples). It must be noted that our MRSDCI/631 l+G(3df) values are more exact than those of Ishii et al. [4,5], both because of the use of a larger basis set and inclusion of more reference configurations in the CI. However, the geometries used in the calculations (DFT ones) are probably somewhat shifted from the true MRSDCI/6-3 1 l+G(3df) minima. Therefore, the values of -1.46 and -2.72 kcal mall’

Structure

(Theochem)

422 (1998)

133-141

139

may be taken as lower and upper limits to the best theoretical estimation of the actual isomerization energy. The values predicted by B3VWN (-1.99 kcal mall’) and B3LYP (-2.14 kcal mol-‘) are well within the allowed range mentioned before. To obtain a better estimation of the isomerization energy, we can employ the results shown in Table 4. Here are collected the CBS-4, CBS-Lq and CBS-Q results which, in order of increasing accuracy, predict isomerization energies of -3.65, -2.90 and -1.75 kcal mall’, respectively. This is another indication that the true isomerization energy lies in the interval pointed out above. These latter model chemistry results, however, cannot be used as accurate measures of the isomerization energy since they are, in a sense, “semiempirical” procedures which have an estimated error of about 2 kcal mall’. With respect to the energy barriers, one observes the same facts. The SDCI + Q value of Ishii et al. [4,5] is 6.21 kcal mall’, while our own MRSDCI/6-3 11+G(3df)// B3LYP/6-31 l+G(3df) value is 7.47 kcal mall’. Both the MP2 (5.10 kcal mol-‘) and SVWN (3.70 kcal mol-‘) barriers are too low. The B3VWN barrier (7.70 kcal mol-‘) is slightly too high, while the B3LYP barrier is completely in agreement with our own MRCI result (although it is probably higher than the actual barrier). With respect to geometries (Table 2), one sees that both B3VWN and B3LYP calculations give MgN and NC distances in agreement with the SDCI calculations. These are in turn, about 0.02 A larger than those obtained at the Hartree-Fock level. SVWN and MP2 calculations are wrong for opposite reasons. SlaterVWN gives a reasonable CN bond length but a too short MgN bond (much shorter than HartreeFock), while MP2 gives a reasonable MgN bond but a too large NC bond. In the case of the MgCN isomer and assuming that the B3LYP numbers are again correct, the same situation arises: MgC bond too short for SVWN and CN bond too large for MP2. The same situation is observed with respect to the transition state, with the added caveat that the MgCN angle given by SVWN calculations is too large, and there is agreement between MP2 and the other DFT methods. Finally, another estimation of the accuracy of the DFT calculations presented here can be made by looking at the rotational constants presented in Table 6. As

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previously mentioned, we used a mixed method to make the comparison with experiment, since the vibration-rotation constants were not calculated with the data in this paper but taken from Ishii et al. [4,5]. Accepting that this procedure is reasonable, then the value obtained from the B3LYP/63 1l+G(3df) geometry optimization of MgNC (5950.6 MHz) is very well in agreement with the experimental result (5966.9 MHz). A better comparison can be made between the equilibrium rotational constants (which then involves no data except those effectively calculated in this paper). The equilibrium rotational constant B, determined by Ishii et al. [4,5] is 5882.8 MHz, while that obtained at the Becke3LYP/6-311+G(3df) level by us is 5893.7 MHz, i.e. a difference of 0.2% between the results. The B3VWN result, probably just by chance, is astonishingly close to the SDCI one (5882.7 vs. 5882.8 MHz). The difference between the MP2 and SDCI results is more than three times larger than between SDCI and B3LYP. Another aspect of these calculations that must be taken into account is that the equilibrium rotational constant for MgCN is predicted at 5057.6 MHz (in this case in complete agreement with the MP2 and B3VWN methods). This value may be useful in checking for some of the unexplained millimeter lines found in the spectrum of the envelope of the carbon star IRC + 10216. What is more, very recently Ma et al. [21] calculated that the equilibrium rotational constant of AlNC is about 5882 MHz, totally overlapping the value of Ishii et al. [4,5] for the B, of MgNC. Therefore, it cannot be ruled out that AlNC is producing the observed lines instead of MgNC. Consideration of the MCN isomers instead (MgCN B, is around 5058 MHz, while AlCN B, is around 4982 MHz) and identification of their lines should give a method for solving this conflict.

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MRCI calculations, including single and double excitations as well as Davidson’s correction for quadruple excitations, were performed on the three species. The following conclusions were obtained from the analysis of the former results: B3LYP/6-3 1 l+G(3df) calculations are well converged with respect to the basis set and the choice of exchange-correlation functional to provide precise values for the structure and thermochemistry of the process studied. The values obtained for these properties are as accurate as the best ab initio ones. B3LYP/6-3 1 l+G(3df) calculations predict, in agreement with SDCI, MRSDCI and CBS calculations, that MgNC is more stable than MgCN. MP2 calculations, on the contrary, err in predicting MgCN as the most stable isomer. This error is also present in local density functional calculations (SVWN method). B3LYP/6-3 1 l+G(3df) calculations predict a barrier height in agreement with SDCI and MRSDCI calculations (7.46 kcal mol-’ vs. 6.21 and 7.47 kcal mall’, respectively). B3LYP/6-31 l+G(3df) calculations predict an equilibrium rotational constant which is only 0.2% different from the one predicted at the SDCI level of theory (5893.7 vs. 5882.8 MHz, respectively). As a general conclusion, we have demonstrated in this paper that Becke3LYP calculations using an extended enough basis set are able to give results as accurate as those obtained with the much more costly SDCI and MRSDCI methods. It is clear that the relative facility of the DFI calculations with respect to configuration interaction, coupled with the accuracy demonstrated in this paper in the specific case of the MgCN/MgNC system, can make them the method of choice for the analysis of still unexplained lines in the spectra of this and other similar stars.

5. Conclusions In this paper, we have performed post-HartreeFock MP2 and density functional geometry optimizations (using different exchange and correlation potentials) of the stable species MgNC and MgCN and the transition state connecting them. Additionally, CBS calculations at the CBS-4, CBS-Lq and CBS-Q levels were performed on the two stable species, and

Acknowledgements O.N. Ventura thanks the Alexander von HumboldtStiftung for a fellowship in Germany during which part of this work was done. This work is part of a project sustained by the InterAmerican Bank for Development (BID) and Conicyt-Uruguay.

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