Benchmark calculations with correlated molecular wave functions. II

Benchmark c@ctilations with correlated II. Configuration interaction calculations

molecular wave functions. on first row diatomic hydrides

Kirk A. Peterson, Rick A. Kendall, and Thorn H. Dunning, Jr.a) Molecular Science Research Center, Pacific Northwest Laboratory,b) Richland,

Washington 99352

(Received 11 January 1993; accepted22 April 1993) Potential energy functions have been calculated for the electronic ground statesof the first row diatomic hydrides BH, C.& NH, OH, and HF using single- (HF+ 1+2) and multi(GVB + 1 + 2 and CAS + 1+2) reference internally contracted single and double excitation configuration interaction (CI) wave functions. The convergenceof the derived spectroscopic constants and dissociation energies with respect to systematic increases in the size of the one-particlebasis set has beeninvestigatedfor each method using the correlation consistentbasis sets of Dunning and co-workers. The effect of augmenting the basis sets with extra diffuse fmlctions has also been addressed. Using sets of double (cc-pVDZ) through quintuple (cc-pV5Z) zeta quality, the complete basis set (CBS) limits for E,, D,, r,, and w, have been estimatedfor each theoretical method by taking advantageof the regular convergencebehavior. The estimated CBS limits are compared to the available experimental results, and the intrinsic errors associatedwith each theoretical method are discussed.The potential energy functions obtained from GVB + 1 + 2 and CAS + 1f 2 calculations are observedto yield very comparable spectroscopicconstants,with errors in D, ranging from 0.4 kcal/mol for BH to 2.9 kcal/mol for HF. The contraction errors associatedwith the internally contracted multireferenceCI have also been calculated for each species;while found to increasefrom BH to HF, they are, in general, small for all calculated spectroscopic constants. For the cc-pVDZ basis sets, spectroscopic constants have also been determined from full CI calculations. I. INTRODUCTION

The description of fundamental molecular processes using computational electronic structure techniques often requires a sophisticated treatment of electron correlation. However, the resulting accuracy of the correlated molecular wave functions can vary greatly with the size of the one-particle basis set used to represent the molecular orbitals. Often a more accurate correlated electronic structure method is used with a less accurate one-particle basis set. This leads to erratic results that limit our understanding of the true errors associatedwith the chosencorrelated method. The inherent accuracy of a correlated electronic structure method can only be assessedif the complete basis set (CBS) limit can be determined. Unfortunately, a regular convergencepattern is not observedupon extending the basis sets in common use today. Thus, it has not been possibleto estimate the intrinsic errors in correlated molecular wave functions and, hence, in molecular properties such as D,, r,, w,, etc. Although very large basis sets have been developed that have the potential of yielding very accurate results, e.g., the basis sets basedon atomic natural orbitals (ANO) ,* the systematics of these basis sets in regard to their convergencetoward the CBS limit have not been well explored. In addition, the AN0 sets are not the most efficient sets to use in molecular calculations due to the very large number of primitive functions. On the other hand, the correlation a)Electronic mail addresses: ka-pete&n&$gov, ra-kendali&pnl. gov, tb-dunning @ pnl.gov. “The Pacific Northwest Laboratory is operated for the U.S. Department of Energy by Battelle Memorial Institute under contract DE-AC0676RL0 1830. 1930

J. Chem. Phys. 99 (3), 1 August 1993

0021-9606/93/99(3)/l

consistent basis sets recently developed by Dunning and co-wgrkers2-4form a family of basis sets that are compact, convergesystematically to the CBS limit, and are well defined with respect to increases in size and accuracy. In thesebasis sets,groups of correlating s, p, d,... functions are added in shells to the atomic orbitals. Each function within a shell contributes a nearly equal amount to the correlation energy. By using systematically larger correlation consistent basis sets, it has been found that many molecular properties converge smoothly to an asymptotic limit. Given the construction of the basis sets, it is reasonableto assume that this limit corresponds to the CBS limit. By comparing the CBS limits to experimental measurements, it is possible to determine the intrinsic errors associated with a chosen electronic structure method. The present work is the second in a series of benchmark studies investigating the convergenceof molecular potential energy functions calculated with different correlated methods. In the first of this series,5the electronic ground states of the diatomic hydrides of the second row (A.lH, SiH, PH, SH, and HCl) were characterized using multireference configuration interaction (MRCI) techniques and correlation consistent basis sets through quintuple zeta quality. Similar work involving both the first and secondrow homonuclear and heteronucleardiatomics is in progress.6*7 In the current work, the potential energy functions of the first row diatomic hydrides BH, CH, NH, OH, and .&_ HF have been computed using singles and doubles configur&oxi interaction ((?I) wave functions. The refer- ence wave functions used in these CI calculations include Hartree-Fock (HF) , generalized valence bond (GVB ) , and complete active space (CAS) . 930/l 5/$6.00

0 1993 American Institute of Physics

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Peterson, Kendall, and Dunning, Jr.: Benchmark

HF wave functions are the standard in molecular electronic structure calculations. GVB and CAS wave functions account for the nondynamical correlation effects required to obtain a qualitatively correct description of bond breaking, excitation energies, etc. The CI wave functions HF+1+2, GVB+1+2, and CAS+1+2 take into account dynamical correlation effects. The inclusion of dynamical correlation effects is required for quantitative predictions of molecular properties. The convergence of the resulting spectroscopic constants and dissociation energies has been investigated at each level of theory. It has been found that the calculated values of E,, De, and r, vary smoothly with increasing basis set size. By exploiting this regular behavior, limiting values-an estimate of the complete basis set (CBS) limit-can be obtained. The derived CBS limits can then be compared to the available experimental data to obtain the intrinsic errors associatedwith each of the correlated wave functions. II. COMPUTATIONAL

METHODOLOGY

The majority of the calculations reported in this paper were carried out with the MOLPR092 suite of ab initio electronic structure programs8 In the first step, HF, GVB, and CASSCF calculations were performed. The resulting orbitals were then used in subsequentHF+ 1 + 2 and internally contracted multireference CIg”o calculations (GVB+ 1+2 and CASSCF+ 1+2). While the errors associated with the internal contraction have been studied previously, only relatively small basis sets were employed.g Thus, a number of large basis set uncontracted CASSCF+ 1+2 calculations have been carried out using the COLUMBUS series of programs.” A. Basis sets

The correlation consistent polarized valence basis sets of Dunning and co-workers2-4 have been used in the present work. The double, triple, quadruple, and quintuple zeta sets, which are denoted by cc-pVXZ (X=D, T, Q, and 5>,’ correspond to generally contracted12basis sets of [3s2pld], [4s3p2dlf], [%4p3d2flg], and [6s5p4d3f2glh], respectively, for the first row atoms. In contrast to AN0 basis sets,’which employ a fixed number of (sp) primitives, the size of the (sp) primitive sets increase from (9s4p) in the cc-pVDZ set to ( 14~8~)in the cc-pV5Z set. Thus, thesebasis sets systematically approach the HartreeFock limit. In addition, the polarization functions in the cc-pVXZ sets are uncontracted, primitive Gaussian-type functions. The correlation consistent basis sets for hydrogen are defined in a similar manner, but in each case include one less function per angular momentum symmetry. Correlation consistent basis sets augmented by additional diffuse functions in each angular momentum symmetry have also been derived by Kendall et al3 and are denoted by aug-cc-pVXZ. These sets provide a more accurate description of negative ions, long range molecular interactions, etc. For all species,augmented sets with X=D, T, and Q have been used to test the basis set convergenceof the regular cc-pVXZ basis sets. For the casesof OH and

calculations.

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HF, where considerable ionic character is present in the wave functions, i.e., H+F- character, an aug-cc-pV5Z basis set13has also been employed. B. CAS and GVB wave functions

In the CAS calculations,‘47”5all of the valence molecular orbitals arising from the atomic 1sorbital of hydrogen and the 2s and 2p orbitals of the first row atoms were included in the active space (2+4a, lrx, and l?~,,).Qualitatively, these correspond to the AH bonding (3~) and antibonding (40) orbitals and the first row atom 2s (2~) and nonbonding lone pair orbitals ( 1~). The la orbital corresponding to the 1satomic orbital of the first row atom was optimized, but left doubly occupied in all configurations. For CH(X”II) and OH(X ‘II), orbitals with the correct spatial symmetry were obtained by state averaging the two degenerate2H, and ‘I$, states. Furthermore, in the cases of OH and HF steps were taken to minimize the mixing of the lu and 20 orbitals, which can lead to poorer CI results when the la core orbital is not correlated.16*‘7 The mixing was minimized by carrying out two separate MCSCF calculations. In the first step, both the lo and 2a orbitals were constrained to be doubly occupied with the active space as previously described. The second MCSCF calculation then used these orbitals as a starting guesswith the la orbital now frozen (doubly occupied and not reoptimized); in these calculations, excitations were allowed out of the 20 orbital. This has the largest effect at the dissociation limit, where the 20 orbital is exactly doubly occupied and can mix strongly with the la orbital. In this case, the above procedure has no effect on the MCSCF energy, but greatly improves the CI results. The GVB wave functions were computed in a MCSCF procedure using a subset of the CAS configurations. For NH(X 38-), OH(X’H), and HF(X lx’), these consisted of just the direct product of the occupied orbitals of 7-r symmetry with the configurations 12223>, 1~2~3a40, and 122242. In the casesof BH(X ix+) and CH(X ‘II), additional configurations were included to account for the 2s~2p near-degeneracyeffect.‘* Specifically, these involved configurations of the type 2a2+ 12. C. hF+1+2, functions

GVB+l+S,

and CASSCF+1+2

wave

The orbitals obtained in the HF, GVB, and CAS calculations were used in subsequentsingle and double excitation configuration interaction calculations. For the GVB + 1+2 and CASSCF+ 1+2 wave functions, the internally contracted MRCI method of Werner and Knowlesg’to was used. All single and double excitations were taken with respect to the MCSCF referencefunctions, and the configurations with two electrons in the external orbital spacewere internally contracted. For the CI calculations on CH and OH, only one component of the doubly degenerateIl state was calculated from the state-averaged orbitals. Excitations out of the lo orbital were not allowed (frozen core approximation). Thus, effects due to corecore and core-valence correlation have not beenaddressed

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Peterson, Kendall, and Dunning, Jr.: Benchmark calculations.

in this work. Since molecular iriteractions are dominated by valence effects, the neglect of core-core and corevalencecorrelation is not likely to be important here.lg In addition, the correlation consistent basis sets were not designedto treat nonvalencecorrelation and their use in such calculations could lead to somewhat erratic convergence behavior. While internal contraction of double excitations is expected to have only a small effect on the calculated specLroscopicconstantsand dissociation energies,9’20 a number of uncontractedcalculations were carried out to determine the actual contraction errors. Conventional singles and doublesMRCI calculations were carried out for each species using the CAS wave functions with the cc-pVQZ basis set. The orbitals were identical to those used in the internally contracted cases.In addition, for OH we determined the variation in the error upon enlarging the basis set from cc-pVDZ to cc-pVTZ to cc-pVQZ. With the exception of BH, where the internally contracted and uncontracted MRCI’s are identical (CAS reference), the internally contracted CI resulted in four to six times fewer variational parametersthan the correspondinguncontracted casesfor the other speciesof this series. This, however, was not a significant factor for these species,since the largest uncontracted MRCI calculation carried out in this study involved only 137 382 parameters (for OH). The internal contraction approach can be even more advantageousin larger molecular systems, where uncontracted MRCI calculations becomeintractable.21’22 D. Potential energy functions constants

and spectroscopic

Potential energy functions (PEFs) were calculated for eachspeciesby fitting seven’energyvalues that coveredthe range -0.3+0.4ao to polynomials of sixth deSpectroscopicconstants were then degree in b=r-r,. rived from the resulting PEF coefficientsby the usual second order perturbation theory expressions.23 The separated energieswere computed in a supermoleculeapproach at r=50ao. For the GVB, CAS, GVB + 1+2, and CAS + 1-t 2 wave functions, this is equivalent to adding the appropriate atomic energies. For the HF and HF + 1+2 wave functions, where the supermoleculecalculations were not possible,the energiesof the isolated ground state atoms were computed. To remain consistentwith the supermoleculeresults, the separatedatoms were computed in C,, symmetry, and for carbon and oxygen, the degenerate 2p, and 2p, components of the ‘P ground state were state averaged. E. Extrapolation

to the complete

basis set limit

Smoothly varying basis set dependencehas been observedfor quantities such as E,, D,, r,, and w, when using correlation consistent basis sets.592k26 In most cases,this behavior is well describedby a simple exponentialfunction of the form A(X)

=A(

00) + BewCX,

(1)

0.1 1

II

I DZ

I QZ

I TZ

I 5Z

I

FIG. 1. Convergence of the calculated correlation energies for the oxygen atom (HF+ 1 + 2) and OH hydroxyl radical (CAS + 1 + 2). The convergence of the dissociation energy of OH is also plotted. The lines are fits to Eq. (1).

whereX is the cardinal number of the basis set (2, 3,4, and 5 for double, triple, quadruple, and quintuple zeta sets, respectively) and A ( CO>, B, and C are adjustableparameters determinedin a nonlinear least squaresprocedure.For X-t CO,the parameterA ( CO> correspondsto the estimated complete basis set limit for the molecular property A. The use of integers for X is a direct consequenceof the manner in which the basis sets are constructed and reflects the monotonic convergenceof basis set contributions for each angular symmetry as observedfor the first and secondrow atoms.2’5In the present work, exponential fits have been determined for E,, D,, and r, for eachAH speciesat each level of theory. Although the computed harmonic frequencies w, generally exhibit regular convergencetoward an asymptotic limit, they are not well representedby Eq. ( 1) . However, the cc-pV5Z or aug-cc-pV5Zvalues are expected to be quite close to the CBS limit. Exponential convergenceof atomic correlation energies for the correlation consistent basis sets has ,recently been demonstratedby Woon and Dunning’ for the second row atoms. Not surprisingly, we find this also to be true for the first row atoms (see also Ref. 2). Figure 1 compares the rate of convergenceof the correlation energyof atomic oxygen (HF+ 1+2) and the hydroxyl radical (CAS+ 1+2). The convergencerate, as measuredby the slope ( C) , is remarkably similar to the two species,and the fit of the energiesto Eq. ( 1) is observedto be very good in both cases.The fact that C is nearly identical for 0 and OH implies that energy differences,i.e., D, will also converge exponentially with essentially the same slope. This is also illustrated in Fig. 1. Ill. RESULTS AND DISCUSSION A. Calculated

spectroscopk

constants

Spectroscopicconstantscalculatedfor the ground electronic states of each speciesfor each basis set and level of

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Peterson, Kendall, and Dunning, Jr.: Benchmark calculations.

theory are compared to the available experimental values in Tables I-V. To provide a rigorous comparison between theory and experiment, the experimental 0, valuesin these tables have been approximately corrected for spin-orbit effects, which are not included in the present calculations. The corrected De for the HF molecule, e.g., is obtained by adding one third of the splitting between the J= l/2 and J=3/2 states of 2P atomic fluorine Q=~~pt+$w~1,2)

--Q2J3,2)

1

(2)

to the measuredDe. This formula assumesthat spin-orbit effects are completely quenchedin HF. Using the atomic excitation energiesof Moore,27the correction for the De of HF amounts to +0.38 kcal/mol. Corrections for the other species can be obtained in a similar manner. For CH(X ‘Ii) and OH(X 211),the correction includes cancellations due to the molecular spin-orbit splitting between states, the contribution of which is the 2111,2and 2H113,z given by - (A/2), whereA is the spin-orbit constant taken from the compilation of Huber and Herzberg.28The resulting corrections for BH, CH, NH, and OH amount to only (in kcal/mol) 0.03, 0.04, 0.00, and 0.02, respectively, and have been neglected;therefore, only HF is affected. While it is outside the scope of this work to make an exhaustive comparison of our results to previous ab initio work, in the following we have included comparisonsto a few recent results using large basis sets and high levels of electron correlation. 1. BH, CH, and NH

While the majority of the spectroscopic constants of BH are well known experimentally, there is still some uncertainty in the value of the dissociation energy. Previous experimental studies have yielded a value of 82.2 kcal/ mo1,28while Bauschlicher et al.2g recommendeda value of 84.8AO.5 kcal/mol for De from [5s6pSd2flg]/[4s3~2d] AN0 basis set MRCI calculations. The estimated CBS limit at the CAS+ 1+2 level for both the cc-pVXZ [Table I(a)] and aug-cc-pVXZ [Table I(b)] basis sets is 84.4 kcal/mol. This is nearly unchanged from the values directly calculated with the cc-pV5Z (84.4 kcal/mol) and aug-cc-pVQZ (84.2 kcal/mol) basis sets. Using the estimates of Bauschlicher et a1.29 for the effects of corevalence correlation (0.24 kcal/mol) and an estimate for the effects of a larger active space in the MRCI (0.15 kcal/mol) ,30we obtain a value of 84.8 kcal/mol, which is in excellent agreement with the results of Bauschlicher et al. 2g

The results for CH (Table II) are similar to those for BH, where the effects of the diffuse functions were also very small. The estimated CBS limit for D, at the CAS+ 1+2 level of theory (83.0 kcal/mol) is smaller than experiment by 0.9 kcal/mol. The correspondingvalue using a GVB referencefunction (GVB f 1 + 2) is too low by 1.1 kcal/mol. These results for De can be compared to the large AN0 basis set results of Bauschlicher and Langhoff calculated using the MCPF method3’*3’(81.3 kcal/mol) (Ref. 33) and MRCI (82.9 kcal/mol).34 For both the CAS + 1+2 and GVB + 1-1-2 methods, our calculated

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spectroscopicconstantsare in excellent agreementwith experiment using either the cc-pVQZ or cc-pV5Z basis sets. For the ground state of NH, the dissociation energy is also not well known experimentally. A range for De of 80.5-84.7 kcal/mol has been recommendedby Hofzumahaus and Stuh1.35MRCI calculations by Bauschlicher and Langhoff 34using the same size AN0 basis set as for BH (Ref. 29) and CH (Ref. 34,) resulted in an estimate of 82.3f 0.7 kcal/mol for D,. The estimated CBS limit from the CAS + 1+ 2 calculations (Table III) of 8 1.4 kcal/mol is in good agreementwith this latter value, especially after estimates for core correlation (0.25 kcal/mol) (Ref. 29) and a larger MRCI active space (0.9 kcal/mol) (Ref. 30) are included (De= 82.5 kcal/mol). An alternate estimate of the equilibrium dissociation energy of NH can be obtained by assuming the relative error in the correlation treatment (using the estimated CBS values) of NH is approximately equal to the averageof those for CH and OH (seebelow). This also yields a predicted De for NH of 82.5 kcal/mol. As observedpreviously for BH and CH the spectroscopic constants computed with the aug-cc-pVXZ basis sets for NH are nearly identical to those calculated with the cc-pVXZ sets. 2. OH and HF

Spectroscopicconstants calculated for OH(X ‘II) and HF(X ‘X+) are shown in Tables IV and V, respectively. For both of these species,the addition of diffuse functions to the basis sets has a more substantial effect than the other membersof this series.For CAS + 1 + 2 calculations on the ground state of the OH molecule, the aug-cc-pVQZ basis set yields values for r, and De, which differ from the ccpVQZ values by 0.0007 A and 0.7 kcal/mol, respectively. For HF, the differencesare slightly larger at 0.0010h; and 0.9 kcal/mol. As expected,at the quintuple zeta level, the differencesare much sma11e&-0.0002A and 0.2 kcal/mol for OH and 0.0004 A and 0.2 kcal/mol for HF. In each case, however, the estimated CBS limits for De (CAS+ 1+2) differ by just 0.1 kcal/mol. Our best directly calculated results for the equilibrium dissociation energy of OH 104.8 kcal/mol [CAS+ 1+2/ aug-cc-pV5Z from Table IV(B)] can be compared to the experimental value of 106.6kcal/mol (Ref. 28) and to the previous a& initio result of Langhoff and co-workers34J36’37 (105.9 kcal/mol) obtained using a large reference space (including nonvalenceconfigurations) in their MRCI calculations. Our CASSCF + 1+ 2/aug-cc-pV5Z result for HF (138.6 kcal/mol [Table V(B)]) is somewhat smaller than the CCSD(T) result of Martin3* (139.7), which was calculated with the cc-pVQZ basis set. Our best computed De’s for OH and HF are smaller than experiment by 1.8 and 3.0 kcal/mol, respectively. These errors are a result of the use of (a) MRCI referencefunctions that only include excitations among the orbitals in the valencespace;(b) the limitation of the excitation level to a maximum of double excitations; and (c) internal contraction of the doubly excited configurations. The use of the multireference analog of the Davidson correction39 to estimate the effects of

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*

Peterson, Kendall, and Dunning, Jr.: Benchmark calculations. II

TABLE I. Calculated and experimental spectroscopic constants for the ground state X ‘Z+ of BH (A) With the cc-pVXZ basis sets. (B) With the aug-cc-pVXZ basis sets.

Method

Basis set

0,

4

(hattrees)

Expt.a (4

(cm-‘)

we%

(cm-‘)

4

a,

(cm-‘)

(cm-‘)

1.2324

2366.9

49.4

12.021

0.412

cc-pVDz cc-pVTZ cc-pVQZ cc-pvsz Estimated CBSb

-25.125 337 -25.129 973 -25.131 351 -25.131615 -25.13179

62.4 64.0 64.3 64.3 64.3(64.3)

1.2360 1.2221 1.2203 1.2200 1.2200

2492.6 2483.0 2487.3 2488.2

44.1 42.6 42.8 42.9

11.951 12.225 12.261 12.267

0.3656 0.3740 0.3762 0.3753

HF+1+2

cc-pVDz cc-pvTZ cc-pVQZ cc-pvsz Estimated CBSb

-25.210 859 -25.225 650 -25.229 859 -25.230 935 -25.23141

77.3 81.2 82.1 82.3 82.4( 82.4)

1.2535 1.2332 1.2311 1.2305 1.2306

2362.1 2372.0 2380.0 2381.6

47.1 47.3 46.9 47.2

11.621 12.005 12.046 12.058

0.3876 0.4118 0.4093 0.4099

GVB

cc-pVDZ cc-pVTZ cc-pVQZ cc-pvsz Estimated CBSb

-25.177 -25.184 -25.186 -25.186 -25.186

880 453 176 466 64

74.2 76.6 76.9 77.0 77.0(77.0)

1.2645 1.2480 1.2465 1.2462 1.2462

2294.2 2302.8 2307.8 2308.9

48.8 46.9 47.2 47.3

11.418 11.722 11.751 11.757

0.3998 0.4068 0.4079 0.4070

cc-pVDZ cc-pVTZ cc-pVQZ cc-pvsz Estimated CBSb

-25.215 -25.230 - 25.234 -25.235 -25.236

084 544 879 979 46

79.0 83.0 84.0 84.2 84.3(84.3)

1.2562 1.2358 1.2337 1.2330 1.2332

2339.2 2347.3 2355.5 2357.1

48.6 48.9 48.6 48.9

11.570 11.955 11.997 12.010

0.3960 0.4220 0.4197 0.4204

CASSCF

cc-pVDZ cc-pVTZ cc-pVQZ cc-pvsz Estimated CBSb

-25.179 238 -25.185 683 -25.187 369 -25.187 656 -25.187 83

75.1 77.4 77.7 77.7 77.7(77.7)

1.2674 1.2512 1.2496 1.2493 1.2493

2267.5 2274.4 2279.8 2281.0

50.4 48.5 48.8 48.9

11.366 11.663 11.693 11.698

0.4111 0.4187 0.4198 0.4190

CASSCF+ 1+2

cc-pVDZ cc-pVTZ cc-pVQZ cc-pvsz Estimated CBSb

-25.215 180 -25.230 735 -25.235 093 -25.236 198 -25.236 68

79.1 83.2 84.1 84.4 84.4( 84.4)

1.2562 1.2358 1.2337 1.2330 1.2332

2338.6 2346.9 2354.9 2356.4

48.6 48.9 48.6 48.9

11.570 11.955 11.996 12.010

0.3962 0.4223 0.4199 0.4207

RHF

aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ Estimated CBSb

-25.126 427 -25.130 248 -25.131428 (-25.13195)

62.9 64.1 64.3 (64.3)

1.2328 1.2213 1.2201 (1.2200)

2479.9 2485.4 2488.3

42.6 42.9 42.9

12.013 12.241 12.265

0.3668 0.3762 0.3763

HF+1+2

aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ Estimated CBSb

-25.213 663 -25.226 436 -25.230 112 (-25.23160)

78.0 81.5 82.2 (82.4)

1.2505 1.2331 1.2311 (1.2308)

2342.4 2370.8 2379.4

46.9 47.5 47.2

11.676 12.008 12.046

0.3969 0.4129 0.4102

GVB

aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ Estimated CBSb

-25.179 113 -25.184 702 -25.186 231 (-25.186 81)

74.7 76.7 76.9 (77.0)

1.2612 1.2476 1.2464 (1.2463)

2285.4 2304.6 2308.6

47.3 47.0 47.2

11.479 11.731 11.753

0.3995 0.4075 0.4078

aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ Estimated CBSb

-25.218 066 -25.231 374 -25.235 141 (-25.236 63)

79.8 83.3 84.1 (84.3)

1.2536 1.2358 1.2337 (1.2334)

2316.6 2345.5 2354.7

48.4 49.1 48.8

11.618 11.955 11.996

0.4060 0.4233 0.4207

CASSCF

aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ Estimated CBSb

-25.180 -25.185 -25.187 (-25.187

444 915 421 99)

75.6 77.5 77.7 (77.7)

1.2641 1.2507 1.2495 (1.2494)

2259.0 2276.3 2280.7

48.8 48.6 48.8

11.426 11.672 11.694

0.4103 0.4195 0.4197

CASSCF+ 1 t-2

aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ Estimated CBSb

-25.218 200 -25.231 578 -25.235 358 (-25.236 85)

79.9 83.5 84.2 (84.4)

1.2537 1.2358 1.2337 (1.2334)

2316.0 2344.9 2354.0

48.5 49.1 48.9

11.616 11.955 11.996

0.4063 0.4236 0.4209

RHF

GVB+l+Z

09

we

(kcal/mol)

GVB+1+2

‘Reference 28. bValues in parentheses were obtained from three-point (VDZ, VTZ, and VQZ) fits to Eq. (1). J. Chem. Phys., Vol. 99, No. 3, 1 August 1993

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Peterson, Kendall, and Dunning, Jr.: Benchmark calculations.

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TABLE II. Calculated and experimental spectroscopic constants for the ground state X *II of CH. (A) With the cc-pVXZ basis sets. (B) With the aug-cc-pVXZ basis sets. we Method

Basis set

(hazees)

cc-pVDZ cc-pVTZ cc-pVQZ cc-pV5Z Estimated CBSb

-38.268 - 38.277 -38.279 -38.279 -38.280

(kcakol)

Expt.a (4

(cm

-1

1

02% (cm-‘)

4 -1 (cm )

a, (cm

-‘I

83.9

1.1199

2858.5

63.0

14.457

0.534

782 032 342 917 17

54.7 56.8 57.2 57.3 57.3(57.3)

1.1179 1.1052 1.1039 1.1035 1.1036

3048.7 3036.7 3043.7 3047.1

58.8 54.0 54.9 55.1

14.509 14.844 14.879 14.890

0.4815 0.4740 0.4776 0.477 1

cc-pvsz Estimated CBSb

-38.375 268 -38.403 447 -38.411284 -38.413 602 -38.414 44

73.5 79.0 80.4 80.9 81.0(80.9)

1.1399 1.1190 1.1167 1.1161 1.1162

2851.6 2879.3 2893.9 2898.6

64.1 59.9 60.4 60.8

13.954 14.481 14.539 14.557

0.5149 0.5182 0.5178 0.5181

GVB

cc-pVDZ cc-pVTZ cc-pVQZ cc-pvsz Estimated CBSb

-38.302 -38.310 -38.312 -38.313 -38.313

887 672 985 529 82

65.1 67.0 67.3 67.4 67.5 (67.4)

1.1517 1.1378 1.1362 1.1357 1.1358

2708.9 2707.0 2716.9 2720.5

72.5 67.0 67.8 68.1

13.670 14.005 14.046 14.057

0.5696 0.5589 0.5624 0.5625

GVB+l+Z

cc-pVDZ cc-pVTz cc-pVQZ cc-pvsz Estimated CBSb

‘-38.379 -38.407 -38.415 -38.418 -38.419

067 888 847 182 01

75.1 80.7 82.2 82.6 82.8(82.7)

1.1437 1.1229 1.1207 1.1200 1.1201

2806.8 2832.2 2846.4 2850.8

67.9 63.6 64.0 64.4

13.862 14.379 14.436 14.454

0.5345 0.5382 0.5373 0.5380

CASSCF

cc-pVDz cc-pVTZ cc-pVQZ cc-pvsz Estimated CBSb

-38.304 -38.312 -38.314 -38.315 -38.315

749 368 662 200 50

66.3 68.0 68.4 68.5 68.5(68.5)

1.1521 1.1386 1.1369 1.1364 1.1365

2696.5 2693.8 2704.3 2707.9

73.0 67.5 68.4 68.8

13.660 13.986 14.028 14.040

0.5766 0.5663 0.5698 0.5699

CASSCF+ I+2

cc-pVDZ cc-pVTZ cc-pVQZ cc-pvsz Estimated CBSb

-38.379 -38.408 -38.416 -38.418 -38.419

273 242 228 570 40

75.2 80.9 82.4 .82.9 83.0(83.0)

1.1438 1.1230 1.1208 1.1201 1.1202

2806.2 2831.7 2845.8 2850.2

67.7 63.3 63.7 64.0

13.859 14.377 14.434 14.452

0.5340 0.5376 0.5367 0.5374

RHF

aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ Estimated CBSb

-38.271 -38.277 -38.279 (-38.280

336 762 561 26)

55.8 57.2 57.3 (57.3)

1.1153 1.1044 1.1037 (1.1036)

3049.4 3043.3 3045.7

57.7 54.4 54.9

14.575 14.867 14.886

0.4797 0.4770 0.4777

HF+1+2

aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ Estimated CBSb

-38.381760 -38.405 569 -38.411 998 (-38.414 38)

75.0 79.7 80.7 (80.9)

1.1364 1.1184 1.1167 (1.1165)

2854.5 2883.9 2894.7

64.3 59.7 60.5

14.040 14.497 14.541

0.5212 0.5198 0.5181

GVB

aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ Estimated CBSb

-38.304 875 -38.311 246 -38.313 153 (-38.313 97)

66.0 67.3 67.4 (67.5)

1.1490 1.1369 1.1359 (1.1358)

2709.8 2712.5 2718.8

70.9 66.8 67.7

13.734 14.028 14.052

0.5666 0.5606 0.5624

GVB+I-t2

aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ Estimated CBSb

-38.385 -38.410 -38.416 (-38.418

809 074 574 95)

76.7 81.5 82.5 (82.7)

1.1406 1.1224 1.1207 (1.1205)

2806.2 2835.9 2846.8

68.2 63.3 64.1

13.938 14.393 14.437

0.5416 0.5393 0.5378

CASSCF

aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ Estimated CBSb

-38.306 671 -38.312 918 -38.314 823 (-38.315 66)

67.1 68.3 68.5 (68.5)

1.1493 1.1376 1.1366 (1.1365)

2698.1 2699.4 2706.2

71.3 67.3 68.4

13.727 14.011 14.035

0.5732 0.5680 0.5698

CASSCF+ 1+2

aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ Estimated CBSb

-38.386 -38.410 -38;416 (-38.419

76.8 81.7 82.7 (82.9)

1.1407 1.1225 1.1208 (1.1206)

2805.4 2835.3 2846.2

67.9 + 63.0 63.8

13.935 14.390 14.434

0.5409 0.5387 0.5371

RHF

HF+1+2

cc-pVDz cc-pVTZ

c+PVQZ

(W

J,

062 442 958 33)

*Reference 28. bValues in parentheses were obtained from three-point (VDZ, VTZ, and VQZ) fits to &f. ( 1). J. Chem. Phys., Vol. 99, No. 3, 1 August 1993 Downloaded 27 May 2009 to 140.123.79.230. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/jcp/copyright.jsp

d 1936

i

in

Peterson, Kendall, and Dunning, Jr.: Benchmark calculations. II

TABLE III. Calculated and experimental spectroscopic constants for the ground state X 32- of NH. (A) With the cc-pVXZ basis sets. (B) With the aug-cc-pVXZ basis sets.

Method

Basis set

Et? (hartrees)

(lccakrol)

Expt.’ (A)

% (cm-‘)

06-G (cm-‘)

4 (cm--‘)

a, (cm-‘)

1.0362

3282.3

78.3

16.699

0.6490

RHF

cc-pVDZ cc-pVTZ cc-pVQZ cc-pvsz Estimated CBSb

-54.959 618 - 54.973 794 - 54.977 561 -54.978 561 -54.978 93

45.1 48.1 48.6 48.8 48.8(48.7)

1.0290 1.0186 1.0175 1.0174 1.0174

3518.6 3542.2 3548.0 3550.5

66.7 65.3 65.6 65.6

16.934 17.282 17.319 17.323

0.5706 0.5737 0.5754 0.5733

HF+1+2

cc-pVDZ cc-pVTZ cc-pVQZ cc-pvsz Estimated CBSb

-55.086 -55.132 -55.145 -55.149 -55.150

892 519 397 434 85

69.4 76.4 78.5 79.1 79.4(79.3)

1.0519 1.0346 1.0323 1.0319 1.0319

3253.7 3331.3 3348.9 3353.4

75.5 73.0 73.0 72.8

16.205 16.752 16.826 16.839

0.6239 0.6258 0.6238 0.6215

GVB

cc-pVDZ cc-pVTz cc-pVQZ cc-pvsz Estimated CBSb

- 54.983 179 -54.997 017 -55.cKN 880 -55.001860 - 55.002 28

59.9 62.7 63.2 63.4 63.4(63.4)

1.0596 1.0478 1.0463 1.0460 1.0460

3103.8 3141.6 3154.2 3158.0

91.5 88.7 88.7 88.9

15.970 16.332 16.379 16.388

0.7124 0.7107 0.7094 0.7073

cc-pVDz cc-pVTZ cc-pVQZ cc-pvsz Estimated CBSb

-55.089 -55.135 -55.148 -55.152 -55.153

017 121 091 149 57

70.7 78.0 80.2 80.9 81.1(81.0)

1.0563 1.0394 1.0372 1.0368 1.0368

3184.9 3257.6 3274.7 3279.2

82.3 79.3 79.1 79.2

16.070 16.597 16.667 16.680

0.6587 0.6597 0.6571 0.6544

cc-pVDz cc-pVTZ cc-pVQZ cc-pvsz Estimated CBSb

-54.985 896 - 54.999 65 1 -55.003 490 -55.004 460 -55.004 88

61.6 64.3 64.9 65.0 65.0(65.0)

1.0590 1.0475 1.0461 1.0458 1.0458

3111.3 3144.5 3157.2 3160.7

89.5 86.5 86.7 86.8

15.988 16.341 16.385 16.394

0.7032 0.7014 0.7007 0.6988

cc-pVDZ cc-pvTZ cc-pVQZ cc-pvsz Estimated CBSb

-55.089 -55.135 -55.148 -55.152 -55.154

71.0 78.4 80.5 81.2 81.4(81.4)

1.0566 1.0396 1.0375 1.0371 1.0371

3185.0 3258.5 3275.2 3279.4

82.1 79.1 78.8 78.7

16.061 16.591 16.658 16.671

0.6570 0.6574 0.6545 0.6522

GVB+1+2

CASSCF

CASSCF+1+2

W

d,

534 673 634 684 10

RHF

aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ Estimated CBSb

- 54.964 768 -54.974 978 - 54.977 956 (-54.979 18)

47.4 48.7 48.8 (48.8)

1.0250 1.0183 1.0175 (1.0174)

3538.1 3545.2 3549.8

66.7 64.9 65.4

17.067 17.292 17.319

0.5731 0.5724 0.5739

HF+1+2

aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ Estimated CBSb

- 55.099 492 -55.136 282 -55.146 718 (-55.150 85)

72.5 77.6 78.9 (79.4)

1.0473 1.0346 1.0325 (1.0321)

3274.6 3330.9 3349.2

75.7 71.7 72.9

16.349 16.750 16.819

0.6303 0.6206 0.6219

GVB

aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ Estimated CBSb

-54.988 048 - 54.998 163 -55.001250 (-55.002 61)

62.0 63.2 63.4 (63.5)

1.0548 1.0473 1.0462 (1.0460)

3131.1 3147.4 3157.2

90.4 87.8 88.5

16.116 16.348 16.382

0.7107 0.7067 0.7075

aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ Estimated CBSb

-55.101924 -55.138 977 -55.149 439 (-55.153 55)

74.0 79.3 80.6 (81.1)

1.0520 1.0396 1.0374 (1.0369)

3201.8 3256.3 3274.6

82.1 77.8 79.1

16.202 16.591 16.661

0.6646 0.6538 0.6553

CASSCF

aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ Estimated CBSb

-54.990 682 - 55.cOO750 -55.003 840 (-55.005 21)

63.7 64.8 65.0 (65.1)

1.0544 1.0471 1.0460 (1.0458)

3135.6 3150.0 3160.1

88.3 85.7 86.6

16.128 16.354 16.388

0.7018 0.6982 0.6990

CASSCF+ 1 i-2

aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ Estimated CBSb

-55.102 410 -55.139 512 -55.149 975 (-55.15408)

74.3 79.6 81.0 (81.4)

1.0523 1.0399 1.0377 (1.0372)

3202.0 3257.0 3275.0

81.9 77.6 78.8

16.193 16.581 16.651

0.6624 0.6515 0.6527

GVB+l+Z

“Reference 28. bValues in parentheses were obtained from three-point (VDZ, VTZ, and VQZ) fits to Eq. (1). J. Chem. Phys., Vol. 99, No. 3, 1 August 1993

Downloaded 27 May 2009 to 140.123.79.230. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/jcp/copyright.jsp

Peterson, Kendall, and Dunning, Jr.: Benchmark calculations.

II

1937

TABLE IV. Calculated and experimental spectroscopic constants for the ground state X ‘II of OH. (A) With the cc-pVXZ basis sets. (B) With the aug-cc-pVXZ basis sets.

Basis set

E, (hartrees)

0, (kcal/mol )

0, (cm-‘)

106.6

0.9697

3737.8

RHF

cc-pVDz cc-pVTZ cc-pVQZ cc-pvsz Estimated CBS

-75.389 561 -75.413 480 -75.419 757 -75.421472 -75.422 05

65.0 69.0 69.8 70.0 70.0

0.9572 0.9505 0.9495 0.9495 0.9493

4024.5 4052.6 4055.4 4056.2

HF+1+2

cc-pVDz cc-pVTz cc-pVQZ cc-pvsz Estimated CBS

-75.552 776 -75.625 729 -75.647 879 -75.655 190 -75.658 15

91.9 99.4 101.7 102.4 102.7

0.9759

cc-pVDz cc-pVTZ cc-pVQZ cc-pvsz Estimated CBS

-75.412 -75.436 - 75.442 -75.444 -75.445

727 374 747 458 09

79.6 83.3 84.1 84.3 84.3

cc-pVDz cc-pVTZ cc-pVQZ cc-pv5z Estimated CBS

-75.555 147 -75.628 755 -75.651044 -75.658 400 -75.66135

CASSCF

- cc-pVDz cc-pVTz cc-pVQZ cc-pvsz Estimated CBS

-75.414 -75.437 -75.443 -75.445 -75.446

CASSCF+ 1+2

we% (cm-‘)

4 (cm-‘)

a, (cm-‘)

84.9

18.911

0.7242

75.3 74.3 14.0 74.2

19.406 19.681 19.722 19.722

0.6540 0.6586 0.6582 0.6563

3764.1 3824.2 3836.0 3836.4

82.0 78.9 79.2 79.1

18.670 19.055 19.132 19.134

0.6978 0.6942 0.6954 0.6934

0.9817 0.9735 0.9721 0.9720 0.9719

3611.5 3656.6 3668.5 3670.7

97.7 95.5 95.3 95.5

,18.450 18.762 18.816 18.820

0.7878 0.7890 0.7850 0.7832

93.4 101.3 103.7 104.4 104.7

0.9797 0.9705 0.9686 0.9686 0.9684

3694.5 3743.2 3753.0 3752.7

87.6 84.3 84.5 84.4

18.525 18.878 18.952 18.952

0.7279 0.7252 0.7266 0.7247

063 605 958 663 30

80.4 84.0 84.8 85.0 85.1

0.9825 0.9744 0.973 1 0.9730 0.9729

3605.4 3648.4 3660.3 3662.4

96.4 94.0 93.9 94.1

18.420 18.727 18.777 18.781

0.7825 0.7828 0.7795 0.7777

cc-pVDZ cc-pVTZ cc-pVQZ cc-pvsz Estimated CBS

-75.555 300 -75.629 050 -75.651 359 -75.658 720 -75.66167

93.5 101.5 103.8 104.6 104.9

0.9798 0.9706 0.9688 0.9688 0.9686

3694.1 3743.4 3753.0 3752.6

87.5 84.2 84.4 84.3

18.521 18.874 18.944 18.944

0.7273 0.7242 0.7256 0.7236

RI-IF

aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ aug-cc-pV5Z Estimated CBS

-75.398 -75.415 -75.420 -75.421 -75.422

589 406 345 587 19

68.8 69.9 70.1 70.1 70.1

0.9542 0.9509 0.9496 0.9494 0.949 1

4051.0 4046.8 4055.2 4057.0

77.1 73.1 73.8 74.2

19.529 19.663 19.719 19.725

0.6593 0.6525 0.6572 0.6563

HF+1+2

aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ aug-cc-pV5Z Estimated CBS

-75.574 -75.632 -75.650 -75.656 -75.658

660 268 227 022 57

96.9 100.9 102.3 102.6 102.8

0.9746 0.9674 0.9647 0.9641 0.9636

3761.4 3807.2 3830.6 3834.9

82.9 76.9 79.0 79.1

18.720 18.999 19.107 19.128

0.7063 0.6840 0.6934 0.6934

GVB

aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ aug-cc-pV5Z Estimated CBS

-75.421414 -75.438 282 -75.443 320 -75.444 570 -75.445 21

83.1 84.1 84.3 84.3 84.4

0.9778 0.9739 0.9723 0.9721 0.9718

3649.9 3655.7 3668.9 3670.9

98.2 93.7 95.0 95.4

18.597 18.746 18.808 18.817

0.7880 0.7782 0.7830 0.7828

aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ aug-cc-pV5Z Estimated CBS

-75.577 -75.635 -75.653 -75.659 -75.661

426 429 436 242 77

98.6 102.9 104.3 104.6 104.8

0.9789 0.9721 0.9694 0.9689 0.9683

3684.4 3723.9 3746.3 3750.1

88.1 82.1 84.3 84.4

18.555 18.816 18.921 18.941

0.7363 0.7144 0.7246 0.7249

CASSCF

aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ aug-cc-pV5Z Estimated CBS

-75.422 -75.439 -75.444 - 75.445 -75446

686 492 525 774 42

83.9 84.8 85.1 85.1 85.1

0.9786 0.9748 0.9732 0.9730 0.9727

3642.9 3647.8 3660.7 3662.7

96.8 92.3 93.6 94.0

18.567 18.712 18.773 18.780

0.7826 0.7722 0.7775 0.7773

CASSCF+ 1+2

aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ aug-cc-pV5Z Estimated CBS

-75.577 -75.635 -75.653 -75.659 -75.462

645 738 753 564 09

98.7 103.1 104.5 104.8 105.0

0.9790 0.9722 0.9695 0.9690 0.9684

3684.3 3723.9 3746.2 3750.0

88.0 82.0 84.2 84.3

18.552 18.812 18.917 18.936

0.7355 0.7134 0.7236 0.7238

Method

*

Expt.’ (A)

GVB

GVB+1+2

(B)

GVB+1+2

0.9640 0.9640 0.9637

‘Reference. 28. J. Chem. Phys., Vol. 99, No. 3, 1 August 1993 Downloaded 27 May 2009 to 140.123.79.230. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/jcp/copyright.jsp

1938

Peterson, Kendall, and Dunning, Jr.: Benchmark calculations.

II

TABLE V. Calculated and experimental spectroscopic constants for the ground state X ‘Z+ of HF. (A) With the cc-pVXZ basis sets. (B) With the aug-cc-pVXZ basis sets.

Method

E, (hartrees)

Basis set

141.6

Expt. (A)

WG (cm-‘)

4 (cm-‘)

a, (cm-‘) .i

0.9168

4138.3

89.9

20.956

0.798

85.6 82.9 82.9 83.3

21.673 21.848 21.896 21.896

0.7642 0.7419 0.7488 0.7490

RHF

cc-pVDz cc-pvTZ cc-pVQZ cc-pv5z Estimated CBS

-

100.019 710 100.058 460 100.068 184 100.070 926 lod.07171

93.2 99.0 99.9 100.2 100.2

0.9015 0.8979 0.8969 0.8969 0.8968

4440.2 4481.1 4476.5 4474.3

I-w+1+2

cc-pVDZ cc-pVTZ cc-pVQZ cc-pvsz Estimated CBS

-

100.219 803 100.322 996 100.355 449 100.366 524 100.37127

123.6 132.6 135.2 136.0 136.3

0.9166 0.9122 0.9105 0.9107 0.9104

4208.7 4261.5 4258.1 4252.5

88.3 84.1 85.0 85.2

20.965 21.167 21.247 21.238

0.7856 0.7546 0.7678 0.7687

GVB

cc-pVDz cc-pvTZ cc-pVQZ cc-pvsz Estimated CBS

-

loo.042 970 100.08 1455 100.091265 100.094 003 100.094 84

107.8 113.4 114.4 114.7 114.8

0.9211 0.9159 0.9146 0.9 146 0.9144

4061.8 4130.2 4133.4 4132.9

101.4 98.0 97.8 98.1

20.761 20.997 21.057 21.057

0.8678 0.8390 0.8430 0.8431

cc-pVDz cc-pVTZ cc-pVQZ cc-pv5z Estimated CBS

-

100.222 328 100.326 227 100.358 817 100.369 938 100.374 67

125.2 134.6 137.3 138.1 138.4

0.9198 0.9160 0.9145 0.9147 0.9144

4144.1 4185.7 4179.8 4173.5

92.1 87.8 88.6 88.8

20.820 20.993 21.062 21.052

0.8080 0.7774 0.7907 0.7917

cc-pVDZ cc-pVTZ cc-pVQZ cc-pvsz Estimated CBS

-

100.043 937 100.082 318 100.092 121 100.094 856 100.095 69

108.4 113.9 115.0 115.3 115.3

0.9218 0.9166 0.9152 0.9152 0.9150

4055.1 4123.0 4126.4 4125.9

100.5 97.0 96.8 97.2

20,729 20.965 21.029 21.029

0.8638 0.8346 0.8386 0.8387

cc-pVDZ cc-pVTZ cc-pVQZ cc-pvsz Estimated CBS

- 100.222 469 - 100.326 548 -100.359 166 - 100.370 299 - loo.375 03

125.3 134.8 137.5 138.4 138.7

0.9198 0.9161 0.9146 0.9148 0.9145

4143.6 4185.6 4179.4 4173.0

92.1 87.8 88.6 88.8

20.820 20.988 21.057 21.048

0.8078 0.7769 0.7903 0.7913

RHF

aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ aug-cc-pV5Z Estimated CBS

-

100.033 820 100.061464 100.069 039 100.071064 100.07185

98.8 100.1 100.3 loo.3 100.3

0.9002 0.8991 0.8973 0.8971

4466.3 4464.9 4471.0 4473.0

93.5 82.0 82.7 83.2

21.736 21.789 21.877 21.889

0.7848 0.7365 0.7481 0.7487

I=+1+2

aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ aug-cc-pV5Z Estimated CBS

-

100.251703 100.332 480 100.358 978 100.367 758 100.372 01

130.9 134.6 136.0 136.2 136.5

0.9192 0.9149 0.9116 0.9111

4165.8 4222.9 4244.2 4246.6

94.3 82.7 84.9 85.1

20.849 21.041 21.198 21.221

0.8127 0.7462 0.7670 0.7689

aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ aug-cc-pV5Z Estimated CBS

-

100.056 655 100.084 439 100.092 107 100.094 140 100.094 95

113.1 114.5 114.8 114.8 114.8

0.9188 0.9170 0.9149 0.9147

4104.7 4121.4 4129.8 4131.9

107.2 96.2 97.3 98.0

20.865 20.947 21.043 21.054

0.8825 0.8281 0.8410 0.8425

aug-cc-pVDZ aug-co-pVTZ aug-cc-pVQZ aug-cc-pV5Z Estimated CBS

- 100.254 579 - 100.335 820 - 100.362 379 -100.371180 -100.37541

132.7 136.7 138.1 138.4 138.6

0.9227 0.9189 0.9155 0.9151

4094.4 4146.3 4165.9 4167.6

97.5 86.2 88.3 88.6

20.689 20.860 21.016 21.034

0.8350 0.7680 0.7894 0.7916

CASSCF

aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ aug-cc-pV5Z Estimated CBS

-100.057 572 -100.085 295 - 100.092 960 - 100.094 993 - 100.095 81

113.7 115.1 115.3 115.3 115.4

0.9194 0.9176 0.9156 0.9153

4098.4 4114.8 4122.9 4124.9

106.3 95.3 96.4 97.0

20.838 20.920 21.011 21.023

0.8785 0.8234 0.8366 0.8381

CASSCF+ 1+2

aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ aug-cc-pV5Z Estimated CBS

- 100.254 820 - 100.336 172 -109.362736 -100.371543 -100.375 76

132.8 136.9 138.4 138.6 138.8

0.9228 0.9190 0.9156 0.9152

4093.8 4146.0 4165.4 4167.2

97.5 86.2 88.4 88.6

20.684 20.856 21.011 21.029

0.8348 0.7676 0.7890 0.7912

GVB+1+2

CASSCF

CASSCF+1+2

03)

% (cm-‘)

(k&mol)

GVB

GVB+l+Z

‘Taken from Ref. 28 and corrected for relativistic effects. See the text. J. Chem. Phys.,Vol.

99, No. 3, 1 August 1993

Downloaded 27 May 2009 to 140.123.79.230. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/jcp/copyright.jsp

Peterson, Kendall, and Dunning, Jr.: Benchmark calculations. 2390

1939

II -.

-~

2370 T-V-

,,

i _______

- ____

-_-

y=-

:

t I ____--_-_.__

:

-

‘, 2880

---;=--;2&jo

/I-

$I:: - 2800

2290 -

BH!

2270t

’

CH

r IF

i :

z 2780

I

E 5 E Is 8 s 0”

81 78 71

DZ

TZ

QZ

5Z

=

t --_----_---_---_- -4 140 135

-s- aug-cc-pvxz

130

HF m DZ

TZ

QZ

-52

DZ

FIG. 2. Dissociation energies 0. from CAS -I- 1+2 calculations with the cc-pVXZ and aug-cc-pVXZ basis sets. The solid lines are fits to Eq. (-1).

higher excitations reduces the errors to just -0.3 (OH) and - 1.0 (HF) kcal/mol with the valence CASSCF referencesand aug-cc-pV5Z basis sets. 3. Trends for the BH-HF series

Figures 2-4 summarize the basis set convergencefor O,, r,, and w,, respectively, at the CAS + l-t2 level for each species.Smooth convergencewith respectto increases 1.260 1.255 1.250 1.245 1.240 1.235 1.230 jyi(-qN”~fL-=

TZ

QZ

52

FIG. 4. Fundamental frequencies o, from CAS+ 1+2 calculations with the cc-pVXZ and aug-cc-pVXZ basis sets.

in the basis set size is observed,especially for D, and r,. While the calculated harmonic frequenciesare not, in general, well representedby Eq. ( 1), good convergenceis observed by the quadruple zeta level. The largest differences in Figs. 2-4 betweenthe cc-pVXZ and aug-cc-pVXZ basis sets occur generally in the VDZ basis sets. Of particular interest are the OH and HF results for r, and w, , where the converged values undershoot and overshoot the experiment values, respectively. These are examples of the case when g better basis set leads to somewhatworse agreement with experiment, even when employing a relatively high level of electron correlation. Using the estimated complete basis set limits for De obtained by fitting the cc-pVXZ CAS+ 1f2 rqults to Eq. ( 1), the basis set convergencerates for BH-HF can be compared. Figure 5 shows the differencesbetweenthe estimated CBS limits and the cc-pVXZ values for D, at the CAS + 1-t 2 level bf theory. The r&e of changewith basis set is remarkably similar among the membersof this series, though BH and CH convergesomewhat more rapidly toward the complete basis set limit. Exponential convergence toward the CBS limit with the correlation consistent basis sets is again demonstrated in Fig. 5, where the fits to Eq. ( 1) are also shown.

~----%==--+:~~~ ::$----TY-b?%J 1.030 w

1 -

’ DZ

TZ

~-OZ

1 5z -.

0.960

0.935 0.930 0.925

B. internally calculations

-o- aug-cc-pvxz

0.920 0.9i5

0.940~

-

~~- .

FIG. 3. Equilibrium distances r, from CAS+ 1+2 calculations with the cc-pVXZ and aug-cc-pVXZ basis sets. With the exception of the

aug-cc-pVXZ valuesfor HF, thesolidlinesarefits to Eq. ( 1).

contracted

versus uncontracted

MRCI

Spectroscopic constants derived from uncontracted _ GAS+ 1+2 potential energy functions (MRCI) are compared to the internally contracted ones (CMRCI) and experiment in Table VI for the cc-pVQZ basis set. As expected, the size of the contraction errors for the

spectroscopic constantsincreases with the numberof cor-

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I

1940

Y

Peterson, Kendall, and Dunning, Jr.: Benchmark calculations.

5 LE B g a 8

v

HF

+ .

OH NH

.

CH

.

E3H

I1

i

a” 6? c! 0”

I VDZ

I VlZ

I VQZ

I v5z

I

FIG. 5. Convergence of the dissociation energies from CAS+ 1+2 calculations to the estimated complete basis set limit. The lines are fits to Eq. (1).

related electrons, being largest for the HF molecule. For the ground state of OH, where the internal contraction results in the greatest savings over the uncontracted case ( 137382 uncontracted CSFs vs 21 647 contracted CSFs), the contraction errors (ValcMRol-Val~& are just 1.88 mhartree, -0.4 kcal/mol, -0.OC07 A, and 6.6 cm-’ for E,, D,, r,, and o,, respectively. Perhapsas expected,the contraction errors in E, for NH ( 1.73 mhartree), OH (1.88 n&r-tree), and HF (1.40 mhartree) using the ccpVQZ basis set are larger than those found in similar benchmark calculations previously reported using double zeta plus polarization (DZP) sets.g

d

II

To investigate the basis set dependenceof the internal contraction, uncontracted MRCI calculations have also beencarried out on the OH ground state with the cc-pVDZ and cc-pVTZ basis sets. The calculated contraction errors in E,, D, , r, , and o, for eachbasis set are shown in Table VII. In general,the errors rise steeply from the cc-pVDZ values, more than doubling the contraction error in E, from 0.70 mhartree (cc-pVDZ) to 1.63 mhartree (ccpVTZ). Increasing the basis set size to cc-pVQZ only slightly increasesthe contraction error ( 1.88 mhartree) over the cc-pVTZ values.From these results, it would appear that small basis set calibration studies should be viewed with caution, since significant correlation effects not apparent with a small basis may occur when a larger basis set is used. Overall, however, the errors incurred by the internal contraction are small in relation to the remaining deviations from experiment, especially considering the large reduction in the size of the variational problem. C. Comparison calculations

of CAS+ I+2

calculations

and full Cl

In Table VIII, we report the results of full CI (FCI) calculations40’41 with the cc-pVDZ basis set on all of the first row diatomic hydrides. CAS+1+2 and CAS+ 1f2+Q ( +Q includes the multireference analog of the Davidson correction39)have also beenincluded. The same orbital set was used in both sets of calculations. FCI calculations on thesespecieshave been reported previously by Bauschlicher and co-workers29’34,42 using similar sized basis setsbasedon AN0 generalcontractions. These studies indicated that uncontracted CAS + 1 + 2 calculations are capableof yielding results in excellent agreementwith FCI (cf. Refs. 43 and 44). For the cc-pVDZ basis sets,

TABLE VI. A comparison of the total energies, dissociation energies, and spectroscopic constants obtained from internally contracted (CMRCI) conventional uncontracted (MRCI) CASSCF+ 1+2 calculations with the cc-pVQZ basis sets.

Species

Method

(hazees)

0,

(kcal/mol)

5 (4

we (cm-‘)

%G (cm-‘)

4 (cm-‘)

a, (cm-‘)

and

BH CMRCI MRCI Expt.’

-25.235 093 -25.235 093

84.1 84.1

1.2337 1.2337 1.2323

2354.9 2354.9 2366.9

48.6 48.6 49.4

11.996 11.996 12.021

0.4199 0.4199 0.4120

CMRCI MRCI Expt.”

-38.416 228 -38.417 162

82.4 82.5 83.9

1.1208 1.1212 1.1199

2845.8 2843.6 2858.5

63.7 63.6 63.0

14.434 14.425 14.457

0.5367 0.5364 0.5340

CMRCI MRCI Expt?

-55.148 634 -55.150 365

80.5 80.7

1.0375 1.0382 1.0362

3275.2 3269.5 3282.3

78.8 78.6 78.3

16.658 16.635 16.699

0.6545 0.6535 0.6490

CMRCI MRCI Expt.”

-75.651 359 -75.653 241

103.8 104.2 106.6

0.9688 0.9695 0.9697

, _ 3753.0 3746.4 3737.8

84.4 84.0 84.9

18.944 18.917 18.911

0.7256 0.7233 0.7242

CMRCI MRCI Expt.

- 100.359 166 - 100.360 567

137.5 138.0 141.6

0.9 146 0.9152 0.9168

4179.4 4173.4 4138.3

88.6 88.1 89.9

21.057 21.029 20.956

0.7903 0.7874 0.7980

CH

NJ3

OH

HF

“Reference 28. J. Chem. Phys., Vol. 99, No. 3, 1 August 1993 Downloaded 27 May 2009 to 140.123.79.230. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/jcp/copyright.jsp

Peterson, Kendall, and Dunning, Jr.: Benchmark calculations. TABLE VII. (Vhcr-Valma)

The basis set dependence of the contraction errors of the internally contracted CI method for OH.

Basis set

4 (mhartree)

D, (kcal/mol)

2,

cc-pVDz CC-pVTZ cc-pVQZ

0.703 1.631 1.882

-0.30 -0.38 -0.37

-0.ooo2 -0.0005 -0.0007

we (cm-‘) 0.9 I 4.4 6.6

AD, between the CAS+ 1+2 and FCI calculations increase-smonotonically from 0.11 kcal/mol in BH to 1.27 kcal/mol in HF. The differencesin r, and w, are markedly smaller, varying from 0.0001 8, in BH to 0.0005 A in HF for r, and from 4.2 cm- ’ in CH to 0.5 cm-’ in HF for w,. The Davidson correction appearsto be quite effective in accounting for the neglect of higher excitations in the CAS+ 1+2 calculations. For De, the +Q correction dramatically improves the agreement with the FCI results, reducing the maximum error to just 0.21 kcal/mol (in HF). The +Q correction improves r, for all of the hydrides except NH and improves w, for all except NH and OH. For r, and o,, where the differencesare small, it is important to keep in mind the possible inaccuracies associated with the numerical procedureusedto calculate these quantities. In addition, it should be noted that CAS+ 1+2+Q overshoots the FCI total energy in each case, except for HF. The above discussionclearly only applies to the polarized double zeta basis sets. This set accounts for only a fraction of the total correlation energy (66% in HF), and

1941

II

hence,the conclusions drawn above may not be fully representativeof those that would be obtainedwith more complete basis sets. The fact that the “error” in D, for HF from the CAS + 1 + 2 calculations with the cc-pVDZ basis set is only 1.3 kcal/mol, whereasit increasesto more than 3.0 kcal/mol at the CBS limit, indicates that there are significant correlation effectsincluded in the larger set that are either absent or poorly describedin the cc-pVDZ set.

D. Choice of hydrogen

basis set-CH

and HF

Usually in ab initio calculations on molecular species containing hydrogen, the number of basis functions on the nonhydrogenatoms greatly outnumber those on hydrogen. To more fully addressthe question of basis set balance,the effect of combining cc-pV(X- l)Z sets on hydrogen with cc-pVXZ sets on carbon and fluorine on the computed values of De, r,, and o, has been investigatedfor the CH and HF molecules.The results at the CAS + 1+ 2 level are displayed in Fig. 6. It can be observedfrom Fig. 6 that the only substantial differencein using the cc-pV(X- 1>Z sets for hydrogen occurs when X= T, i.e., cc-pVTZ on C or F and cc-pVDZ on H. Interestingly, the effects are nearly identical for CH and HF. It would appearthen that when using basis sets larger than cc-pVTZ, the smaller cc-pV (X- l)Z sets could be used for hydrogen with little loss in accuracy, resulting in significant savingsin computational time.

TABLE VIII. Spectroscopic constants for the tlrst row diatomic hydrides obtained from internally contracted CAS+ 1 +2 (CAS-CI) calculations with the cc-pVDZ basis sets.B*b 0, (cm-‘)

%50

Species

Method

(hazees)

(hartrees)

(kcai?mol)

(2,

and full CI (FCI)

%A (cm-‘)

BH CAS-CI CAS-CI+Q

2338.6 2340.0 2339.9

48.6 48.6 48.6

2806.2 2809.7 28 10.4

67.7 67.3 67.4

1.0566 1.0570 1.0567

3185.0 3184.5 3187.6

82.1 81.5 81.4

93.46 94.25 94.40

0.9798 0.9802 0.9801

3694.1 3693.7 3695.3

87.5 86.7 86.8

125.26 126.32 126.53

0.9198 09202 0.9203

4143.6 4142.7 4143.1

92.1 91.3 91.3

FCI

-25.215 180 -25.215 961 -25.215 490

-25.089 129 -25.089 829 -25.089 266

79.10 79.15 79.21

1.2562 1.2561 1.2561

CAS-CI CAS-CI+Q FCI

-38.379 273 -38.381 835 -38.380 790

-38.259 464 -38.261 339 -38.260 193

75.18 75.61 75.68

1.1438 1.1437 1.1436

CAS-CI CAS-CI+Q FCI

-55.089 534 -55.093 065 -55.092 219

-54.976 320 - 54.979 045 - 54.977 829

71.04 71.55 71.78

CAS-CI CAS-CI+Q FCI

-75.555 300 -75.560 243 -75.559 780

-75.406 355 -75.410 052 -75.409 338

CAS-CI CAS-CI+Q FCI

- 100.222 469 - 100.228 432 - 100.228 646

- 100.022 854 - 100.027 128 - 100.027 008

CH ,_

NH

OH

HF

‘With the CC-pVDZ basis sets, the resulting number of variational parameters (CMRCI)/determinants CH, 873/116 320 for NH, 901/623 680 for OH, and 775/2 342 800 for HF.

(FCI)

were 786/6129 for BH, 908/31424 for

?he additionof themultireference analogof the Davidson correction to the CAS+ 1+2 is denoted by CAS-CI+Q. J. Chem. Phys., Vol. 99, No. 3, 1 August 1993 Downloaded 27 May 2009 to 140.123.79.230. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/jcp/copyright.jsp

Peterson, Kendall, and Dunning, Jr.: Benchmark calculations.

FIG. 6. cc-pV(Xcalculated HF.

IV. CONCLUSIONS

04 HI=

(a) CH

II

One of the primary goals of the current work was to examine the convergenceof the dissociation energiesand spectroscopic constants of the first row hydrides for the new correlation consistentbasis sets.Table IX summarizes the root-mean-square(rms) errors in the spectroscopic constants calculated at the HF+ 1+2, GVB f 1 f2, and i ;‘=- CAS + 1+2 levels of correlation for, each basis set. The CAS + 1 + 2 values for the rms errors in 0,) r, , and w, are plotted in Fig. 7. For the cc-pVDZ basis sets,the errors are large, especially for the computed dissociation energies. The rms error in D, from the CAS+ 1+ 2 calculations is 13.0or 11.2kcal/mol abovethe CBS limit; the errors range from 5.7 kcal/mol in BH to 16.3 kcal/mol in HF. Use of as ...--=i--=‘ . ‘-*the cc-pVTZ basis set dramatically improves all of the calculated spectroscopicconstants. The rms errors from the CAS+ 1f2 calculations decreasefrom 13.0 to 5.0 kcal/ mol for D,, from 0.020to 0.003 A for r,, and from 61.1 to 31.4 cm-’ for w,. The change-fromthe cc-pVTZ set to the cc-pVQZ set is less dramatic, but still significant. For example, for the cc-pVQZ set, the rms error in D, (CAS + 1 + 2) is reducedby another 2.2-2.8 kcal/mol, which is just 1.0 kcal/mol abovethe CBS limit. In general, the cc-pVTZ set appearsto be.a good compromisebetween basis set size and accuracy.This fact has also beennoted by Tbe effect of combining the hydrogen cc-pVXZ and Del Bene and co-workers in their studies of hydrocarbon 1)Z basis sets with the carbon/fluorine cc-pVXZ sets on the (CAS + 1 + 2) values of De, r, , and o, (a) for CH and (b) for and carbocation stabilities4’and hydrogen bonding,46as well as by Martin3* in his CCSD(T) study of atomization energies.

TABLE IX. Root-mean-square (rms) errors for the spectroscopic constants obtained from HF+ 1+2, GVB+ 1+2, and CAS+ 1+2 calculations for each basis set.

D,

0,

“ey ) (cm

0.0168 0.0031 0.0050 0.0052 0.0053

40.4 19.8 86.4 86.1

2.5 5.3 4.9 4.9

0.423 0.131 0.198 0.200

0.0247 0.0299 0.0257 0.0266

9.3 5.2 4.0

0.0123 0.0017 0.0039

19.9 54.8 71.8

2.8 5.9 4.5

0.304 0.062 0.154

0.0160 0.0326 0.0241

cc-pVDZ cc-pVTZ cc-pVQZ cc-pvsz Estimated CBS

13.2 5.3 3.0 2.3 2.1

0.0203 0.0028 0.0016 0.0013 0.0015

60.9 31.5 23.9 20.2

3.6 1.3 1.0 1.1

0.529 0.016 0.061 0.053

0.0108 0.0128 0.0070 0.0062

aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ

7.6 3.3 2.2

0.0158 0.0028 0.0011

57.5 19.5 15.4

4.7 2.1 1.0

0.419 0.088 0.035

0.0192 0.0153 0.0064

cc-pVDz cc-pVTZ cc-pVQZ cc-pvsz Estimated CBS

13.0 5.0 2.8 2.1 1.8

0.0204 0.0029 0.0016 0.0012 0.0014

61.1 31.4 23.9 20.1

3.5 1.2 0.9 0.9

0.534 0.079 0.059 0.051

0.0102 0.0126 0.0063 0.0060

aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ

7.5 3.1 1.9

0.0159 0.0029 0.0011

57.8 19.6 15.3

4.6 2.1 0.9

0.423 0.092 0.036

0.0187 0.0155 0.0061

Method

Basis set

(kcal/mol )

m+1+2

cc-pVDz cc-pVTz cc-pVQZ cc-pvsz Estimated CBS

14.8 1.2 5.0 4.4 4.1

aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ GVB+l+Z

CAS+1+2

(cm-‘)

4

(cm-‘)

ae

(cm-‘)

J. Chem. Phys., Vol. 99, No. 3, 1 August 1993

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Peterson, Kendall, and Dunning, Jr.: Benchmark calculations.

II

i E % Y 8 G 0”

v5z 251

est. CBS _-.-_

1.

p.

67 8 d”

.,

4

.-Q 3 P s! Lm G? 8 L_

-.a .k

60

zx w 3” 6 3 g

101

._., VDi!

vri!

vclz

._.

_ .L

v5z

FIG. 7. Root-mean-square (rms) errors in De, r, , and OJ,for each of the cc-pVX2 basis sets from CAS + 1+2 calculations.

Another goal of this work was to determine the inherent accuracy of selectedconfiguration interaction methods applied to the model system of the first row diatomic hydrides. After removing basis set effects by extrapolating to the complete basis set limit (see Sec. II E), the resulting values can be compared with experiment to yield the inherent accuracy or intrinsic error in a particular method for that property. Figure 8 illustrates the deviations from experiment of the estimated CBS limits for D,, r,, and w, for the HF+ 1+2 and internally contracted GVB+ 1+2 and CAS+ 13-2 methods. In this figure, the experimental D, values for BH and NH were taken to be 84.8 and 82.5 kcal/mol, respectively, which representthe best estimates from this and other2g,34theoretical work. The estimated CBS limits for o, (and r, for HF) were taken from the best directly calculated values, i.e., the cc-pV5Z or aug-ccpV5Z values (Tables I-V). As expected,the errors in the HF+ 1+2 method are much larger than either of the two multireference techniques.The errors in all three methods are observed to increase nearly monotonically with the number of electrons. For the CAS+ 1+2 D, (CBS) values, the averagedeviation from linearity is just 0.23 kcal/ mol. The averagedeviation is decreasedto 0.17 kcal/mol when the deviations from experiment are expressedas a function of the number of valence electron pairs it (n - 1)/2 instead of the total number of valenceelectrons n. An exception to this behavior is the trend for r,, where the intrinsic errors in NH for CAS + 1+ 2 and GVB + 1 + 2 are somewhatlarger than expectedfrom the corresponding

,,

..l 3”

-2o-

t

BH

*

CH

NH

OH

HF

FIG. 8. Intrinsic errors in De, r,, and w, from HF+ 1 j-2, GVB+ 1+2, and CASSCF+ 1+2 wave functions. The calculated values were taken from estimates of the complete basis set limit (CBS) or from calculations with the cc-pV5Z basis set (see the text).

results for CH and OH. In general, the GVB+ 1+2 method yields results in excellent agreement with the larger CAS + 1+ 2 calculations. This is especially true for the harmonic frequency, where the two methods result in nearly identical errors. The excellent performance of the CAS+ 1+2 method compared to experiment has been exemplified previously for a large variety of molecular systems.43 Finally, we find that the errors incurred by contraction of the doubly excited configurations in the multireference CI calculations are small but nonnegligible. The contraction errors in D,, r,, and w, for the cc-pVQZ set range from 0.1 kcal/mol in CH to 0.5 kcal/mol in HF, from 0.0004 A in CH to 0.0013 A in OH and from 2.2 cm-’ in CH to 6.7 cm-’ in NH. (MRCI and CMRCI are identical for BH. ) The error in the total energy for the cc-pVQZ set is found to be substantially larger than that for the cc-pVDZ set; in OH the error increasesfrom 0.7 to 1.9 mhartrees; however, the corresponding error in D, increasesby just 0.07 kcal/mol. Nonetheless,small basis set calibration studies should be viewed with caution, since significant correlation effects not apparent with a small basis may occur when a larger basis set is used. In general, the internally contracted GVB -t 1 i-2 and CAS+ l-1-2 methods continue to show great promise, yielding accurate dissociation energiesand spectroscopic constants for the

J. Chem. Phys., Vol. 99, No. 3, 1 August 1993 Downloaded 27 May 2009 to 140.123.79.230. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/jcp/copyright.jsp

1944

Peterson, Kendall, and Dunning, Jr.: Benchmark calculations.

first row hydrides at a fraction of the cost of uncontracted calculations. ACKNOWLEDGMENTS

This work was supported by the Division of Chemical Sciencesin the Office of Basic Energy Sciencesof the U.S. Department of Energy at Pacific Northwest Laboratory under Contract No. DE-AC06-76RL0 1830. KAP acknowledgesthe support of the Northwest Collegeand University Association for Science (Washington State University) under Grant No. DE-FG06-89ER-75522 with the U.S. Department of Energy. Computational resourcesfor this work were provided by the Division of Chemical Sciencesand by the Scientific Computing Staff, Office of Energy Research,at the National Energy Research Supercomputer Center (Livermore, CA). The authors would like to thank Dr. D. E. Woon, Dr. S. S. Xantheas,and Dr. D. F. Feller for many stimulating discussionsthroughout the course of this work. The assistanceof Professor H.-J. Werner with the MOLPR092 program package and for helpful discussionsis gratefully acknowledged.The help of Professor P. J. Knowles with the FCI module within MOLPR092 was greatly appreciated.We would also like to gratefully acknowledge Dr. R. Shepard for assistance with the latest version of the COLUMBUS MRCI codes. ‘J. Almlijf and P. R. Taylor, J. Chem. Phys. 86,407O (1987). ‘T. H. Dunning, Jr., J. Chem. Phys. 90, 1007 (1989). ‘R. A. Kendall, T. H. Dunning, Jr., and R. J. Harrison, J. Chem. Phys. 96, 6796 ( 1992). 4D. E. Woon and T. H. Dunning, Jr., J. Chem. Phys. 98, 1358 (1993). ‘D. E. Woon and T. H. Dunning, Jr., J. Chem. Phys. 99, 1914 (1993). 6K. A. Peterson and T. H. Dunning, Jr. (to be published). ‘D. E. Woon and T. H. Dunning, Jr. (to be published). ‘MOLPRO92 is a suite of ab initio programs written by H.-J. Werner and P. J. Knowles with contributions by J. Almlof, R. D. Amos, M. Deegan, S. T. Elbert, C. Hampel, W. Meyer, K. A. Peterson, R. M. Pitzer, E.-A. Reinsch, A. J. Stone, and P. R. Taylor. ‘H.-J. Werner and P. J. Knowles, J. Chem. Phys. 89, 5803 (1988). ‘OP. J. Knowles and H.-J. Werner, Chem. Phys. Lett. 145, 514 (1988). “R. Shepard, I. Shavitt, R. M. Pitzer, D. C. Comeau, M. Pepper, H. Lischka, P. G. Szalay, R. Ahlrichs, F. B. Brown, and J.-G. Zhao, Int. J. Quantum Chem. Symp. 22, 149 (1988). ‘*R. C. Raffenetti, J. Chem. Phys. 58, 4452 (1973). 13The correlation consistent and augmented correlation consistent basis

II

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