Some observations about quantum chemistry software GAUSSIAN

doi:10.15406/oajs.2019.03.00134

Open Access Journal of

eISSN: 2575-9086

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Review Article Volume 3 Issue 2

Some observations about quantum chemistry software GAUSSIAN

Mohit K Sharma

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Amity Centre for Astronomy & Astrophysics, Amity Institute of Applied Sciences, Amity University, India

Correspondence: Mohit K Sharma, Amity Centre for Astronomy & Astrophysics, Amity Institute of Applied Sciences, Amity University, Noida 201313, India

Received: December 21, 2018 | Published: April 3, 2019

Citation: Sharma MK. Some observations about quantum chemistry software GAUSSIAN. Open Access J Sci. 2019;3(2):75-79. DOI: 10.15406/oajs.2019.03.00134

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Abstract

When laboratory study of some molecule is not available, one may plan to use data obtained from Quantum Chemistry software, such as GAUSSIAN, MOLPRO, NWCHEM, etc. For our investigation of cosmic molecules, we need reliable data for rotational and centrifugal distortion constants. For some molecules, we have obtained these data with the help of Quantum Chemistry software GAUSSIAN and compared them with those obtained from the laboratory studies. We have found that in some cases, the two sets of data are very close to each other whereas in some cases, they differ very much. As the laboratory measurements provide the most reliable data, one would like to use the GAUSSIAN data only when the laboratory data are available. Thus, an obvious question arises how to decide the reliability of GAUSSIAN data, when for that particular molecule no laboratory data are available. Further, when the laboratory data are available, no one would like to use the GAUSSIAN data.

Introduction

In a cosmic object having molecules, kinetic temperature in general is very low; few tens of Kelvin. Thus, one is concerned with the rotational levels in the ground vibrational state and ground electronic state. The rotational and centrifugal distortion constants, electric dipole moment can be used for calculation of energies of rotational levels and radiative transition probabilities (Einstein A-coefficients) for radiative transitions between the levels. We have investigated some molecules where laboratory data are available and for the same molecules we have obtained the data with the help of GAUSSIAN also. We have found that for some molecules, the two sets of data are in good agreement whereas for some molecules, they differ very much. As the laboratory data are the most reliable, one would like to use the GAUSSIAN data only in absence of the laboratory data. Thus, an obvious question arises how to decide the reliability of GAUSSIAN data. We are aware of the fact that the frequencies of spectral lines obtained from the GAUSSIAN data are not as accurate as required by the astronomers. However, the GAUSSIAN data can play important role in getting qualitative results about a molecule. We could not succeed in running the CCSD and CCSD (T) methods for the GAUSSIAN, as the computer program broke down each time during the execution. Therefore, we have employed the functional B3LYP method, i.e., Becke’s three parameter exchange function B³ (Becke¹) with Lee, Yang and Parr’s gradient corrected exchange-correlation functional.²

Investigation

In the present discussion, we have considered the following molecules following sections.-to be deleted.

Cyclopropenone

Guillemin et al.,³ have recorded spectrum of cyclopropenone (c-C₃H₂O) and have derived rotational and centrifugal distortion constants for Watson’s rotational operator written in I^r representation and - to be deleted with A-type reduction, given in Table 1 (column 2). Sharma et al.⁴ have optimized the cyclopropenone with the help of GAUSSIAN 2009 Frisch et al.⁵ using B3LYP method and cc-pVDZ basis set. The values are given in Table 1 (column 3). The two sets of data are in good agreement. The deviations of rotational constants A, B and C, with respect to their experimental values are 0.46%, 1.18% and 0.90%, respectively.

Constant	Laboratory	cc-pVDZ
A	32040.73	31894.85
B	7825.046	7733.81
C	6280.685	6224.503
$Δ J$	1.79362×10⁻³	1.651250766×10⁻³
$Δ J K$	33.7882×10⁻³	3.271020188×10⁻²
$Δ K$	50.65×10⁻³	4.379488485×10⁻²
$δ J$	0.38536×10⁻³	3.533088298×10⁻⁴
$δ K$	22.156×10⁻³	2.093510188×10⁻²
H_J		2.937852086×10⁻¹⁰
H_JK		6.851055671×10⁻⁸
H_KJ		−1.128055614×10⁻⁷
H_K		9.251718141×10⁻⁸
h_J		2.362038947×10⁻¹⁰
h_JK		3.968188988×10⁻⁸
h_K		1.205246347×10⁻⁶

Table 1 Rotational and centrifugal distortion constants in MHz of c-C₃H₂O

Titanium dihydride

Inspired with good agreement between two sets of data for c-C₃H₂O, Sharma et al.,⁶ decided to go for the investigation of titanium dihydride (TiH₂) for which laboratory data are not available. They⁶ have optimized the molecule TiH₂ with the help of GAUSSIAN 2009 Frisch et al.,⁵ where B3LYP method and cc-pVTZ basis set are used. The rotational and centrifugal distortion constants obtained for Watson’s rotational operator written in I^r representation and - to be deleted with A-type reduction are given in Table 2. The outcome of the investigation is very exciting.

Constant	cc-pVTZ	Constant	cc-pVTZ
A	2.8589602 × 10⁵	$Φ J$	2.037108491 × 10⁻³
B	1.2520818 × 10⁵	$Φ J K$	−1.928681064 × 10⁻²
C	8.707408 × 10⁴	$Φ K J$	−1.946479675 × 10⁻²
$Δ J$	6.004343	$Φ K$	5.110638046 × 10−1
$Δ J K$	−4.186548023 × 10¹	$φ J$	1.014000418 × 10⁻³
$Δ K$	2.549058853 × 10²	$φ J K$	−3.557138924 × 10⁻³
$δ J$	2.465123	$φ K$	1.085768474 × 10⁻¹
$δ K$	2.332384

Table 2 Rotational and centrifugal distortion constants in MHz of TiH₂

Ethylene oxide

Pan et al.⁷ recorded spectrum of ethylene oxide (c-C₂H₄O) and have derived rotational and centrifugal distortion constants for Watson’s rotational operator written in I^r representation and – to be deleted with A-type reduction, given in Table 3 (column 2). Sharma et al.⁸ have optimized the ethylene oxide with the help of GAUSSIAN 2009 Frisch et al.⁵ bf using B3LYP method and cc-pVDZ basis set. The values of data are given in Table 3 (column 3). The two sets of data are in good agreement. The deviations of rotational constants A, B and C, with respect to their experimental values are -0.79%, -0.58% and -0.70%, respectively. It again provided us a confidence about our investigation of TiH₂ Sharma et al.⁶

Constant	Laboratory	cc-pVDZ
A	25483.89	25685.72
B	22120.85	22249.95
C	14097.84	14197.62
$Δ J$	51.1883 × 10⁻³	50.79096319 × 10⁻³
$Δ J K$	−70.4938 × 10⁻³	−71.09013012 × 10⁻³
$Δ K$	27.6541 × 10⁻³	28.41532834 × 10⁻³
$δ J$	−9.01689 × 10⁻³	8.836730565 × 10⁻³
$δ K$	3.3491 × 10⁻³	−6.556467036 × 10⁻³
$Φ J$	0.2456 × 10⁻⁶	−5.960452772 × 10⁻⁸
$Φ J K$	−5.2164 × 10⁻⁶	−4.838170644 × 10⁻⁶
$Φ K J$	15.7370 × 10⁻⁶	15.30527314 × 10⁻⁶
$Φ K$	−10.638 × 10⁻⁶	−10.40655085 × 10⁻⁶
$Φ J$	−0.05097 × 10⁻⁶	−2.887999339 × 10⁻⁸
$Φ J K$	1.4297 × 10⁻⁶	−1.411514955 × 10⁻⁶
$φ K$	−17.8633 × 10⁻⁶	1.713117251 × 10⁻⁵
L_J	−0.1210 × 10⁻⁹
L_JJK	−0.1288 × 10⁻⁹
L_JK	0.624 × 10⁻⁹
L_KKJ	−0.800 × 10⁻⁹
L_K	0.892 × 10⁻⁹
l_J	−0.00367 × 10⁻⁹
l_JK	0.0921 × 10⁻⁹
l_KJ	−0.448 × 10⁻⁹
l_K	0.679 × 10⁻⁹
P_K	−1.114 × 10⁻¹²

Table 3 Rotational and centrifugal distortion constants (MHz) of c-C₂H₄O

Vinylidene

Inspired with good agreement between two sets of data for c-C₃H₂O and for c-C₂H₄O, we decided to go for the investigation of vinylidene (H₂CC) for which also laboratory data are not available. bf Sharma et al.⁹ have optimized the molecule H₂CC with the help of GAUSSIAN 2009 Frisch et al.⁵ employing the B3LYP method in conjunction with four basis sets, cc-pVTZ, aug-cc-pVDZ, aug-cc- pVTZ and aug-cc-pVQZ. The resulting rotational and centrifugal distortion constants for Watson’s rotational operator written in I^r representation and - to be deleted with S-type reduction are given in Table 4. There is good agreement between the data obtained from different basis sets.

Constant	cc-pVTZ	aug-cc-pVDZ	aug-cc-pVTZ	aug-cc-pVQZ
A ×10⁻⁵	2.858903	2.858903	2.858903	2.858903
B ×10⁻⁴	3.993411	3.993411	3.993411	3.993411
C ×10⁻⁴	3.503965	3.503965	3.503965	3.503965
D_J ×10³	42.70791	43.44087	44.28356	44.55227
D_JK	20.98798	18.94745	20.44459	20.4197
D_K	5.317725	6.440168	5.879314	5.933398
d₁ ×10²	−1.442126677	−1.373607832	−1.445080323	−1.452037644
d₂ ×10²	−2.675152631	−2.408896481	−2.609261594	−2.613141728
H_J ×10⁶	−9.085110924	−7.573403608	−8.601743486	−8.655849617
H_JK ×10³	2.717971	2.280665	2.564823	2.580959
HK_J ×10²	−1.854934803	−1.597951879	−1.709596957	−1.731162015
H_K ×10²	2.401038	2.151629	2.272677	2.29427
h₁ ×10⁶	−1.524539329	−1.248551723	−1.444404960	−1.443374339
h₂ ×10⁶	4.698862	3.929762	4.456302	4.485417
h₃ ×10⁶	1.651997	1.367133	1.5717	1.57211

Table 4 Rotational and centrifugal distortion constants in MHz of H₂CC

Silanone

Bailleux et al.¹⁰ have recorded spectrum of silanone (H₂SiO) and derived rotational and centrifugal distortion constants for Watson’s rotational operator written in I^r representation and - to be deleted with A-type reduction, given in Table 5 (column 2). Sharma et al.¹¹ have optimized the molecule H₂SiO with the help of GAUSSIAN 2009 Frisch et al.⁵ bf employing B3LYP method in conjunction with three basis sets, aug-cc-pVDZ, aug-cc-pVTZ and aug-cc-pVQZ. The values are given in Table 5 (columns 3-5). There is very good agreement between the four sets of data. The deviations of rotational constants A, B and C obtained for the basis set aug-cc-pVQZ, with respect to their experimental values are 0.24%, 0.53% and 0.18%, respectively.

Constant	Experiment	cc-pVDZ	aug-cc-pVDZ	aug-cc-pVTZ	aug-cc-pVQZ
A ×10⁵	1.666573	1.62688	1.62316	1.658067	1.662584
B ×10⁻⁴	1.867939	1.787253	1.78186	1.842979	1.858002
C ×10⁻⁴	1.674277	1.610344	1.605601	1.65862	1.671235
$Δ J \times 10^{2} k$	1.75216	1.631609	1.647716	1.66202	1.676962
$Δ J K \times 10^{1}$	6.02486	5.543688	5.632878	5.839659	5.871728
$Δ K$	7.5	8.199677	8.090008	8.443277	8374.246
$δ J \times 10^{3}$	2.0811	1.822749	1.836778	1.876133	1.906645
$δ K \times 10^{1}$	4.13	3.503961	3.550486	3.660305	3.689542
$Φ J \times 10^{9}$		6.733706	6.296932	5.253595	5.657116
$Φ J K \times 10^{6}$	4.757	7.800663	7.879044	8.266248	8.41835
$Φ K J \times 10^{5}$	-4.774	-1.57875	-1.796	-2.14959	-2.2458
$Φ K \times 10^{3}$		1.443688	1.377452	1.435596	1.415752
$φ J \times 10^{9}$		3.572809	3.531365	3.408102	3.524366
$φ J K \times 10^{6}$		4.031514	4.065714	4.256998	4.334719
$φ K \times 10^{4}$		4.511626	4.605502	4.727325	4.732419

Table 5 Rotational and centrifugal distortion constants in MHz of H₂SiO

cis-Formic acid

Winnerwisser et al.¹² have recorded spectrum of cis-Formic acid (cis-HCOOH) and derived rotational and centrifugal distortion constants for Watson’s rotational operator written in I^r representation and - to be deleted with A-type reduction, given in Table 6 (column 2). Sharma et al.¹³ have optimized the molecule cis-HCOOH with the help of GAUSSIAN 2009 Frisch et al.⁵ bf employing B3LYP method in conjunction with three basis sets, aug-cc-pVDZ, aug-cc-pVTZ and aug-cc-pVQZ. The values are given in Table 6 (columns 3-5). There is very good agreement between the four sets of data. The deviations of rotational constants A, B and C obtained for the basis set aug-cc-pVQZ, with respect to their experimental values are -1.16%, -0.22% and -0.46%, respectively. All these data provided us a encouragement about our investigations of TiH₂ and H₂CC molecules.

Constant	Lab		Optimization
		aug-cc-pVDZ	aug-cc-pVTZ	aug-cc-pVQZ
A	86461.62	85967.44	87387.25	87478.32
B	11689.18	11617.78	11690.94	11715.35
C	10284	10234.65	10311.44	10331.7
$Δ J \times 10^{3}$	8.35515	6.594446	6.564108	6.564716
$Δ J K \times 10^{3}$	−71.4412	259.8124	274.8887	275.2381
$K \times 10^{3}$	2361.672	2176.623	2296.741	2303.991
$δ J \times 10^{3}$	1.41773	0.592251	0.556347	0.55381
$δ K \times 10^{3}$	40.747	115.2922	118.6733	118.4331
$Φ J \times 10^{8}$	1.064	−0.4527703926	−0.4722888293	−0.4808865771
$Φ J K \times 10^{6}$	−0.2974	9.566051	10.98867	11.10552
$Φ K J \times 10^{6}$	−9.673	108.8903	119.0774	119.4857
$Φ K \times 10^{6}$	185.11	1.389687	1.452612	1.434686
$φ J \times 10^{9}$	2.317	0.108608	0.08907	0.084311
$φ J K \times 10^{6}$	−0.73	0.746964	0.783595	0.775275
$φ K \times 10^{6}$		37.1677	39.04597	38.76245
L_K × 10⁹	−20.2
l_JK × 10⁹	0.558

Table 6 Rotational and centrifugal distortion constants (MHz) of cis-HCOOH

Disilicon

McCarthy et al.¹⁴ has recorded spectrum of disilicon (Si₂C) and have derived rotational and centrifugal distortion constants for Watson’s rotational operator written in I^r representation and - to be deleted with S-type reduction, given in Table 7 (column 2). Sharma et al.¹⁵ have optimized the molecule Si₂C with the help of GAUSSIAN 2009 Frisch et al.⁵ employing the B3LYP method in conjunction with three basis sets, aug-cc-pVDZ, aug-cc-pVTZ and aug-cc-pVQZ. The values are given in Table 7 (columns 3-5). There is large disagreement between the laboratory data and those obtained from GAUSSIAN. The deviations of rotational constants A, B and C obtained for the basis set aug-cc-pVQZ, with respect to their experimental values are -51.89%, 20.23% and 15.28%, respectively. These large deviations perturbed us and lead to a question about the reliability of GAUSSIAN data.

Constant	Experimental	aug-cc-pVDZ	aug-cc-pVTZ	aug-cc-pVQZ
A	64074.34	115272.4	141935.4	133191.5
B	4395.621	3648.742	3597.055	3655.86
C	4102.028	3536.791	3508.148	3558.194
D_J ×10³	9.7315	18.02061	28.55172	17.97574
D_JK	−0.8572075	−7.016988202	−17.432464312	−9.250582631
D_K×10⁻²	0.235881	7.258966	27.69195	12.60339
d₁ ×10³	1.519832	2.2482	3.425177	2.169344
d₂ ×10¹	0.51591	1.269923	2.405429	1.420247
H_J ×10⁷	−0.41349	−6.979665512	−26.90729235	−4.538089470
H_JK ×10⁴	0.93298	9.032487	48.46837	10.80401
H_KJ ×10¹	−0.0188755	−2.856368246	−22.85802143	−4.878977881
HK	0.044863	26.42362	320.7195	61.69333
h_j ×10⁸	−0.5231	−11.16426814	−43.12215486	−6.341531159
h_k ×10²		1.388191	7.346143	3.083056
h_jk ×10⁵	−0.6586	−2.147381766	−9.373151002	−1.964934254

Table 7 Rotational and centrifugal distortion constants of Si₂C in MHz

Discussion

When got good agreement between the laboratory data and those obtained with the help of GAUS- SION for c-C₃H₂O, c-C₂H₄O, H₂SiO and cis-HCOOH, we felt encouraged that in absence of lab- oratory data for a particular molecule, at least qualitative analysis of the molecule could be done with the help of the GAUSSIAN data. But, a large disagreement between the two sets of data for Si₂C has shattered down all the confidence. Thus, an obvious question irises how to decide the reliability of GAUSSIAN data, when laboratory data are not available. Further, when the laboratory data are available, no one would like to use the GAUSSIAN data. We Sharma et al.¹⁶ have earlier presented some observations about the Quantum Chemistry software MOLPRO. Werner et al.¹⁷ About the computer code MOLSCAT Hutson et al.,¹⁸ we Sharma et al.¹⁹ have presented some observations. About the observations, someone may respond. - to be deleted These observations however - to be deleted provide some awareness to the users of the GAUSSIAN, MOLPRO and MOLSCAT.

Acknowledgments

Author is grateful to Hon’ble Dr. Ashok K. Chauhan, Founder President, Hon’ble Dr. Atul Chauhan, Chancellor, and Hon’ble Vice Chancellor Dr. Balvinder Shukla, Amity University for valuable support and encouragements. He is thankful to the SERB, DST, New Delhi for awarding the NPDF.