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Physics & Astronomy International Journal

Mini Review Volume 2 Issue 4

Some observations about MOLPRO

Mohit Kumar Sharma,1 Monika Sharma,2 Suresh Chandra1

1Amity Center for Astronomy & Astrophysics, Amity University, India
2School of Studies in Physics, Jiwaji University, India

Correspondence: Suresh Chandra, Amity Center for Astronomy & Astrophysics, Amity Institute of Applied Sciences, Amity University, Sector?125, Noida 201313, U.P, India, Fax 9198-1800-5663

Received: May 10, 2018 | Published: July 6, 2018

Citation: Sharma MK, Sharma M, Chandra S. Some observations about MOLPRO. Phys Astron Int J. 2018;2(4):286-288. DOI: 10.15406/paij.2018.02.00100

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Abstract

In equilibrium, coordinates of atoms in a molecule are expressed with respect to the origin situated at the center–of–mass of the molecule. In the quantum mechanical software MOLPRO, we have found that the center–of–mass of molecule does not coincide with the origin of the coordinate system. Rather it lies in a random manner. The problem becomes more severe when, for example, one wants to know the separation between two interacting particles in the scattering process. There appears need to make amendment in MOLPRO, so that the origin of coordinate system coincides with the center–of–mass of the molecule in equilibrium.

Keywords: ISM: molecules, interaction potential, MOLPRO

Introduction

For quantum mechanical calculations of atomic systems, some software, e.g., Frischet et al.1, Werner et al.2 & Valiey et al.3 etc. are in use in science. For scattering between a molecule of interest and a colliding partner (generally taken as H2 molecule for interstellar medium), a common procedure is to calculate the interaction potential between them. For convenience, the H2 molecule is taken as structure–less particle and is often replaced by He atom, as both of them have 2 electrons and 2 protons.4–15 In the process, the molecule is first optimized and the cartesian coordinates (xi, yi, zi) of the atoms of molecule in equilibrium are obtained. The Cartesian coordinates (xcm, ycm, zcm) of the center–of–mass of the molecule are expressed as

x cm = m i x i   m i , y cm = m i y i m i , z cm = m i z i   m i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaamiEaSWdamaaBaaajeaibaqcLbmapeGa am4yaiaad2gaaKqaG8aabeaajugib8qacqGH9aqpjuaGdaWcaaGcba qcLbsacqGHris5caWGTbWcpaWaaSbaaKqaGeaajugWa8qacaWGPbaa jeaipaqabaqcLbsapeGaamiEaSWdamaaBaaajeaibaqcLbmapeGaam yAaaqcbaYdaeqaaaGcpeqaaKqzGeGaaiiOaiabggHiLlaad2gal8aa daWgaaqcbasaaKqzadWdbiaadMgaaKqaG8aabeaaaaqcfa4dbiaacY cajugibiaadMhal8aadaWgaaqcbasaaKqzadWdbiaadogacaWGTbaa jeaipaqabaqcLbsapeGaeyypa0tcfa4aaSaaaOqaaKqzGeGaeyyeIu UaamyBaKqba+aadaWgaaqcbasaaKqzadWdbiaadMgaaKqaG8aabeaa jugib8qacaWG5bqcfa4damaaBaaajeaibaqcLbmapeGaamyAaaqcba YdaeqaaaGcpeqaaKqzGeGaeyyeIuUaamyBaKqba+aadaWgaaqcbasa aKqzadWdbiaadMgaaKqaG8aabeaaaaqcfa4dbiaacYcajugibiaadQ hajuaGpaWaaSbaaKqaGeaajugWa8qacaWGJbGaamyBaaqcbaYdaeqa aKqzGeWdbiabg2da9KqbaoaalaaakeaajugibiabggHiLlaad2gaju aGpaWaaSbaaKqaGeaajugWa8qacaWGPbaajeaipaqabaqcLbsapeGa amOEaKqba+aadaWgaaqcbasaaKqzadWdbiaadMgaaKqaG8aabeaaju gib8qacaGGGcaakeaajugibiabggHiLlaad2gajuaGpaWaaSbaaKqa GeaajugWa8qacaWGPbaajeaipaqabaaaaaaa@89B4@

where m i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaamyBaSWdamaaBaaajeaibaqcLbmapeGa amyAaaqcbaYdaeqaaaaa@3D2A@ denotes the mass of the i–th atom. The origin of coordinate system is generally taken at the center–of–mass of the molecule, so that xcm=0, ycm=0, zcm=0.

For a clear presentation, in the present discussion, we have taken the case of the interaction between H2CS (thioformaldehyde) and He atom. The H2CS is a planar molecule (say, lying in the yz–plane) as shown in Figure 1 and following the symmetries, the coordinates of its atoms in equilibrium may be expressed as given in Table 1. For coincidence of center–of–mass with the origin of coordinate system, we get the relation

2 m H z 1 + m C z 2 = m S z 3 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaaGOmaiaad2gajuaGpaWaaSbaaKqaGeaa jugWa8qacaWGibaal8aabeaajugib8qacaWG6bWcpaWaaSbaaKqaGe aajugWa8qacaaIXaaajeaipaqabaqcLbsapeGaey4kaSIaamyBaSWd amaaBaaajeaibaqcLbmapeGaam4qaaqcbaYdaeqaaKqzGeWdbiaadQ hal8aadaWgaaqcbasaaKqzadWdbiaaikdaaKqaG8aabeaajugib8qa cqGH9aqpcaWGTbqcfa4damaaBaaajeaibaqcLbmapeGaam4uaaWcpa qabaqcLbsapeGaamOEaSWdamaaBaaajeaibaqcLbmapeGaaG4maaqc baYdaeqaaaaa@5591@

Figure 1 Geometry of the H2CS molecule in equilibrium.

Atom

x

y

z

H

0

y1

–z1

H

0

–y1

–z1

C

0

0

–z2

S

0

0

 z3

Table 1 Atomic coordinates of H2CS in equilibrium.

where m H MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaamyBaKqba+aadaWgaaqcbasaaKqzadWd biaadIeaaSWdaeqaaaaa@3D6D@ , m C MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaamyBaSWdamaaBaaajeaibaqcLbmapeGa am4qaaqcbaYdaeqaaaaa@3D04@ and m S MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaamyBaKqba+aadaWgaaqcbasaaKqzadWd biaadofaaSWdaeqaaaaa@3D78@ are atomic masses of hydrogen, carbon and sulpher, respectively. The positions of atoms of H2CS are now kept fix. For calculation of interaction potential between H2CS and He atom, one can put He atom at a point expressed in polar coordinates ( r,θ,φ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaamOCaiaacYcacqaH4oqCcaGGSaGaeqOX dOgaaa@3F38@ ) as shown in Figure 2. The Cartesian coordinates (xʹ, yʹ, zʹ) of He atom are

x'=r sin θ cos φ, y'=r sin θ sin φ, z'=r cos θ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaamiEaiaacEcacqGH9aqpcaWGYbGaaeii aiaadohacaWGPbGaamOBaiaabccacqaH4oqCcaqGGaGaam4yaiaad+ gacaWGZbGaaeiiaiabeA8aQjaacYcacaqGGaGaamyEaiaacEcacqGH 9aqpcaWGYbGaaeiiaiaadohacaWGPbGaamOBaiaabccacqaH4oqCca qGGaGaam4CaiaadMgacaWGUbGaaeiiaiabeA8aQjaacYcacaqGGaGa amOEaiaacEcacqGH9aqpcaWGYbGaaeiiaiaadogacaWGVbGaam4Cai aabccacqaH4oqCaaa@6433@

For interaction between H2CS and He atom, the coordinates are given in Table 2. Then, the energies are calculated as:

  1. Energy E1( r,θ,φ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaamOCaiaacYcacqaH4oqCcaGGSaGaeqOX dOgaaa@3F38@ ) of H2CS + He.
  2. Energy E2( r,θ,φ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaamOCaiaacYcacqaH4oqCcaGGSaGaeqOX dOgaaa@3F38@ ) of H2CS while He atom is present as a ghost atom.
  3. Energy E3( r,θ,φ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaamOCaiaacYcacqaH4oqCcaGGSaGaeqOX dOgaaa@3F38@ ) of He atom while all atoms of H2CS are present as ghost atoms.

Figure 2 Interaction between H2CS and He atom.

Atom

x

y

z

H

0

y1

–z1

H

0

–y1

–z1

C

0

0

–z2

S

0

0

z3

He

Table 2 Coordinates for interaction between H2CS and He.

Here, the concept of ghost atom is introduced in order to consider the Basis Set Su–perposition Error (BSSE).16 The interaction potential V( r,θ,φ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaamOCaiaacYcacqaH4oqCcaGGSaGaeqOX dOgaaa@3F38@ ) between H2CS and He atom is

V( r, θ, φ )= E 2 ( r, θ, φ )+ E 3 ( r, θ, φ ) E 1 ( r, θ, φ ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaamOvaKqba+aadaqadaGcbaqcLbsapeGa amOCaiaacYcacaqGGaGaeqiUdeNaaiilaiaabccacqaHgpGAaOWdai aawIcacaGLPaaajugib8qacqGH9aqpcaWGfbWcpaWaaSbaaKqaGeaa jugWa8qacaaIYaaajeaipaqabaqcfa4aaeWaaOqaaKqzGeWdbiaadk hacaGGSaGaaeiiaiabeI7aXjaacYcacaqGGaGaeqOXdOgak8aacaGL OaGaayzkaaqcLbsapeGaey4kaSIaamyraKqba+aadaWgaaqcbasaaK qzadWdbiaaiodaaSWdaeqaaKqbaoaabmaakeaajugib8qacaWGYbGa aiilaiaabccacqaH4oqCcaGGSaGaaeiiaiabeA8aQbGcpaGaayjkai aawMcaaKqzGeWdbiabgkHiTiaadweal8aadaWgaaqcbasaaKqzadWd biaaigdaaKqaG8aabeaajuaGdaqadaGcbaqcLbsapeGaamOCaiaacY cacaqGGaGaeqiUdeNaaiilaiaabccacqaHgpGAaOWdaiaawIcacaGL Paaaaaa@7138@

The interaction potential V( r,θ,φ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaamOCaiaacYcacqaH4oqCcaGGSaGaeqOX dOgaaa@3F38@ ) is calculated for various positions of He atom and is used as input in the computer code MOLSCAT17,18 to calculate the scattering cross sections for collisional transitions between rotational levels, as a function of energy of colliding partner. These cross sections are averaged over the Maxwellian distribution to get the scattering rate coeffcients, as a function of kinetic temperature in the medium.12–15

We have found that on optimization of H2CS with MOLPRO, the center–of–mass does not coincide with the origin of coordinate system. On inclusion of He atom, we do not know if the origin of polar coordinates ( r,θ,φ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaamOCaiaacYcacqaH4oqCcaGGSaGaeqOX dOgaaa@3F38@ ) (expressing the position of He atom) is at the center–of–mass of H2CS, or at the origin defined in the MOLPRO, or somewhere else. Under such circumstances, it is difficult to have information about relative separation between the H2CS molecule and He atom, which is essentially required.

Optimization of H2CS

On 01 April 2014, we have optimized the H2CS with MOLPRO (Version 2012.1, Copyright, University College Cardiff Consultants Limited, 2008) by using the method CCSD (T) and basis set cc–pVDZ. The coordinates of atoms obtained are given in Table 3, which provide the center–of–mass at

x cm =0.00,  y cm =0.00,  z cm =0.1612625506 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaamiEaSWdamaaBaaajeaibaqcLbmapeGa am4yaiaad2gaaKqaG8aabeaajugib8qacqGH9aqpcaaIWaGaaiOlai aaicdacaaIWaGaaiilaiaabccacaWG5bWcpaWaaSbaaKqaGeaajugW a8qacaWGJbGaamyBaaqcbaYdaeqaaKqzGeWdbiabg2da9iaaicdaca GGUaGaaGimaiaaicdacaGGSaGaaeiiaiaadQhal8aadaWgaaqcbasa aKqzadWdbiaadogacaWGTbaajeaipaqabaqcLbsapeGaeyypa0JaaG imaiaac6cacaaIXaGaaGOnaiaaigdacaaIYaGaaGOnaiaaikdacaaI 1aGaaGynaiaaicdacaaI2aaaaa@5DB1@  (1)

Atom

x

y

z

H

0.0

1.765973450

–3.050725593

H

0.0

–1.765973450

–3.050725593

C

0.0

0.00

–1.940275913

S

0.0

0.00

1.150376265

Table 3 Atomic coordinates of H2CS (in Bohr).

On 21 September 2017, we have again optimized the H2CS with MOLPRO (Version 2015.1, Copyright, TTI GmbH Stuttgart, 2015) by using the same method CCSD(T) and the same basis set cc–pVDZ. The coordinates of atoms obtained are given in Table 4, which provide the center–of–mass at

x cm =0.00,  y cm =0.00,  z cm =0.4667993088 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaamiEaSWdamaaBaaajeaibaqcLbmapeGa am4yaiaad2gaaKqaG8aabeaajugib8qacqGH9aqpcaaIWaGaaiOlai aaicdacaaIWaGaaiilaiaabccacaWG5bWcpaWaaSbaaKqaGeaajugW a8qacaWGJbGaamyBaaqcbaYdaeqaaKqzGeWdbiabg2da9iaaicdaca GGUaGaaGimaiaaicdacaGGSaGaaeiiaiaadQhal8aadaWgaaqcbasa aKqzadWdbiaadogacaWGTbaajeaipaqabaqcLbsapeGaeyypa0JaaG imaiaac6cacaaI0aGaaGOnaiaaiAdacaaI3aGaaGyoaiaaiMdacaaI ZaGaaGimaiaaiIdacaaI4aaaaa@5DCB@ (2)

It shows the shifting of the center–of–mass without any reason.

Atom

x

y

z

H

0.0

1.765967499

–2.745177896

H

0.0

–1.765967499

–2.745177896

C

0.0

0.00

–1.634732411

S

0.0

0.00

1.455909829

Table 4 Atomic coordinates of H2CS (in Bohr).

Discussion

The comparison of y–coordinates in Tables 3 & 4 shows that either the values are changed or the accuracy of data is up to the 4th or 5th decimal place. The comparison of z–coordinates shows a large variation in the values. In equations (1) and (2): (i) The value xcm=0.00 is not surprising, as the H2CS lies in the yz–plane. (ii) The two H atoms lie symmetrically opposite on the two sides of z–axis and therefore the value ycm=0.00, as per expectation. (iii) Non–zero value of zcm is surprising, as the center–of–mass of a molecule (in equilibrium) is generally taken at the origin of coordinate system. Two different values for zcm may be interpreted that the center–of–mass is placed in a random manner in the MOLPRO. There is difference of 0.305536758 Bohr between the positions of center–of–mass when the H2CS is optimized with the help of MOLPRO on two different dates (01 April 2014 and 21 September 2017). It should not be the case. One may say that the molecule is shifted along the z–axis. But, the problem appears to know about the separation between H2CS and He atom while calculating interaction between them.

This problem was submitted for consideration of the organizers of MOLPRO as well as the MOLPRO users, but no solution emerged out. None of them could tell how to get separation between the H2CS molecule and He atom.

We have also optimized the Glycolaldehyde (C2H4O2) with the help of MOLPRO. The coordinates obtained are given in Table 5. This is case of three–dimensional molecule. These coordinates provide the center–of–mass at

x cm =0.089435584,  y cm =0.033493791,  z cm =0.000006947 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaamiEaSWdamaaBaaabaqcLbmapeGaam4y aiaad2gaaSWdaeqaaKqzGeWdbiabg2da9iaaicdacaGGUaGaaGimai aaiIdacaaI5aGaaGinaiaaiodacaaI1aGaaGynaiaaiIdacaaI0aGa aiilaiaabccacaWG5bWcpaWaaSbaaeaajugWa8qacaWGJbGaamyBaa WcpaqabaqcLbsapeGaeyypa0JaeyOeI0IaaGimaiaac6cacaaIWaGa aG4maiaaiodacaaI0aGaaGyoaiaaiodacaaI3aGaaGyoaiaaigdaca GGSaGaaeiiaiaadQhal8aadaWgaaqcbasaaKqzadWdbiaadogacaWG TbaajeaipaqabaqcLbsapeGaeyypa0JaaGimaiaac6cacaaIWaGaaG imaiaaicdacaaIWaGaaGimaiaaiAdacaaI5aGaaGinaiaaiEdaaaa@67CB@     (3)

It also shows that the center–of–mass of Glycolaldehyde does not coincide with the origin of coordinate system. We have optimized other molecules also with the help of MOLPRO and similar situation of non–coincidence of center–of–mass of molecule and the origin of coordinate system is found.

Atom

x

y

z

C

–0.962276889  

0.973356353

0.000270231

C

1.371041657

–0.680834308

0.000332592

O

3.483477674

0.147262577

0.000003779

O

–3.113843465

–0.620559603

–0.000640617

H

0.978640027

–2.736504842

0.000990216

H

–0.883628377

2.190534619

–1.672012667

H

–0.884340804

2.189412121

1.673439411

H

–4.620335021

0.387972112

0.000922186

Table 5 Coordinates of Glycolaldehyde (in Bohr).

Conclusion

In equilibrium, the center–of–mass of a molecule should coincide with the origin of coordinate system. We have found that for the considered molecules, it is not the case. The problem is found to become more severe, for example, when one wants to know the separation between the two colliding partner for scattering process. There appears need to make amendment in MOLPRO, so that the origin of coordinate system coincides with the center–of–mass of a molecule in equilibrium.

Acknowledgements

We are grateful to Hon’ble Dr. Ashok K. Chauhan, Founder President, Hon’ble Dr. Atul Chauhan, Chancellor and Prof.(Dr.) Balvinder Shukla, Vice–Chancelllor, Amity University for valuable support and encouragement. MKS is thankful to the SERB, DST, New Delhi for award of National Postdoctoral Fellowship.

Conflict of interest

Author declares there is no conflict of interest.

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