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Performance-of-the-Vienna-ab-initio-simulation-package-(VASP)-in-chemical-applications_2003_Journal-

Performance of the Vienna ab initio simulation package (VASP)

in chemical applications q

Guangyu Sun a,1,Jeno

¨Ku ¨rti a,b ,Pe ´ter Rajczy b ,Miklos Kertesz a,*,Ju ¨rgen Hafner c ,Georg Kresse c

Department of Chemistry,Georgetown University,Washington,DC 20057-1227,USA

Department of Biological Physics,Eo

¨tvo ¨s University,Budapest,Pa ´zma ´ny P.se ´ta ´ny 1/A,H-1117Hungary c

Institute for Materials Physics,University of Vienna,Sensengasse 8/12,A-1090Vienna,Austria

Received 24August 2002;accepted 11October 2002

Abstract

Five different density functionals in combination with ultra-soft pseudopotentials and plane wave basis sets were used to optimize the geometries of common chemical systems using solid state program Vienna ab initio simulation package (VASP).These systems included diatomics,N 2,O 2,F 2and CO,and carbon based organic systems,ethane,ethylene,acetylene,1,3-butadiene,1,3,5-hexatriene,benzene,biphenyl,naphtalene graphene,polyethylene and all-trans -polyacetylene.The four functionals based on the generalized gradient approximation gave very good agreement on bond lengths and angles as compared with each other,with localized Gaussian basis set calculations and with experimental values.Reasonable results were also obtained for vibrational frequencies of selected normal modes of benzene and for torsional potentials of 1,3-butadiene and biphenyl.On the other hand,local density approximation tends to underestimate bond lengths.The performance of VASP for these properties is very similar to Gaussian type implementations of density functional theory explaining its successes in molecular,solid state,surface and polymer applications.q 2003Elsevier Science B.V.All rights reserved.

Keywords:Density functional theory;Vienna ab initio simulation package;Testing density functionals and basis sets;Torsional potential;Solid state

1.Introduction

Density functional theories (DFTs)are very successful techniques for understanding

the electronic,structural and vibrational properties of large molecular systems.Well-known quantum chemical computational packages like GAUSSIAN 98contain DFT as an option.The Vienna ab initio simulation package (VASP)is an efﬁcient DFT code developed recently [1–3]for studying 3D bulk systems with periodic boundary condition.Most applications so far have been based on plane-wave basis set and ultrasoft pseudopotential approximation,although the newer version contains an all-electron option.Plane wave basis sets are

Journal of Molecular Structure (Theochem)624(2003)37–45

www.elsevier/locate/theochem

q Preliminary results were presented at the 1999sanibel symposium.

Present address:Laboratory of Medicinal Chemistry,NCI-Frederick,NIH,376Boyles St.,Frederick,MD 21702,USA.

*Corresponding author.Tel.:þ1-202-687-5761;fax:þ1-202-687-6209.

E-mail address:kertesz@georgetown.edu (M.Kertesz).

somewhat unusual for molecular applications, because of the association of plane wave basis sets with free electron like systems.Of course when a basis set is large enough,such associations are groundless.For instance,VASP proved to be very useful in investigating diamond,graphite and carbon nanotubes[4–6],and numerous other chemical applications that involve electronic sys-tems that are not free electron-like[7–12]. However,it is an open question that to what extent VASP is com

parable with traditional, quantum chemical ab initio programs based on local(atom centered Gaussian)basis sets.Our aim was to test the performance of VASP for geometries and vibrational frequencies of simple systems.

We have selected a few common chemical problems.We focused on optimizing geometries for which DFT is usually quite reliable.Four diatomics,including N2,O2,F2and CO,and a number of carbon-based systems that are proto-typical,ethane,ethylene,acetylene,1,3-butadiene, 1,3,5-hexatriene,benzene,biphenyl,naphthalene, graphene,polyethylene and trans-polyacetylene were calculated.We have also looked at a number of selected vibrational frequencies of benzene.An important area of application of total energy calculations is determining the energy differences of various isomers,conformers and tautomers.For testing purposes we have studied two well-under-stood rotational barriers where DFT is known to perform rather well:butadiene and biphenyl[13]. The optimized geometries of polyethylene and all-trans-polyethylene were calculated.Furthermore, the bond length alternation problem in all-trans-polyacetylene,which poses a serious challenge[14] to any total energy method,is addressed.

Fig.1depicts some of the molecules studied.

南画十六观2.Computation details

In the VASP(version 4.4.2)calculations the geometries of N2,O2,F2,CO,ethane,ethylene, acetylene,butadiene,1,3,5-hexatriene,benzene, biphenyl,naphthalene,polyethylene,all-trans-poly-acetylene and graphene were optimized with local density approximation(LDA)as well as with Generalized Gradient Approximations(GGA).Sev-eral GGA functionals,including Perdew–Becke (PB)[15],Langreth–Mehl-Hu(LM)[16,17],Per-dew–Wang86(PW86)[18]and Perdew–Wang91 (PW91)[19],were used to test their performance. The ultra-soft LDA pseudopotentials were used for LDA calculations,while the ultra-soft pseudopo-tentials generated for PW91exchange functional were used for all GGA calculations.For the pseudopotentials default cut-off energies were used(290eV for C,350eV for N,400eV for O and425eV for F).

Tetragonal lattices were utilized for all systems except for benzene and graphene where hexagonal lattices were used.A1£1£1k-point mesh was used for all molecular systems.For polymeric systems,30 k-points including the end points,and for graphene 30£30£1k-point mesh,were used.Since VASP always employs three-dimensional periodic boundary condition,a minimum of6A˚inter-molecular distance was kept for all systems to ensure that the inter-molecular interaction is sufﬁciently small.The geometry convergence criterion was set on forces where l F max l¼0.001eV/A˚.The convergence in total energy proved to be always better than0.001eV.

The vibrational frequencies of the four diatomics and four selected normal modes of benzene (2A1g%2B2u)were obtained by the‘frozen phonon’calculations.This involved point by point total energy calculations and were done manually, because it is not automatic in VASP.For the diatomics,a parabolicﬁt was done to the total energies calculated in seven points around the equilibrium,using0.05A˚steps.In the case of benzene,a two dimensional quadraticﬁt was done to nine points on the potential energy surface,using 0.01A˚steps in both directions,for each of the symmetry species.Calculations for the vibrational frequencies were carried out by both LDA and PW91exchange functionals.

For comparative purposes,calculations involving molecular systems were also done using PW91 functional with the GAUSSIAN98package[20].

The torsional potential energy curves of butadiene and biphenyl were obtained by the rigid rotor model, where during the potential scan the bond lengths and angles were keptﬁxed at the optimized values of the most stable conformer.

G.Sun et al./Journal of Molecular Structure(Theochem)624(2003)37–45 38

3.Results and discussion

神经氨酸酶抑制剂

Extensive experimental and theoretical efforts have been devoted to understand the structures and various physical properties of the species studied here.Our purpose of this study,however,is to test the performance of VASP program on molecular systems,thus only the most recent experimental and theoretical data will be listed and compared to our results.

The theoretical bond lengths and vibrational frequencies of N 2,O 2,F 2and CO calculated with LDA and PW91functionals are listed in Table 1together with the experimental values [21–24]and theoretical values calculated with localized Gaussian basis set using GAUSSIAN 98.In general,the VASP calculated bond lengths of diatomics agree with experimental results,with the largest difference

being 0.015A

˚for LDA and 0.030A ˚for PW91.The somewhat large deviation of 0.030A

˚for O 2given by PW91shows the performance of VASP on an open shell system.In general,LDA gives shorter bond lengths than PW91for all four diatomics studied here.

When different implementations of PW91are compared,both GAUSSIAN 98and VASP give reasonab

le results.VASP calculations [25]have been applied earlier to O 2and CO using the Perdew–Zunger (PZ)functional resulting in bond lengths for O 2and CO and vibrational frequency for CO agree well with our PW91results,while the frequency for O 2is predicted at 1552cm 21.The agreement between the Gaussian 6-31G*calcu-lation and the plane-wave calculation is remarkably close.The quality of calculated vibrational frequen-cies is comparable with that of the calculated bond lengths,and would require some scaling [26]to achieve acceptable agreement with experiment.

The calculated and experimental [27]structural parameters of ethane,ethylene and acetylene are listed in Table 2.Both LDA and GGA give reasonable agreement on bond lengths and bond angles in these systems.Earlier local-density func-tional calculations [28]on ethylene and acetylene using VASP agree well with current results.A closer inspection shows that LDA gives bond lengths for all C–C bonds shorter than experimental

ones with the largest absolute deviation of 0.023A

˚.All GGA approaches studied here give improved agreements over LDA for C–C bonds.Bond angles are well predicted by both LDA and GGA.Overall,VASP results are very similar to the 6-31G*Gaussian results on ethane,ethylene and acetylene using the same functional.

校园流行语Table 3lists the calculated geometrical parameters of trans -1,3-butadiene.As in the above cases,VASP results agree well with those of experimental [29]and earlier theoretical studies [30,31].All GGA func-tionals give correct predictions on the bond lengths,while LDA predictions of the single and double CC

bonds are too short by 0.034and 0.018A

˚,respect-ively.Both GGA and LDA give very good agreement on bond angles.Again,the Gaussian basis set

6-31G*

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Fig.1.Some molecular and polymeric systems studied in this work.

G.Sun et al./Journal of Molecular Structure (Theochem)624(2003)37–4539

results are very close to the plane wave basis set (VASP)results.

Using the optimized geometrical parameters of trans -1,3-butadiene,the torsional potential of buta-diene was calculated by LDA and PW91.Fig.2shows the VASP results and two other curves calculated with GAUSSIAN 98by PW91PW91/6-31G*,one by the rigid rotor model and one by the relaxed scan.It should be noted that only rigid rotor calculations are possible within VASP.Also shown are earlier relaxed scans by SCF and MP2[13].The overall shapes of our three rigid rotor curves are very similar.These curves also agree with the relaxed scan curve except around the cis -conformation,where the largest changes in structural parameters occur.

As compared with the SCF and MP2results,the DFT curves give a higher trans –gauche barrier and a bigger trans –gauche energy difference.The relaxed PW91curve has a cis –gauche energy difference of 0.1kcal/mol,while the rigid rotor PW91curves have cis –gauche energy differences more like that by SCF and MP2.

To further test the performance of VASP on conjugated systems,the torsional potential of

Table 1

The theoretical and experimental bond lengths and vibrational frequencies of selected diatomic molecules

Bond length Vibrational frequency

LDA

PW91PW91PW91/6-31G*a Exp.LDA PW91PW91PW91/6-31G*a Exp.b

N 2 1.109 1.113 1.116 1.098c 2313229423642331(2360)d O 2e 1.223 1.237 1.228 1.208d 1616151715761556(1580)d F 2 1.398 1.424 1.418 1.412c 1063101510171110(–)f CO

1.138

1.145

1.148

1.128g

2145

2116

2127

2143(2170)g

Bond lengths in A

˚,frequencies in cm 21.Calculations refer to VASP results except otherwise noted.a This work.GAUSSIAN 98calculations.

b Experimentally measured frequencies and,in parenthesis,harmoni

c values.c Taken from Ref.[21].

d Taken from Ref.[22].

e Open shell calculations.

f Taken from Ref.[24].g

Taken from Ref.[23].

Table 2

惠灵顿医院The theoretical and experimental bond lengths of ethane,ethylene and acetylene

LDA

PB LM PW86PW91PW91PW91/6-31G*a Exp.b CH 3CH 3

R C –C 1.508 1.528 1.521 1.531 1.529 1.531 1.531R C –H 1.102 1.099 1.108 1.099 1.098 1.102 1.096A C –C –H 111.7111.5111.6111.4111.4111.4A H –C –H 107.2107.4107.3107.4107.4107.5107.8CH 2CH 2

R C y C 1.320 1.327 1.332 1.330 1.329 1.338 1.339R C –H 1.094 1.091 1.101 1.090 1.090 1.093 1.085A C y C –H 121.7121.8121.7121.8121.8121.8A H –C –H 116.6116.3116.7116.4116.4116.4117.8CHCH

R C x C 1.195 1.200 1.207 1.201 1.199 1.214 1.203R C –H

1.072

1.066

1.078

1.065

1.066

1.073

1.061

Bond lengths in A

˚,bond angles in degree.Calculations refer to VASP results except otherwise noted.a This work.GAUSSIAN 98calculations.

Experimental values are taken from ref.Ref.[27].

G.Sun et al./Journal of Molecular Structure (Theochem)624(2003)37–45

biphenyl was calculated,again by LDA and PW91. The results are shown in Fig.3along with earlier predictions from literature.As noted by Karpfen et al.[13],the HF and MP2methods predict that the staggered conformation has lower energy than the eclipsed one,while the DFT methods show the reversed trend.The most stable conformations predicted by HF and MP2have torsion angles between40and508,and between30and408by DFT methods.Our VASP results follow this general trend in that both curves of LDA and PW91show that the staggered conformation is less stable than the eclipsed one and the most stable conformer lies between30and408.It is note-worthy that the LDA predicted relative energy of the staggered conformation is about1kcal/mol higher than obtained by the more reﬁned GGA functionals.

Again we observe that the6-31G*Gaussian basis set calculations are very similar to the VASP calculations if the same functional is used in the rigid rotor context.

Table4lists the VASP calculated and experimental [32–36]geometrical parameters of graphene and benzene as well as the frequencies of four selected normal modes of benzene.All four GGA function

als give good agreement with experimental results on benzene structural parameters,while the LDA gives C–C bond length short by0.010A˚.The same trend can be seen in the calculated bond length of graphene.VASP and GAUSSIAN98perform very similarly with the same density functional.

Using frozen phonon approximation,we were able to obtain vibrational frequencies of four selected normal modes of benzene,namely,two A1g and two B2u.The low frequency A1g is excellent,and gives a good a posteriori justiﬁcation for the use of this method for the Radial Breathing Mode(RBM)studies

Table3

The theoretical and experimental geometrical parameters of trans-1,3-butadiene

LDA PB LM PW86PW91B3LYP/6-31G*a PW91PW91/6-31G*b Exp.c R1 1.331 1.341 1.343 1.343 1.339 1.341 1.349 1.349 R2 1.433 1.448 1.445 1.451 1.448 1.458 1.454 1.467 R3 1.099 1.095 1.106 1.095 1.094 1.091 1.097 1.108 R4 1.096 1.092 1.102 1.092 1.091 1.088 1.094 1.108 R5 1.092 1.089 1.099 1.089 1.089 1.086 1.092 1.108 A1124.0124.5123.9124.5124.1124.3124.3124.4 A2116.2116.3116.3116.2116.4116.2116.3114.7 A3120.7121.4120.7121.3121.3121.6121.4120.9 A4122.0121.8122.0121.8121.8121.8121.8120.9

Bond lengths in A˚,angles in deg.See Fig.1for parameter deﬁnitions.Calculations refer to VASP results except otherwise noted.

a Taken from Refs.[30,31].

b This work.GAUSSIAN98calculation.

c Taken from Ref.[29]

Fig.2.Torsional potentials of1,3-butadiene around the central CC

single bond.Solid lines by VASP(rigid rotor),dashed lines by

簧片GAUSSIAN98using6-31G*basis set.SCF and MP2curves are

based on data from Ref.[13].

G.Sun et al./Journal of Molecular Structure(Theochem)624(2003)37–4541

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