comparative study on formamide–water complex

Comparative Study on Formamide-Water Complex

M. NAGARAJU, G. NARAHARI SASTRYMolecular Modeling Group, Organic Chemical Sciences, Indian Institute of Chemical Technology,Tarnaka, Hyderabad 500 007, AP, India

Received 12 May 2009; accepted 20 May 2009Published online 3 November 2009 in Wiley InterScience (www.interscience.wiley.com).DOI 10.1002/qua.22368

ABSTRACT: The hydrogen bonding of 1:1 complexes formed between formamideand water molecule have been investigated systematically using Hartree–Fock (HF),hybrid density functional theory (B3LYP), and post-Hartree–Fock (MP2 and CCSD(T))methods with range of basis sets 6-31G(d), cc-pVXZ (X � D, T, Q) and aug-cc-pVYZ(Y � D, T). Three stable structures are considered on the potential energy surface offormamide and water system. The optimized geometric parameters and interactionenergies for various isomers at different levels are estimated. The IR frequencies,intensities, and frequency shifts are reported. This study shows that B3LYP/aug-cc-pVDZ method gives better performance for formamide-water complexes. © 2009 WileyPeriodicals, Inc. Int J Quantum Chem 110: 1994–2003, 2010

Key words: formamide-water complex; hydrogen bond; scaling factors; ab initiocalculations

Introduction

N oncovalent interactions play crucial role inthe determination of structures and functions

of many biological molecules. The three-dimen-sional architectures of proteins are stabilized by arange of noncovalent interactions such as ion-pair-ing, hydrogen bond (H-bond), cation-�, �-� inter-

actions, and so forth [1–5]. One of the most impor-tant noncovalent interactions is H-bond. It plays anessential role in the properties of various materials[6–8] such as synthetic polymers, biomolecules,and molecular solids and fluids. In addition, theyare responsible for the conformational preferencesof a large number of molecules [9] and producesignificant modifications in the kinetics and mech-anism of enzymatic reactions [10]. Studying how apair of noncovalent interactions mutually influenc-ing each other is interesting in its own right [11]. Itis well established that CAO��HON H-bonds playcritical role in the structure and properties of pro-teins and nucleic acids as well as in the behavior ofmany solvent systems [12–16]. Formamide is one of

Correspondence to: G. N. Sastry; e-mail: [email protected] grant sponsor: DST (Swarna Jayanthi Fellowship

Grant).Contract grant sponsor: CSIR.Additional Supporting Information may be found in the

online version of this article.

International Journal of Quantum Chemistry, Vol 110, 1994–2003 (2010)© 2009 Wiley Periodicals, Inc.

the simplest molecules usually chosen as model forstudying biological systems exhibiting the peptidetype of bonding as in proteins. H-bonding com-plexes of formamide such as formamide-water, for-mamide-methanol can serve as model systems forprotein-water and protein-solvent interactions. Be-cause of the simplicity of this model, the character-ization of the H-bond interactions between waterand formamide has been of considerable interest toexperimentalists and theoreticians. Many theoreticaland experimental investigations performed on thissystem [17–39]. However, earlier studies [17–23] car-ried out with small basis set or with fixed monomergeometries. Fu et al. [24] carried out benchmark stud-ies on formamide-water complexes at HF (6-311��G(d,p)), B3LYP (6-31G to 6-311��G(2d,2p)),and MP2 (6-311��G(d,p)) levels of theory. H-bondenergies were reported by Liu et al. [25] at MP2 levelwith basis sets 6-31G(d,p), 6-311�G(d,p), cc-pVDZ,and aug-cc-pVDZ. H-bond energies at B3LYP andMP2 levels with basis set 6-311��G(2d,2p) were re-ported [27, 29]. Symmetry-adapted perturbationtheory and atoms in molecules theory was used atMP2/6-31�G(d,p) method [30]. H-bond energy de-termination has been one of the most actively pur-sued topics by computational chemists, and a rangeof computational methods has been used over theyears to model this quantity. As accurate estimationof H-bond energy and computational time are highimportance, we undertook a systematic analysis toestimate the relative performance of current line ofcomputational methods. In recent years, DFT, espe-cially the B3LYP method, appears to be the methodof choice, when compared with the conventionalelectron correlation method (MP2), because of itscomputational economy. Thus, wherever possible,it has become our practice to use this more econom-ical variant compared with the MP2 and CCSD(T)methodologies. Therefore, the main objective of thisstudy is to assess the performance of the hybrid den-sity functional method B3LYP, when compared withthe ab initio methods. In this article, we reported bond-

ing energies between formamide and water mole-cules using various theoretical models and basis sets.The role of basis set size and basis set superpositioneffects on the structural complexation energies areanalyzed in detail. The vibrational frequencies of themonomer and complexes are calculated. Intermolec-ular, intramolecular frequencies and their shifts dueto the complex formation are analyzed. The stablestructures found for this complex is not entirely newand in fact it has been obtained previously.

This study gives the most accurate results for theH-bond interactions between formamide and watercomplexes, and also gives the error range for manyof the commonly used theoretical procedures. Thus,this study provides estimation for the reliabilitywith which computational procedure can be usedfor similar, but much larger systems.

Methods

All calculations were carried out using theGaussian 03 suite of programs [40]. Three distinctformamide-water complexes (see Fig. 1) were con-sidered for the study. All structures were optimized(noncounterpoise optimization (non-CP)) withoutimposing any symmetry constraints at HF, B3LYP,and MP2 level, using basis sets 6-31G(d), cc-pVXZ(X � D, T, Q), and aug-cc-pVYZ (Y � D, T). Fre-quency calculations were done to ascertain the na-ture of stationary points on the potential energysurface. The frequency analysis characterizes thatall conformations considered as minima on the po-tential energy surface. Single point energies are cal-culated at CCSD(T) level on MP2/cc-pVQZ opti-mized geometries with aforementioned basis sets.The H-bond energy was calculated at various levelsof theory using Eq. (1).

�EH-bond � Ecomplex � Mmonomers (1)

FIGURE 1. Formamide-water complexes considered in this study. [Color figure can be viewed in the online issue,which is available at www.interscience.wiley.com.]

FORMAMIDE-WATER COMPLEX

VOL. 110, NO. 10 DOI 10.1002/qua INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY 1995

The binding energies calculated for different levelshave been corrected with basis set superposition error(BSSE) via the standard counterpoise method [41]. Inaddition to this, we performed optimization usingcounterpoise method (CP) at HF, B3LYP, and MP2levels of theory with all aforementioned basis sets.Frequencies are also calculated using CP method.

Results and Discussion

STRUCTURE OF FORMAMIDE AND WATERMONOMER

Before examining methods and basis sets effecton formamide-water complexes, it is appropriate tostudy formamide and water since experimentaldata for geometries, frequencies are available. The-oretically and experimentally many studies havebeen devoted to the structure of formamide [42–

48]. Fogarasi and Szalay [44] investigated the ques-tion of planarity of formamide and computed esti-mates of its Born–Oppenheimer equilibriumstructure at levels of theory up to all-electron VTZCCSD(T). The planarity of the equilibrium of form-amide has been the subject of numerous spectro-scopic and quantum chemical investigations. Theinterested reader can refer Ref. 45 and the originalpublications for details. Table I presents the geo-metrical parameters of formamide and water at HF,B3LYP, and MP2 levels with basis sets 6-31G(d),cc-pVXZ (X � D, T, Q), and aug-cc-pVYZ (Y � D,T). It is observed that CON, NOHs, NOHa (exceptCAO) distances and CNHa, CNHs (except NCO,HsNCHa) angles are in good agreement with theexperimental values at HF method with cc-pVDZbasis set, having deviation 0.001–0.005Å, 0.2–0.5°,respectively. However, deviations from the experi-mental values increases with higher basis set, that

TABLE I ______________________________________________________________________________________________Comparison of the geometrical parameters of formamide and water molecules, optimized at HF, B3LYP, andMP2 levels with various basis sets (6-31G(d), cc-pVXZ (X � D, T, Q), and aug-cc-pVYZ (Y � D, T)), with theCCSD(T)/aug-cc-pVTZ and experimental ones.

Method Basis set

Formamide Water

RCON RNOHs RNOHa RCAO �CNHa �CNHs �NCO �HsNCHa ROH �HOH

HF 6-31G(d) 1.348 0.995 0.993 1.193 121.9 119.3 125.0 180.0 0.947 105.4cc-pVDZ 1.353 1.000 0.997 1.190 120.2 118.0 124.9 157.9 0.946 104.5aug-cc-

pVDZ 1.350 0.996 0.993 1.194 121.2 119.4 124.8 180.0 0.944 105.8cc-pVTZ 1.346 0.991 0.989 1.187 121.2 119.4 125.1 180.0 0.941 105.9aug-cc-pVTZ 1.346 0.992 0.989 1.188 121.2 119.5 124.9 180.0 0.941 106.2cc-pVQZ 1.345 0.991 0.988 1.186 121.2 119.5 125.0 180.0 0.940 106.2

B3LYP 6-31G(d) 1.362 1.011 1.009 1.216 121.8 119.1 125.0 180.0 0.968 103.7cc-pVDZ 1.362 1.011 1.011 1.214 121.6 119.1 125.0 180.0 0.968 102.8aug-cc-


MP2 6-31G(d) 1.363 1.011 1.009 1.225 121.2 118.2 124.7 163.8 0.969 104.0cc-pVDZ 1.372 1.016 1.013 1.219 118.9 116.7 125.0 149.9 0.964 101.9aug-cc-


CCSD(T)/aug-cc-pVTZ[48] 1.356 1.004 1.001 1.212 121.1 119.3 124.6 180.0

Expt [43] 1.352 1.002 1.002 1.219 120.0 118.5 124.7 180.0 0.957 104.5

Distance in Å, angles (�) in degree; s � syn and a � anti with respect to CAO bond.

NAGARAJU AND SASTRY

1996 INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY DOI 10.1002/qua VOL. 110, NO. 10

is, aug-cc-pVDZ, cc-pVTZ, aug-cc-pVTZ, and cc-pVQZ. The CON, NOHs, NOHa distances andCNHa, CNHs angles are in good agreement withthe experimental values at higher levels (B3LYP,MP2) with cc-pVTZ, aug-cc-pVTZ, and cc-pVQZbasis sets compared with lower basis sets (6-31G(d),cc-pVDZ). However for CNHs angle, MP2/6-31G(d) method have good agreement with experi-mental values when compared with higher basissets. The CAO distance and NCO angle at B3LYP/aug-cc-pVDZ method are close to the experimentalresults with deviation 0.001 Å, 0.0°, respectively.The deviation from the experimental values is zeroat MP2 level for CAO distance (cc-pVDZ), NCOangle (aug-cc-pVTZ, cc-pVQZ). The dihedral angleHsNCHa is 180° at all levels of theory with all basissets except cc-pVDZ (HF, MP2), 6-31G(d) (MP2). Inaddition to the geometrical parameters, vibrationalfrequencies are also compared with available exper-imental values at all levels of theory. In this article,we derived the scaling factor for the harmonic fre-quencies for each of the methods (Supporting In-formation Table S1) in terms of the experimentalvalues. Harmonic frequency scaling factors ofNOH, COH, and OOH bonds reveals that B3LYPmethod is consistent with experimental values (seeFig. 2), followed by MP2 and least for HF method.

The study reveals scaling factors of formamide(NOH, COH) with cc-pVDZ (B3LYP) basis set are inexcellent agreement with experimental values, fol-lowed by aug-cc-pVDZ (NOH) and cc-pVTZ (COH),respectively. In case of water also B3LYP methodconsistent with experimental values, with lower basisset (6-31G(d), cc-pVDZ) compared with higher basissets. Geometrical parameters, harmonic frequenciesof formamide and water molecules are reported inTable S1. Lucas et al. [38] reported harmonic scalingfactors for NOH, COH bonds (0.9447) and for OOHbond (0.9472) at MP2/6-31��G(2d,2p) level of the-ory. However in this study, at B3LYP/aug-cc-pVDZlevel, these values are 0.9615, 0.9655, and 0.9626 forNOH, COH, and OOH bonds, respectively. Thisshows that frequencies at B3LYP/aug-cc-pVDZ levelare in good agreement with experimental valueswhen compared with the MP2 level of theory. Thegeometrical parameters and frequency factors revealsthat B3LYP/aug-cc-pVDZ method is reliable for for-mamide molecule when compared with the othermethods and basis sets, while considering the accu-racy and computational time.

FORMAMIDE-WATER COMPLEXES

Geometrical Parameters

Three different configurations for the form-amide-water dimer were studied and shown in Fig-ure 1. Table II presents geometrical parameters offormamide-water complexes obtained throughnon-CP optimization at all levels of theory. At allthe ab initio and DFT (B3LYP) levels used here,optimization was performed with unconstrainedformamide. It is observed that calculated results forthe different methods at different basis sets, thechange in monomer geometries on complexationare relatively small. The CON bond length slightlyshorten while CAO bond length was increased alittle. Other bond lengths involved in the H-bond-ing slightly lengthen. The maximum bond lengthchange is �0.015 Å at all levels theory and basissets. Langley and Allinger [29] reported the geo-metrical parameters at MP2/6-311��G(2d,2p)level of theory. In this study for the geometricalparameters OOH��O distance (I, III), OOH��O,NOH��O, CAO��H angles (III), B3LYP method isconsistent with previous results [29], followed byMP2 method. The maximum deviation in B3LYPmethod is 0.018 Å (OOH��O), 0.8° (OOH��O),4.8° (NOH��O), 1.5° (CAO��H) and in MP2method is 0.048 Å, 1.7°, 4.6°, 1.8°, respectively.

FIGURE 2. Harmonic vibrational scaling factors offormamide and water molecules for NOH (black), COH(blue), and OOH (magenta) bonds at HF, B3LYP, andMP2 levels using basis sets 6-31G(d), cc-pVXZ (X � D,T, Q) and aug-cc-pVYZ (Y � D, T). [Color figure can beviewed in the online issue, which is available at www.interscience.wiley.com.]



For NOH��O (II, III) distance, MP2 method is ingood agreement with previous results when com-pared with B3LYP method, having maximum de-viation 0.083 Å (B3LYP), 0.042 Å (MP2). In B3LYPmethod lower basis sets (6-31G(d), cc-pVDZ) have goodagreement with MP2/6-311��G(2d,2p) method forOOH��O, NOH��O distance, angles except for CAO��Hangle. Similar trend was observed for MP2 method.Lovas et al. [28] reported the geometrical parameters forIII complex at fixed OOH��O angle (143.3°). It is ob-served that geometrical parameters CAO��H, NOH��Oangles (B3LYP), OOH��O distance and angle (HF),NOH��O distance (MP2 followed by B3LYP methods)are consistent with results reported by Lovas et al. [28].Effect of the CP optimization have been studied for thecomplexes considering all basis sets (6-31G(d), cc-pVXZ

(X � D, T, Q) and aug-cc-pVYZ (Y � D, T)) at HF,B3LYP, and MP2 levels of theory (Table S2). Geom-etries obtained from CP method follows similartrend as observed in non-CP method. Only geomet-rical parameters are not adequate to validate thetheoretical methods. It is appropriate to study thevibrational frequency of formamide-water com-plexes and validate with available experimentaldata. In the following sections we discuss about thevibrational frequency of fomamide-water com-plexes obtained from CP and non-CP methods.

Vibrational Frequencies

Vibrational spectroscopy is one of the most use-ful experimental tools to study the H-bonded com-

TABLE II _____________________________________________________________________________________________H-bond distances (Å), angles (°) and CON distances (Å) of formamide-water complex obtained through non-CP optimization at HF, B3LYP, and MP2 levels using basis sets 6-31G(d), cc-pVXZ (X � D, T, Q), andaug-cc-pVYZ (Y � D, T).

Methods Basis set

CON distance (Å) H-bond distance (Å) H-bond angle (°)

Orig I II III I II

III

I II

III

OOH��O NOH��O OOH��O NOH��O

HF 6-31G(d) 1.348 1.341 1.342 1.338 2.023 2.082 2.038 2.156 152.2 170.3 148.4 139.4cc-pVDZ 1.353 1.344 1.343 1.339 2.048 2.068 2.054 2.151 149.5 174.3 147.9 140.2aug-cc-

pVDZ 1.350 1.344 1.345 1.341 2.025 2.156 2.042 2.229 154.4 175.3 146.6 137.1cc-pVTZ 1.346 1.340 1.341 1.336 2.043 2.147 2.068 2.225 155.0 174.7 148.1 138.5aug-cc-

pVTZ 1.346 1.339 1.341 1.336 2.024 2.172 2.049 2.264 158.4 175.4 148.4 137.1cc-pVQZ 1.345 1.339 1.340 1.336 2.033 2.159 2.059 2.246 157.6 174.7 148.3 137.8

B3LYP 6-31G(d) 1.362 1.353 1.355 1.348 1.922 1.952 1.906 1.973 152.5 171.4 151.0 140.6cc-pVDZ 1.362 1.353 1.355 1.348 1.923 1.934 1.892 1.948 150.2 167.1 151.2 141.3aug-cc-


pVTZ 1.356 1.349 1.351 1.345 1.891 2.036 1.893 2.085 161.2 179.5 151.0 136.7cc-pVQZ 1.356 1.348 1.350 1.344 1.909 2.019 1.908 2.070 158.7 177.8 151.9 138.0

MP2 6-31G(d) 1.363 1.354 1.355 1.350 1.957 1.985 1.949 2.016 152.4 172.9 150.7 140.6cc-pVDZ 1.372 1.360 1.361 1.354 1.955 1.969 1.932 1.985 150.9 164.2 151.5 141.2aug-cc-


pVTZ 1.357 1.349 1.352 1.346 1.889 2.000 1.874 2.036 154.6 176.2 151.1 136.9cc-pVQZ 1.354 1.347 1.349 1.343 1.897 1.990 1.878 2.019 156.2 174.0 152.0 137.9

Expt [28] 2.03 1.99 143.3MP2/6-

311��G(2d,2p)[29] 1.907 1.981 1.902 2.002 156.1 173.9 151.1 141.5

NAGARAJU AND SASTRY


plexes. When the vibrational spectra of a free H-Xgroup and those in X-H��Y conventional H-bondsare compared, it is generally observed that the H-Xstretching vibration undergoes a substantial shifttoward a lower frequency and increase in intensity.Table III presents harmonic stretching frequency(cm�1) and intensity (km mol�1) of formamide-water complexes obtained through non-CP optimi-zation at various levels of theory. It is observed thatnonscaled harmonic frequencies of I, II, III com-plexes for NOH, OOH bonds are much closer tothe experimental values at B3LYP level of theorywhen compared with MP2 and HF methods (see

Fig. 3). In this study frequency values at B3LYPmethod are much closer to experimental valuesthan MP2/6-31��G(2d,2p) values reported by Lu-cas et al. [38] for III complex. In B3LYP methodlower basis sets (6-31G(d), cc-pVDZ) have mini-mum deviation from the experimental values whencompared with higher basis sets (cc-pVXZ (X � T,Q), aug-cc-pVYZ (Y � D, T)) having maximumdeviation 71, 75 cm�1 for OOH��O, 47, 134 cm�1 forNOH��O of bonded and nonbonded frequencies,respectively. It is interesting to have a look at thescaled harmonic frequencies, at HF method forOOH��O nonbonded (free OOH), NOH��O

TABLE III ____________________________________________________________________________________________Harmonic stretching frequency (cm�1) and intensities (km mol�1) of formamide-water complexes obtainedthrough non-CP optimization at HF, B3LYP, and MP2 levels using basis sets 6-31G(d), cc-pVXZ (X � D, T, Q),and aug-cc-pVYZ (Y � D, T).

Methods Basis sets

I II III

OOH��O N–H��O

BondedOOH Free OOH

BondedNOH Free NOH

BondedOOH Free OOH

BondedNOH Free NOH

S A S A S A S A

v I v I v I v I v I v I v I v I

HF 6-31G(d) 4013 178 4155 112 3807 183 3944 160 3987 201 4150 108 3779 125 3950 88cc-pVDZ 4052 173 4180 97 3779 192 3931 174 4020 199 4176 103 3752 126 3941 106aug-cc-

pVDZ 4039 250 4216 132 3791 159 3938 156 4026 210 4221 128 3780 98 3949 95cc-pVTZ 4047 215 4201 112 3792 159 3932 149 4028 194 4201 111 3773 106 3943 93aug-cc-

pVTZ 4028 277 4199 135 3790 154 3929 153 4014 221 4199 125 3776 98 3940 93cc-pVQZ 4044 250 4205 125 3792 157 3929 152 4026 208 4204 120 3776 101 3941 93

B3LYP 6-31G(d) 3608 245 3802 49 3482 343 3664 93 3525 395 3793 44 3407 126 3682 72cc-pVDZ 3617 258 3809 39 3459 326 3651 117 3514 429 3802 41 3363 153 3671 87aug-cc-


pVTZ 3603 497 3872 81 3518 248 3667 128 3546 501 3868 70 3478 47 3688 92cc-pVQZ 3630 407 3874 69 3513 263 3666 124 3564 439 3871 65 3463 85 3687 91

MP2 6-31G(d) 3678 197 3867 82 3566 309 3731 148 3621 291 3854 78 3506 127 3740 110cc-pVDZ 3749 198 3920 63 3552 267 3734 152 3674 279 3908 66 3491 156 3753 128aug-cc-


pVTZ 3639 384 3913 106 3561 265 3722 164 3581 492 3907 94 3514 43 3734 117cc-pVQZ 3680 358 3938 96 3571 272 3737 162 3609 447 3930 90 3515 78 3751 119

Expt [20] 3430 3707 3391 3522Expt [38] 3454 3727 3410 3548

Vibrational frequencies (v) in cm�1, intensities (I) in km mol�1; S, symmetric; A, antisymmetric.



bonded and nonbonded (free NOH) scaled fre-quencies are consistent with experimental valueswhereas OOH��O bonded frequencies have maxi-mum deviation (129 cm�1) with experimental valueswhen compared with higher level methods (B3LYPand MP2). When considering OOH��O bonded andnonbonded (free OOH) scaled frequencies it is ob-served that B3LYP method is very close to the exper-imental and higher level method (MP2). The maxi-mum deviation between B3LYP and MP2 method is58 cm�1 (cc-pVDZ) and decreases with higher basissets. The similar trend was observed for NOH��Obonded frequencies, minimum deviation betweenB3LYP and MP2 is 1 cm�1 with aug-cc-pVDZ basisset. When comparing experimental values with

B3LYP results aug-cc-pVTZ basis set shows mini-mum deviation (68 cm�1) followed by aug-cc-pVDZ(75 cm�1) basis set. However in MP2 method, aug-cc-pVDZ shows minimum deviation (74 cm�1) from theexperimental values, followed by aug-cc-pVTZ basisset (77 cm�1). It is also interesting to have a look at thefrequency shifts between the free and bonded stretchvibrations (Table IV). For the formamide-water com-plex, the bonded OOH and NOH stretch are exper-imentally red-shifted by 273 and 138 cm�1, respec-tively. The scaled harmonic red-shifts are slightlyreduced compared with nonscaled red-shifts; maxi-mum deviation is 22 cm�1 at HF method whereas athigher levels deviation decreased to 13, 17 cm�1 forB3LYP and MP2 methods, respectively. For OOH��O

FIGURE 3. Variation of scaled (dot lines) and nonscaled (solid line) frequencies with basis sets obtained throughnon-CP optimization at HF, B3LYP, and MP2 levels of theory (a) for I, (b) for II, (c) and (d) for III complexes, respec-tively. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]

NAGARAJU AND SASTRY


bond scaled and nonscaled red-shift values at B3LYPmethod are very close to experimental valueswhereas for NOH��O bond values at HF method isconsistent with experimental values. In complex III,NOH��O bond scaled and nonscaled red-shifts calcu-lated at B3LYP method with higher basis sets (aug-cc-pVDZ to cc-pVQZ) are close to experimental andprevious results reported at MP2/6-31��G(2d,2p)level of theory [38]. Similar trend was observed for Iand II complexes. The scaled and nonscaled harmonicfrequencies obtained through CP optimization alsofollows similar trend (Table S3).

Hydrogen Bond Energy

Figure 4 presents variation of corrected BSSE(non-CP) H-bond energies with basis sets at HF,

B3LYP, MP2, and CCSD(T) levels of theory for for-mamide-water complexes. The H-bond energies offormamide-water complexes with uncorrectedBSSE, corrected BSSE (non-CP) and corrected BSSEwith CP optimization are presented in Table S5. Tostandardize the theoretical methods for formamide-water complexes, binding energy also consideredfor analysis in addition to the geometrical and vi-brational frequencies. The order of stability of com-plexes (I, II, and III) follows III � I � II previousresults [24, 29, 30, 39]. The general importance ofincluding BSSE corrections in calculated bindingenergies has been well documented in the literature.Table S5 shows the existence of basis set sensitivity.The magnitude of BSSE is decreasing with the basisset enlarged. It is observed that at all levels of theory,dunning basis sets have high magnitude of BSSE

TABLE IV ____________________________________________________________________________________________Scaled and nonscaled harmonic frequency shifts (red-shifts) (cm�1) of formamide-water complexes obtainedthrough non-CP optimization at HF, B3LYP, and MP2 levels using basis sets 6-31G(d), cc-pVXZ (X � D, T, Q),and aug-cc-pVYZ (Y � D, T).

Methods Basis set

I II III

OOH��O NOH��O

Nonscaled Scaled Nonscaled Scaled Nonscaled Scaled Nonscaled Scaled

HF 6-31G(d) �142 �127 �137 �123 �163 �147 �171 �153cc-pVDZ �128 �114 �152 �137 �156 �139 �189 �171aug-cc-

pVDZ �177 �156 �147 �132 �195 �173 �169 �152cc-pVTZ �154 �136 �140 �126 �173 �153 �170 �153aug-cc-

pVTZ �171 �152 �139 �126 �185 �164 �164 �148cc-pVQZ �161 �143 �137 �124 �178 �158 �165 �149

B3LYP 6-31G(d) �194 �189 �182 �174 �268 �263 �275 �263cc-pVDZ �192 �187 �192 �185 �288 �281 �308 �297aug-cc-


pVTZ �269 �260 �149 �144 �322 �310 �210 �202cc-pVQZ �244 �234 �153 �147 �307 �295 �224 �215

MP2 6-31G(d) �189 �183 �165 �156 �233 �225 �234 �221cc-pVDZ �171 �162 �182 �173 �234 �221 �262 �249aug-cc-


pVTZ �274 �261 �161 �153 �326 �311 �220 �209cc-pVQZ �258 �245 �166 �156 �321 �304 �236 �223

MP2/6-31��G(2d,2p) [38] �320 �303 �222 �209

Expt [38] �273 �138



compared with corresponding augmented basis sets.The dunning basis set, cc-pVDZ have high magnitudeof BSSE, followed by split-valence basis set (6-31G(d)).The minimum magnitude of BSSE is observed at HFlevel of theory, followed by B3LYP method. The mag-nitude of BSSE at MP2, CCSD(T) levels are close toeach other. Similar trend was observed in BSSE whenoptimized with CP method. The single point energiesare calculated at CCSD(T) level on MP2/cc-pVQZgeometries with various basis sets. For complex I, theBSSE corrected H-bond energies obtained at MP2level consistent with higher level (CCSD(T)), maxi-mum deviation is 2.07 kJ mol�1 with cc-pVDZ basisset. When comparing H-bond energies at CCSD(T)method with HF, B3LYP methods, maximum devia-tions are 7.12, 3.22 kJ mol�1, respectively. It is ob-served that in HF method deviation increases withenlargement of basis set. Similar trend was observedfor complexes II, III having maximum deviation 5.36,2.7, 1.89, and 11.76, 5.13, 1.22 kJ mol�1 at HF, B3LYP,and MP2 methods, respectively. In all the complexes(I, II, and III) minimum deviation (1.5 kJ mol�1) wasobserved with aug-cc-pVDZ basis set at all levels oftheory. In this study, H-bond energies obtained atB3LYP/aug-cc-pVDZ method have good agreementwith MP2/6-311��G(2d,2p), CCSD(T)//MP2/6-311��G(d,p) results within the range of 1.6 kJ mol�1

[22, 24].The geometrical parameters, frequency and

H-bond energy analyses reveal that B3LYP/aug-cc-

pVDZ has better performance for formamide-watercomplexes.

Conclusions

This article provides systematic analysis of H-bond strength of formamide-water complexes byusing quantum chemical methods. The followingconclusions are drawn from this study:

1. The systematic calculations were performedwith HF, B3LYP, MP2, and CCSD(T) methodsusing different basis sets, 6-31G(d), cc-pVXZ(X � D, T, Q), and aug-cc-pVYZ (Y � D, T).

2. The geometrical parameters of formamide atB3LYP/aug-cc-pVDZ method are in good agree-ment with experimental and higher level values.

3. Frequencies of formamide at B3LYP and MP2levels are closer to the experimental valueswhen compared with HF method. Howeverfrequencies obtained at B3LYP/aug-cc-pVDZmethod are in good agreement with experi-mental values when compared with MP2/6-31��G(2d,2p) results.

4. Three stable structures are considered for form-amide-water complexes wherein cyclic doublebonded structure is the most stable (III) andbinding to carbonyl group (I) is slightly energet-ically favorable than to the amide group(II).

5. The geometrical parameters (non-CP) of for-mamide-water complexes obtained fromB3LYP method are close to higher level (MP2)method and experimental values. Similartrend was observed with geometries obtainedthrough CP optimzation.

6. Scaled and nonscaled harmonic frequencies(non-CP) of formamide-water complexes dem-onstrate that B3LYP method frequencies arecloser to experimental values when comparedwith HF and MP2 results. Frequencies obtainedat B3LYP method with aug-cc-pVDZ basis setconsistent with higher level (MP2) and previ-ously existing results (MP2/6-31��G(2d,2p)).Similar trend was observed for frequencies ob-tained through CP optimization.

7 From the geometrical and frequency analysis,it is observed that B3LYP/aug-cc-pVDZmethod has better performance than othermethods for H-bonding complexes of the typeformamide-water.

8. This method can be applied to understand the

FIGURE 4. For formamide-water complexes (I, black;II, blue; III, magenta) variation of BSSE-corrected ener-gies with basis sets obtained through non-CP optimiza-tion at HF, B3LYP, MP2, and CCSD(T) levels of theory.[Color figure can be viewed in the online issue, which isavailable at www.interscience.wiley.com.]

NAGARAJU AND SASTRY


substituted formamide-water complexes hav-ing more number of atoms, which mimics realbiological systems.

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comparative study on formamide–water complex

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