QTAIM-Based Characteristic Group Infrared Intensities of Amino Acids

Article pubs.acs.org/JPCA

QTAIM-Based Characteristic Group Infrared Intensities of Amino Acids and Their Transference to Peptides Arnaldo F. Silva, Leonardo J. Duarte, and Roy E. Bruns* Institute of Chemistry, University of Campinas, UNICAMP, Cidade Universitária Campinas, PO Box 6154, Campinas, São Paulo 13083970, Brazil ABSTRACT: Dynamic atomic contributions (DACs) to the infrared intensities of 14 amino acids have been transferred to three peptide molecules, glycylglycine, trialanine, and the melanocyte-inhibiting factor MIF-1, to estimate the infrared intensities of the most strategic peptide bands. The DACs of the amino acids and infrared intensities of the peptides were determined at the DFT B3LYP/6-311+(d,p) level. The Quantum Theory of Atoms In Molecules (QTAIM) Charge−Charge Transfer−Dipolar Polarization (CCTDP) model at this Density Functional Theory (DFT) level was used to classify the O−H, NH2, N−H, and CO stretching as well as the NH2 bending characteristic groups for use in the transference procedure. Contrary to the frequencies, the intensities within these groups can have very diverse values, although their electronic structure changes upon vibration have predictable QTAIM behaviors for each group. Compared to the DFT calculated values, the two transferred O−H stretching intensities of the peptides are estimated with a root-mean-square (rms) error of 19.1 km mol−1. Six NH2 symmetric and antisymmetric stretching intensities were determined with a 9.9 km mol−1 error. The eight estimated CO stretching bands have a rms error of 78.0 km mol−1 or 23.6% of the average DFT peptide CO intensity of 328.4 km mol−1. The proposed procedure is applicable to experimental infrared intensities if a calibration set of molecules with known atomic polar tensors and normal coordinate transformations is available.

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INTRODUCTION Amino acids are biomolecules that have been extensively studied in many different fields of science. In computational chemistry, amino acids are often investigated by molecular mechanics1,2 or even ab initio methods3,4. The interest in amino acids is mainly due to the fact that they are monomeric units that build into macromolecules of biological interest, such as enzymes and neurotransmitters. The phenomena involved in the interaction between peptides in biocompatible environments are a subject of much interest4,5 as these interactions determine their conformations and play major roles in biological activities. Even though ab initio and molecular mechanics calculations have been improving greatly in the past few years, there are still many difficulties in obtaining a proper description of even small peptides. For example, a conformational study of trialanine in which six different force fields were evaluated6 resulted in qualitatively and quantitatively inconsistent descriptions. Even though this problem was reported more than 10 years ago, these force fields continue to be used ubiquitously7−9 and even have motivated the creation of a new generation of force fields.10,11 One of the potential reasons could be the lack of appropriate polarization to accurately describe van der Waals interactions such as London dispersion forces. In fact, electrostatic interactions are not correctly described solely by point charge models, and the inclusion of dipolar polarization yields more realistic depictions.12,13 In this © XXXX American Chemical Society

regard, a lot of efforts have been put into developing polarizable force fields especially through quantum chemical topology (QCT) force fields.14,15 The general idea of this theory is to use atoms from small molecules as building blocks in order to predict properties of larger molecules. The theory is based on atomic transferability, the Quantum Theory of Atoms In Molecules (QTAIM) theory,16,17 and the use of atomic multipoles. The exact form of the building blocks is determined by the molecular environment through kriging.18 Due to the subtle form that electronic properties respond to changes in molecular geometry, a machine learning technique called kriging is used to determine the exact form of the building blocks. Kriging is a predictor algorithm that uses known information as calibration data to obtain information on test systems. Our research group has made progress in the last couple of years with the Charge−Charge Transfer−Counter Polarization (CCTCP)19 (previously called Charge−Charge Flux−Dipole Flux20,21 (CCFDF)) model for estimating the intensities of hydrocarbons. It is important to highlight however that this model does not properly describe out-of-plane vibrational intensities of planar molecules. We have also found examples in which the polarization parcel of our model Received: July 30, 2016 Revised: September 29, 2016

A

DOI: 10.1021/acs.jpca.6b07690 J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A does not oppose the charge transfer contribution.22 Therefore, it is more appropriate to call the model Charge−Charge Transfer−Dipolar Polarization, or CCTDP. Therefore, from this point on, we intend to replace the last term of our model, “counter polarization”, by the more general term “dipolar polarization”. More recently, we have shown that infrared intensities can be partitioned into dynamic atomic contributions23 (DACs). These contributions are useful because they permit a detailed study of localized functional groups,24 enabling a thorough investigation of their electronic structures. In that work, many different molecules that have a carbonyl group were studied. Even though the infrared intensities of the molecules ranged from 67.2 to 508.6 km mol−1, they have characteristic electronic structure behavior upon vibration. Nonetheless, a question was raised regarding the transferability and utility of these localized functional groups. Furthermore, the CCTDP model is consistently based on some of the same principles as the QCT theory, in that we also use QTAIM parameters and include polarization for molecular systems through the use of atomic dipoles. However, we have not yet tested the transferabilities of these new parameters. Furthermore, even though methods for obtaining localized functional frequencies have been described in the literature,25 they have not yet been achieved for the infrared intensities obtained through QTAIM parameters. Therefore, in this work, we intend to use the CCTDP model to study characteristic CO, NH2, N−H, and O−H vibrations for several amino acids. We hope to test the transferability of the DACs within a calibration group of amino acids and then use them as building blocks to predict the infrared intensities of peptides. We would also like to investigate the importance of polarization effects on the description of these amino acids and how they affect property transferability.

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∂pσ ∂νj

N

= qj0 +

∑ σi0 i=1

∂qi ∂νj

N

+∑

∂mi , σ

i=1

for σ = ν

∂νj

(1)

and ∂pσ ∂νj

N

=

∑ σi0 i=1

∂qi ∂νj

N

+

∑ i=1

∂mi , σ

for σ ≠ ν

∂νj

(2)

q0j

where is the equilibrium atomic charge of the displaced jth atom, qi and mi,σ are the atomic charge and dipole component of the ith atom, and σ0i is its equilibrium Cartesian coordinate.23 The second term of eq 1 and the first term of eq 2 involve atomic charge rearrangements, and the last terms correspond to changes in the atomic dipoles of all of the atoms owing to this displacement. As such, the polar tensor elements contain DACs to the atomic dipole moment derivatives. Upon transforming to normal coordinates, for k = 1, ..., 3N − 6, σ = x,y,z ⎡ ⎛ ∂p ⎞⎛ ∂νj ⎞⎤ ⎟⎟⎥ = = ∑ ⎢ ∑ ⎜⎜ σ ⎟⎟⎜⎜ ⎢⎣ ⎥ ∂ ∂ ∂Q k ν Q ⎝ j⎠ k ⎠⎦ j=1 ν=x ,y,z ⎝ ∂pσ

N

⎛ ∂p ⎞(j) ∑ ⎜⎜ σ ⎟⎟ ∂Q k ⎠ j=1 ⎝ N

(3)

where Cartesian coordinates of the same atom are grouped together in DACs to dipole moment derivatives with respect to the kth normal coordinate. As such, for σ = x,y,z, j = 1, ..., N ⎛ ∂p ⎞(j) ⎛ ∂νj ⎞ ⎜⎜ σ ⎟⎟ = qj0⎜⎜ ⎟⎟ + ⎝ ∂Q k ⎠ ⎝ ∂Q k ⎠

N

⎛

N

∑ ⎜⎜∑ ν=x ,y,z

⎝ i=1

∂[qi + mi , σ ] ⎞⎛ ∂νj ⎞ ⎟⎟⎜⎜ ⎟⎟ ∂νj ⎠⎝ ∂Q k ⎠ (4)

This derivative includes equilibrium charge, charge transfer, and dipolar polarization contributions owing to displacement of the jth atom in the kth normal coordinate. In general, atomic displacements along one of the Cartesian axes can provoke changes in the charge transfer and polarization contributions in all Cartesian directions, while they only provide nonzero charge contributions in the direction of the displaced atom. Therefore, the last term describes variational tendencies in charge transfer and polarization related to displacements of the jth atom along the three Cartesian directions, each of which is weighted by its importance in the kth normal coordinate. In a more compact form, each DAC can be expressed as contributions from charge movement, charge rearrangement, and atomic dipole change contributions23

THEORY AND COMPUTATIONAL DETAILS

The molecular structures for the amino acids were optimized by the Gaussian0926 program using the Becke three-parameter, Lee−Yang−Parr (B3LYP) hybrid functional with a 6-311G +(d,p) basis set. We have chosen density functional theory for its computational efficiency as B3LYP with Dunning basis sets has been proven to yield good descriptions of amino acid geometries and some vibrational features.27 Furthermore, in a recent paper, 24 our group showed that the CCTDP contributions are not sensitive over a large range of calculational levels, including B3LYP, M06-2X, PBE0, MP2, and QCISD along with cc-pVnZ, n = D, T, and Q basis sets. The infrared analytical intensities and Hessian matrix were provided by Gaussian09 as well. The numerical infrared intensities were obtained by the Placzek program28 through derivatives of AIM atomic charges and dipoles calculated by the AIMALL program.29 To obtain these intensities, each one of the N atoms within a molecule is displaced by 0.01 Å in both positive and negative directions of each Cartesian axis, generating 6N new geometries. It should be noted that all of the calculations as well as the equations given below are within the harmonic oscillator−linear molecular dipole moment function approximation. Within the QTAIM model, for σ,ν = x,y,z, and i,j = 1, ..., N, the polar tensor elements are given by

⎛ ∂p ⎞(j) ⎛ ∂p ⎞(j) ⎛ ∂p ⎞(j) ⎛ ∂p ⎞(j) ⎜⎜ σ ⎟⎟ = ⎜⎜ σ ⎟⎟ + ⎜⎜ σ ⎟⎟ + ⎜⎜ σ ⎟⎟ ⎝ ∂Q k ⎠ ⎝ ∂Q k ⎠C ⎝ ∂Q k ⎠CT ⎝ ∂Q k ⎠DP

Now, the norm of the vector

∂p ̅ ∂Q k

(5)

is proportional to the

square root of the intensity, and it can involve dipole changes in all three Cartesian coordinate directions ⎛ ∂py ⎞(1) ⎛ ∂p ⎞(1) ⎛ ∂p ⎞(1) ∂p̅ x ⎟⎟ j ̅ + ⎜⎜ z ⎟⎟ k ̅ + ⎟⎟ i ̅ + ⎜⎜ = ⎜⎜ ∂ ∂ Q Q ∂Q k ⎝ k⎠ ⎝ ∂Q k ⎠ ⎝ k⎠ ⎛ ∂py ⎞(N ) ⎛ ∂p ⎞(N ) ⎛ ∂p ⎞(N ) x ⎟⎟ j ̅ + ⎜⎜ z ⎟⎟ k ̅ ⎟⎟ i ̅ + ⎜⎜ ··· + ⎜⎜ ⎝ ∂Q k ⎠ ⎝ ∂Q k ⎠ ⎝ ∂Q k ⎠ (6)

Through eq 3 B


Article

The Journal of Physical Chemistry A

Table 1. DFT Frequencies (cm−1) and Infrared Intensities (km mol−1) Calculated Analytically with Gaussian09, Numerically by AIMAll and Placzek, and with the DAC Functional Group Approximation for 14 Calibration Amino Acids amino acida Gly

Ala

Ser

Cys

Met

Asn

Gln

vibration O−H str NH2 ASb NH2 SSc CO str NH2 bend O−H str NH2 AS NH2 SS CO str NH2 bend O−H str hydroxyl O−H str NH2 AS NH2 SS CO str NH2 bend O−H str NH2 AS NH2 SS CO str NH2 bend O−H str NH2 AS NH2 SS CO str NH2 bend O−H str NH2 AS amide NH2 AS NH2 SS amide NH2 SS CO str CO str amide NH2 bend NH2 bend amide O−H str NH2 AS amide NH2 AS NH2 SS amide NH2 SS CO str CO str amide NH2 bend NH2 bend amide

frequency DFT

intensity DFT

intensity AIM

intensity DAC

amino acida

3759 3605 3517 1819 1644 3760 3603 3516 1808 1640 3802

72.6 12.5 4.8 307.8 68.3 74.7 11.1 4.7 316.1 68.4 55.1

77.5 12.4 5.3 303.4 69.5 69.2 9.9 5.3 313.8 69.8 63.0

78.7 12.4 5.3 288.7 59.4 70.2 9.0 5.3 299.3 60.9 65.8

His

3747 3603 3507 1818 1664 3754 3606 3519 1814 1666 3755 3607 3519 1808 1639 3761 3722

63.1 17.5 9.9 298.5 47.1 75.3 18.0 10.2 320.9 37.3 77.8 12.2 6.1 364.3 73.0 81.1 43.4

65.0 17.5 9.8 300.4 46.3 77.0 17.9 10.3 317.8 35.0 77.5 12.8 6.6 374.6 63.3 72.1 42.1

63.9 17.7 10.0 279.5 44.3 78.2 18.0 10.3 299.4 33.4 78.5 12.8 6.5 362.1 52.2 73.4 42.5

3605 3590 3519 1811 1755

24.0 44.2 3.1 332.9 310.3

24.3 45.8 3.4 357.3 314.0

24.4 45.3 3.4 345.5 300.4

1632 1621

123.2 102.0

125.2 102.8

90.9 89.9

3744 3724

64.7 39.4

63.2 38.3

64.1 39.0

3590 3584 3500 1815 1759

8.1 39.6 3.9 282.1 347.3

9.1 39.6 4.9 282.5 385.3

9.2 39.3 5.0 270.5 356.1

1645 1621

60.9 115.1

57.1 118.0

45.6 102.3

⎤ ⎡ N ⎛ (j) ⎞ ⎛ ⎛ ∂p ⎞ ⎛ ∂p ⎞ ∂p ⎞ ∂p Ak = K ⎜⎜ ̅ ⎟⎟ . ⎜⎜ ̅ ⎟⎟ = K ⎢∑ ⎜⎜ ̅ ⎟⎟ . ⎜⎜ ̅ ⎟⎟⎥ ⎢⎣ ⎝ ∂Q k ⎠ ⎝ ∂Q k ⎠⎥⎦ ⎝ ∂Q k ⎠ ⎝ ∂Q k ⎠ j=1

(7)

Ak = Ak(1) + Ak(2) + ··· + Ak(N )

(8)

Asp

Glu

Phe

Tyr

Trp

Pro

vibration O−H str N−H unsat str NH2 AS NH2 SS CO str NH2 bend O−H str O−H str NH2 AS NH2 SS CO str CO str NH2 bend O−H str O−H str NH2 AS NH2 SS CO CO NH2 bend O−H str NH2 AS NH2 SS CO str NH2 bend O−H str O−H str phenol NH2 AS NH2 SS CO str NH2 bend O−H str N−H unsat str NH2 AS NH2 SS CO str NH2 bend O−H str N−H sat str CO str

frequency DFT

intensity DFT

intensity AIM

intensity DAC

3750 3655

61.2 66.5

64.9 65.1

66.2 65.0

3577 3500 1800 1671 3760 3756 3609 3523 1815 1803 1634 3759 3750 3575 3498 1806 1801 1672 3748 3577 3498 1804 1671 3836 3748

7.0 2.4 337.8 30.4 80.3 77 25.2 4.0 345.4 258.2 101.1 67.4 64.6 8.2 3.6 322.5 286.0 30.4 66.8 8.3 4.1 340.3 33.5 67.8 66.7

7.8 3.1 370.4 31.5 64.3 77.5 24.5 3.5 342.4 255.4 105 69.6 62.5 7.5 3.0 323.5 277.6 33.0 64.8 8.1 3.8 353.6 35.0 59 54.1

5.3 3.1 349.7 31.7 77.1 76.7 24.4 3.5 286.0 230.0 87.4 71.3 63.3 7.5 3.0 260.9 257.7 33.2 66.0 8.2 3.8 334.9 34.5 59.0 55.2

3575 3496 1804 1671 3756 3676

8.1 4.1 342.8 32.3 70.6 73.8

8.8 4.7 363.6 30.3 71.6 69.0

8.9 4.7 345.9 30.4 72.6 68.7

3584 3504 1834 1653 3754 3561 1812

4.1 1.3 262.3 38.0 62.5 4.0 276.8

4.1 0.9 262.5 40.5 61.6 5.0 276.6

4.1 0.9 243.4 44.9 62.6 5.3 257.5

a

Abbreviations: Gly = glycine, Ala = alanine, Ser = serine, Cys = cysteine, Met = methionine, Asn = asparagine, Gln = glutamine, His = histidine, Asp = aspartic acid, Glu = glutamic acid, Phe = phenylalanine, Tyr = tyrosine, Trp = tryptophan, and Pro = proline. b AS = antisymmetric stretch. cSS = symmetric stretch.

product of the dipole moment derivative vector for atomic displacement by the total dipole moment derivative vector of the normal mode.18 Thus, the intensity of the kth normal mode is simply a sum of the scalar products of the dynamic atomic dipole moment derivatives of all atoms in the molecule by the dipole moment derivative of that normal mode. Within QTAIM, the directions of the atomic contributions are determined by the sizes of the Cartesian components

As such, a dynamic atomic intensity contribution to a fundamental infrared intensity can be defined as the scalar C


Article


Figure 1. Analytical DFT infrared intensities vs functional group intensities calculated with the DAC approximation for 14 calibration amino acids for (a) O−H, NH2, and N−H vibrations and (b) the CO stretch. AS = antisymmetric stretch and SS = symmetric stretch.

obtained analytically by DFT for the O−H, NH2, and N−H and for the more intense CO stretching results, respectively. Table 2 displays the CCTDP contributions and their couplings for the characteristic vibrations of the amino acids. The CCTDP contributions are rather constant within each vibrational group; therefore, they are arranged in order to highlight their similarities. Figure 2 illustrates the relative importance of the charge, charge transfer, and dipolar polarization contributions for the vibrations of the calibration amino acids. Looking at the average values of the contributions for each vibration, it becomes clear that the dipolar polarization contribution is indispensable to describe the CO stretch. Even though the dipolar polarization contributions are very small for the O−H stretch and the NH2 stretches and bends, their coupling with charge and charge transfer can result in large contributions to the total intensities. For example, the small average dipolar polarization contribution for the O−H stretch is only 16.6 km mol−1, but its coupling with the charge contributes an average of 156.7 km mol−1. The average calculated O−H stretching intensity is only 67.6 km mol−1. The dipolar polarization effect has not been included in previous intensity models. The CCTDP contributions are not only useful for interpreting electronic structure changes that occur during vibrations but are also capable of discriminating vibrations into characteristic groups, depending on their relative values. Figure 3 shows a graph of the three contributions for the vibrations in Table 2. The CO stretches are discriminated from the others by their high polarization values. The NH2 symmetric and antisymmetric stretches, NH2 bends, and O−H stretches are discriminated by increasing charge and charge transfer values. As a result, the average total intensities of these groups also increase in this manner. The dispersion of the points within a specific group is an indicator of transferability of a given vibration as low dispersion indicates similar behavior among the molecules. For example, the polarization that is very important to the description of the CO vibration also seems to be the contribution that varies the most in the 3D graph of Figure 3. To a lesser extent, the same observation holds for the NH2 vibrations.

represented by eq 4 in terms of equilibrium charge displacement, charge transfer, and dipolar polarization. Therefore, the functional group contributions are obtained by displacing the atoms that compose a given characteristic vibration and observing the electronic response of the whole molecular system, including the displaced atoms. Displacing these atoms will cause changes in the charges and dipoles of all atoms of the molecule. In fact, within a specific vibration, the atom that is displaced the most is usually the one that makes the larger dipole moment change contribution. For example, for the O−H bond vibration, the hydrogen atom is practically the only displaced one, and its atomic dipole moment changes much more that of the oxygen dipole.

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RESULTS AND DISCUSSION Table 1 contains the frequencies and intensities calculated by different methods for the selected calibration set of amino acids. As they have many different vibrations, some of the most characteristic ones were selected for analysis in this paper. One can see from the table that the intensities calculated analytically by DFT with Gaussian09 and numerically by Placzek with the AIM parameters agree very well having a rootmean-square (rms) error of only 7.6 km.mol−1. A null numerical integration error from AIMAll would result in zero error. Even more impressive is the fact that the agreement between the analytical values and those estimated using only the DACs of the functional group atoms is almost as good with an rms error of 13.3 km mol−1. Both of these errors are very small as the calculated AIM intensities range from 0.9 to 385.3 km mol−1. Therefore, the DAC functional group approximation is quite accurate for describing electronic changes for normal vibrations as only two or three dynamic atomic intensity contributions are able to account for the intensity of a vibration that theoretically consists of the movement of 10−34 atoms. Therefore, the above results are consistent with the local mode model developed by Henry and co-workers to describe the spectral properties of X−H stretching overtones.30 Even within the harmonic oscillator approximation for which all atoms can be displaced in a normal mode, the main electronic structure changes occur owing to only a few atoms. Figure 1a and 1b illustrate how the approximate DAC functional group vibrations accurately predict the intensities D


Article


Table 2. Charge (C), Charge Transfer (CT), and dipolar polarization (DP) Contributions (km mol−1), and Their Couplings, for the Characteristic Vibrations of the 14 Calibration Amino Acids amino acid Gly Ala Ser Ser Cis Met Asn Gln His Asp Asp Glu Glu Phe Tyr Tyr Trp Pro averages Gly Ala Ser Cis Asn Gln His Met Asp Glu Phe Tyr Trp averages Gly Ala Ser Cis Met Asn Gln His Asp Phe Tyr Trp averages Gly Ala Ser Cis Met Asn Asn Gln Gln His Asp Asp Glu

vibration O−H O−H O−H O−H O−H O−H O−H O−H O−H O−H O−H O−H O−H O−H O−H O−H O−H O−H

str str str hydroxyl str str str str str str str str str str str str str phenol str str

NH2 NH2 NH2 NH2 NH2 NH2 NH2 NH2 NH2 NH2 NH2 NH2 NH2

ASa ASb AS AS AS AS AS AS AS AS AS AS AS

NH2 NH2 NH2 NH2 NH2 NH2 NH2 NH2 NH2 NH2 NH2 NH2

SS SS SS SS SS SS SS SS SS SS SS SS

CO CO CO CO CO CO CO CO CO CO CO CO CO

str str str str str str str str str str str str str

C

CT

DP

2C·CT

2C·DP

2CT·DP

total

383.4 384.3 358.6 384.2 386.3 386.4 385.5 379.8 376.1 366.6 402.7 374.3 382.2 379.5 379.1 358.3 380.8 376.5 379.1 ± 10.7 195.6 197.5 206.9 211.6 213.7 193.8 185.7 200.8 217.4 188.3 187.8 187.3 189.0 198.1 ± 11.0 104.7 101.5 116.6 110.1 103.1 107.1 98.0 99.2 108.4 101.7 101.4 94.0 103.8 ± 6.1 301.7 298.4 334.3 334.1 295.4 293.1 285.2 302.0 322.1 337.7 297.2 312.4 397.3

239.1 240.3 267.7 257.7 237.8 226.5 230.6 255.7 245.4 222.4 253.2 247.9 253.8 240.3 256.9 315.1 252.2 260.3 249.8 ± 20.9 55.1 60.3 51.0 51.5 45.4 63.9 63.9 57.8 46.3 60.5 63.1 63.9 74.2 58.2 ± 8.2 39.6 45.3 38.5 33.6 38.9 33.7 36.3 42.3 34.9 39.5 36.6 45.5 38.7 ± 4.0 279.1 276.9 359.1 346.4 225.4 283.3 437.9 317.7 517.8 342.5 388.2 226.5 424.0

16.2 14.4 26.1 15.9 16.3 15.2 13.2 16.3 16.0 11.2 17.3 17.3 15.6 14.2 13.1 26.4 16.8 17.0 16.6 ± 4.0 7.8 11.4 12.0 11.5 9.1 8.9 10.1 10.3 9.5 13.0 12.6 11.0 10.0 10.6 ± 1.5 12.7 14.4 5.2 6.1 13.4 14.3 12.3 9.8 13.8 9.9 9.8 15.2 11.4 ± 3.3 324.4 327.6 366.6 352.7 321.5 343.6 526.3 328.3 603.0 365.4 451.0 219.2 401.5

−599.7 −603.7 −614.9 −624.5 −601.2 −588.4 −592.2 −619.3 −604.2 −566.9 −633.0 −602.9 −619.6 −600.9 −621.5 −656.8 −611.1 −621.8 −610.1 ± 19.5 −208.5 −217.2 −204.5 −207.9 −196.8 −222.1 −217.0 −215.5 −200.5 −212.4 −215.4 −216.7 −236.5 −213.2 ± 10.1 −120.9 −125.7 −127.1 −116.0 −117.3 −114.9 −117.0 −121.2 −117.8 −118.5 −113.2 −122.9 −119.4 ± 4.3 −500.2 −497.0 −634.4 −590.0 −432.5 −476.9 −604.6 −526.9 −688.2 −543.6 −638.9 −399.9 −723.5

160.5 146.2 192.6 157.2 159.9 151.6 140.3 155.8 154.5 123.8 166.0 160.4 153.3 145.3 139.6 194.4 159.7 158.8 156.7 ± 17.3 −85.4 −89.7 −96.4 −97.6 −86.9 −81.7 −83.8 −86.9 −89.1 −94.9 −93.0 −86.4 −86.4 −89.1 ± 5.0 −58.2 −53.0 −40.7 −37.6 −52.6 −64.8 −54.9 −42.3 −62.7 −46.3 −46.2 −55.4 −51.2 ± 8.7 494.6 507.4 591.6 565.9 502.1 537.3 625.3 499.6 747.4 573.7 681.3 337.8 640.9

−122.3 −112.4 −167.4 −125.8 −122.4 −113.7 −105.2 −125.0 −122.9 −92.7 −128.7 −127.4 −122.8 −113.5 −113.0 −178.4 −126.8 −129.3 −125.0 ± 19.9 47.5 47.6 48.2 48.6 39.8 46.3 48.9 46.2 40.9 53.0 53.0 49.7 53.8 48.0 ± 4.2 27.0 22.7 17.1 13.7 21.1 28.1 30.4 15.2 26.8 17.6 16.4 24.5 21.7 ± 5.7 −596.6 −599.5 −717.0 −691.6 −537.3 −623.2 −956.1 −638.3 −1116.8 −705.2 −836.3 −440.7 −816.9

77.2 69.1 62.7 64.7 76.7 77.5 72.2 63.2 64.9 64.3 77.5 69.6 62.5 64.8 54.2 59.0 71.6 61.5 67.6 ± 7.0 12.1 9.9 17.2 17.6 24.3 9.0 7.8 12.8 24.5 7.5 8.1 8.8 4.1 12.6 ± 6.5 4.9 5.3 9.5 9.9 6.6 3.4 5.0 3.1 3.5 4.0 4.7 1.0 5.1 ± 2.6 303.1 313.8 300.1 317.5 374.6 357.2 314.0 282.4 385.4 370.4 342.4 255.3 323.3

E


Article

The Journal of Physical Chemistry A Table 2. continued amino acid Glu Phe Tyr Trp Pro averages Gly Ala Ser Cis Met Asn Gln His Glu Asp Phe Tyr Trp average His Trp average Asn Gln average Asn Gln average Asn Gln average Pro a

vibration CO CO CO CO CO NH2 NH2 NH2 NH2 NH2 NH2 NH2 NH2 NH2 NH2 NH2 NH2 NH2

str str str str str

bend bend bend bend bend bend bend bend bend bend bend bend bend

N−H unsat str N−H unsat str NH2 AS amide NH2 AS amide NH2 SS amide NH2 SS amide NH2 bend amide NH2 bend amide N−H sat str.

C

CT

DP

2C·CT

2C·DP

2CT·DP

total

281.4 336.3 336.8 334.9 337.7 318.8 ± 28.1 222.4 229.2 241.2 217.4 236.6 296.0 213.2 182.6 185.0 268.1 187.1 184.2 177.9 218.5 ± 36.2 219.7 213.5 216.6 292.3 288.3 290.3 115.9 113.5 114.7 278.1 297.4 287.8 143.7

283.3 348.7 342.8 355.6 394.3 341.6 ± 74.7 169.2 180.5 149.7 171.8 211.5 201.7 162.1 125.1 116.7 189.8 115.3 123.9 101.4 155.3 ± 36.0 29.2 34.4 31.8 47.9 51.5 49.7 23.1 24.9 24.0 134.0 134.9 134.4 59.5

305.3 361.3 363.0 332.8 361.5 369.7 ± 85.3 38.1 42.8 17.2 18.3 50.4 63.1 29.3 8.8 6.8 57.2 7.2 7.8 10.1 27.5 ± 20.6 1.9 0.4 1.1 13.8 13.2 13.5 2.5 1.77 2.1 24.5 26.0 25.3 10.5

−494.3 −548.9 −544.9 −606.6 −639.5 −560.6 ± 87.0 −381.1 −401.6 −368.9 −377.8 −441.4 −481.1 −368.5 −292.0 −283.5 −443.5 −282.9 −291.2 −258.0 −359.3 ± 72.1 −159.7 −168.2 −164.0 −236.7 −243.7 −240.2 −101.0 −103.9 −102.5 −384.1 −397.6 −390.8 −181.3

487.6 564.4 571.0 522.9 572.0 556.8 ± 88.3 181.1 194.5 95.0 111.0 212.0 269.8 157.7 70.0 61.7 240.8 61.2 65.2 69.4 137.6 ± 75.2 −40.6 −17.8 −29.2 −126.5 −122.7 −124.6 14.7 10.9 12.8 164.5 175.5 170.0 −55.6

−585.8 −708.1 −701.5 −677.0 −749.5 −705.4 ± 155.6 −160.6 −175.7 −87.7 −106.0 −205.9 −224.4 −136.9 −63.1 −53.6 −207.3 −52.9 −59.5 −60.3 −122.6 ± 65.5 14.6 6.7 10.6 51.2 51.8 51.5 −9.3 −7.6 −8.4 −114.1 −118.2 −116.1 28.2

277.6 353.6 367.3 262.6 276.5 320.9 ± 40.9 69.2 69.8 46.5 34.7 63.3 125.1 57.1 31.5 33.0 105.0 35.0 30.3 40.5 57.0 ± 29.7 65.1 69.0 67.1 42.1 38.3 40.2 45.8 39.6 42.7 102.9 118.1 110.5 5.0

AS = antisymmetric stretch. bSS = Symmetric stretch.

Figure 2. Magnitude of the charge, charge transfer, and dipolar polarization contributions for each type of vibration of the 14 calibration amino acids, in km mol−1. AS = antisymmetric stretch and SS = symmetric stretch.

It is very noticeable that the points belonging to the CO stretching and NH2 bending groups are more dispersed compared to the other groups, that is, they are the least transferable vibrations among the calibration set amino acids.

The high dispersion of the CO stretching points in Figure 3 does not necessarily rule out the successful transfer of the C O group intensity to other molecules. The polarization contribution standard deviation of 85.3 km mol−1 is about F


Article


Figure 3. 3D graph of the charge, charge transfer, and dipolar polarization contributions for O−H, NH2, and CO vibrations of the 14 calibration amino acids, in km mol−1. AS = antisymmetric stretch and SS = symmetric stretch.

to one another. Interestingly enough, the O−H stretches of acidic, alcoholic, and phenolic hydroxyls all follow the same pattern. NH2 Antisymmetric Stretches. The NH2 antisymmetric stretching intensities are small, with an average of 12.6 km mol−1. Scheme 2 shows the polarities of their CCTDP dipole

double the standard deviation of the total CO group intensity. Furthermore, the CO points could be divided into subgroups. All five outliers in Figure 3 contain two carbonyl bonds; the subgroup on the right contains all of the calibration amino acids with ring substituents, and the simpler amino acids are concentrated in the group on the left. O−H Stretching Vibration. The O−H stretching vibrational intensities form a compact group in Figure 3 that is an indication of good transferability within the calibration set amino acids. The O−H stretching group is dominated by the charge (C) and charge transfer (CT) contributions as they have roughly the same magnitude and are much larger than the polarization parcel. The charge−charge transfer coupling term is negative, indicating that their dipole moment derivative contributions have opposite signs. The sum of these two contributions and their coupling term is always small. For the average O−H stretching values in Table 2, this sum is 18.8 km mol−1. The charge and dipolar polarization coupling term is positive, indicating that both contributions have the same change in polarity for the O−H stretch. Therefore, even though the dipolar polarization contribution is small, its coupling with the charge contribution is not, and their sum results in a large net value, 173.3 km mol−1, for the average O−H group values. All of the charge transfer−dipolar polarization couplings are negative (average of −125.0 km mol−1), concurring with CCTCP model expectations, and its sum with the above two values gives 67.1 km mol−1, agreeing within round-off error with the total O−H group average in Table 2. Scheme 1 illustrates how the polarity changes of these contributions relate

Scheme 2. Directions of the Charge, Charge Transfer, and Dipolar Polarization Contributions to the Dipole Moment Derivative Vectors of the NH2 Antisymmetric Stretches of the Calibration Amino Acids

moment derivative contributions. The charge contribution to the intensity is much larger than the total intensity but is approximately canceled by the negative charge−charge transfer coupling term, giving small negative net values. The other contributions sum to give small positive values. As such, the total intensities are all below 25 km mol−1. There are two obvious divergent antisymmetric NH2 intensities: the asparagine (42.1 km.mol−1) and glutamine (38.3 km.mol−1) amide NH2 stretching vibrations. Large charge contributions that are almost 100 km mol−1 greater than those of the other antisymmetric NH2 charge contributions are the principal reason for this. These amides of course have their NH2 group directly bonded to a carbonyl. As a result, the nitrogen atomic charges in asparagine and glutamine are −1.15 and −1.13 e compared with smaller nitrogen charges for isolated amine groups like the one in glycine for which nitrogen has a −0.96 e net charge. In fact, the more negative charges of the nitrogen atom will cause all of their vibrations to have larger charge contributions to the CCTDP model, as will be discussed in more detail later.

Scheme 1. Directions of the Charge, Charge Transfer, and Dipolar Polarization Contributions to the Dipole Moment Derivative Vectors of the O−H Stretches of the Calibration Set Amino Acids

G


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The Journal of Physical Chemistry A NH2 Symmetric Stretches. The total symmetric NH2 stretching intensities are calculated to be about half or even less than their corresponding antisymmetric intensities. The average symmetric intensity value is 5.1 km mol−1, whereas the antisymmetric one is 12.6 km mol−1. The signs of both NH2 stretching CCTDP contributions are the same, and this is also evident in Scheme 3.

Scheme 4. Directions of the Charge, Charge Transfer, And Dipolar Polarization Contributions to the Dipole Moment Derivative Vectors of the CO Stretches of the Calibration Amino Acids

Scheme 3. Directions of the Charge, Charge Transfer, and Dipolar Polarization Contributions to the Dipole Moment Derivative Vectors of the NH2 Symmetric Stretches of the Calibration Amino Acids

completely canceled by their coupling terms having a net 5.9 km mol−1 contribution to the total intensity. Also, the charge− charge transfer and charge−dipolar polarization average contributions sum to only −3.8 km mol−1. Therefore, the intensities of the carbonyl stretches are largely determined by their charge contributions. In fact, the charge contribution average value for the amino acids, 318.8 km mol−1, is almost the same as the average total intensity of 320.9 km mol−1. Even though spectra of peptides and amino acids have been measured in aqueous media,31 gas-phase experimental data are much scarcer and are not available for the vibrations presented in this paper. However, one could expect that the intensity of the CO stretches of the amino acids in the calibration group should be quite similar to those of formic or acetic acid. Fortunately, these intensities have been measured by modern FTIR equipment in the gas phase by PNNL32 (Pacific Northwest National Laboratory), resulting in total intensities of 345.9 and 307.3 km mol−1 for the CO stretching vibrations of formic and acetic acid, respectively. This is close to the average 320.0 km mol−1 intensity value calculated for the calibration amino acids. This provides evidence as to the quality of the results in Table 2, which supports the interpretation presented in this paper. The CO stretches have a central role in our results and will also be discussed in more detail later in the text. NH2 Bends. The NH2 bending intensities form a more diverse group than the stretching intensity groups, as can be seen in Figure 3. This is mostly due to two types of bending vibrations, amide NH2 bends and more isolated NH2 bends that are removed from the carbonyl group by at least one carbon−carbon bond. The NH2 amide bending intensities of asparagine and glutamine exceed 100 km mol−1, whereas the other NH2 bends have intensities averaging 57.0 km mol−1. This difference is mostly a result of the higher charge contribution (287.8 km mol−1) for the amide NH2 bending intensities relative to the others. As stated previously concerning the antisymmetric stretching vibration, the nitrogen equilibrium charge is almost 0.2 e more negative in the amides. The standard deviations of the charge transfer contributions for this bend are about three to four times the sizes of those for the symmetric and antisymmetric stretches. In contrast to the stretching modes, the bending vibrations follow the CCTCP model and have a large negative charge transfer−dipolar polarization contribution. Scheme 5 illustrates how these contributions are related to each other. N−H Stretches. There are only three N−H stretching vibrations in the amino acid calibration set. Two of these, tryptophan and histidine, involve NH stretches for which the nitrogen atom occupies a position in an unsaturated fivemember ring. These have an average intensity of 67.1 km mol−1. The proline molecule has an N−H stretching vibration of a saturated five-member ring and has a much lower intensity,

The largest difference in the CCTDP contributions of these two group vibrations is found for the equilibrium charge. The average symmetric charge contribution is 103.8 km mol−1, which is also about half of the antisymmetric one, 198.1 km mol−1. Both of these contributions depend on the same equilibrium charge. Furthermore, the atomic displacements of the hydrogen atoms will have very similar amplitudes, but their projections on the directions of net dipole moment change will be different. The symmetric stretch will make a projection of α/ 2°, whereas the antisymmetric one will be [90° − (α/2)], where α is the H−N−H angle. Now, this angle is about 107°, and the cos(α/2)/cos(90° − (α/2)) ratio is 0.74. The ratio of the square roots of the average symmetric and antisymmetric charge contributions to the intensities in Table 2 is (103.8/ 198.1)1/2 = 0.72. The three largest CCTDP contributions depend on the equilibrium charge dipole moment derivative contribution; therefore, it is not surprising that the total NH2 symmetric intensities are systematically calculated to be smaller than the antisymmetric intensities. Again, two intensities stand out: the asparagine (45.8 km mol−1) and glutamine (39.6 km mol−1) amide stretches, which are approximately 10 times stronger than the other NH2 symmetric stretching intensities. Although the signs of the amide CCTDP contributions of the antisymmetric vibrations for these molecules are the same as those for the other antisymmetric stretches in Table 2, the signs for the amide charge−dipolar polarization and charge transfer−dipolar polarization couplings are opposite to those of the other NH2 symmetric vibrations. CO Stretches. The carbonyl stretching group forms the most diverse group of points in Figure 3 and has large and equally important charge, charge transfer, and polarization contributions. The CO stretching vibrations obey the CCTCP model, as shown in Scheme 4. The sum of average charge transfer and dipolar polarization terms is almost H


Article


chosen as it is the simplest peptide available, and trialanine was selected owing to its reported diverse descriptions by different force fields.6 The MIF-1 is a peptide fragment from oxytocin that behaves as a hormone acting as an antidepressant34 and antiparkinsonian. O−H Stretching Vibrations. The predicted DAC intensities for the O−H stretches are quite transferable from the calibration group to the target peptides. The predicted value of 69.1 km mol−1 is consistently a little short of the DFT peptide intensities of 91.4 and 84.3 km mol−1 for glycylglycine and trialanine, respectively, for a rms error of 19.1 km mol−1. NH2 Antisymmetric and Symmetric Stretches. The transferred DAC values of 12.7 km mol−1 for the antisymmetric stretch are in excellent agreement with the DFT value of 11.9 km mol−1 for glycylglycine and 11.0 km mol−1 for trialanine. The small symmetric stretching transferred value of 4.9 km mol−1 is about half of the DFT calculated values of 8.7 km mol−1 for glycylglycine and 10.8 km mol−1 for trialanine. Amide NH2 stretching intensities are transferred to the MIF-1 peptide. The DFT antisymmetric mode intensity is 53.9 km mol−1, and the transferred value is close, 40.6 km mol−1. The symmetric transferred value of 42.3 km mol−1 is also close to the DFT value, 61.1 km mol−1. Overall, these six NH2 symmetric and antisymmetric intensities in the peptides are well reproduced by the amino acid calibration set intensities, having a rms error of 9.9 km mol−1. N−H Peptide Stretches. One NH stretching vibration in each peptide is α to a carbonyl group having a transference value of 66.9 km mol−1. This value is very close to the N−H stretching intensity value of 76.9 km mol−1 in glycylglycine and also to one of the N−H intensities in MIF-1, 65.1 km mol−1. However, it underestimates the stretching intensity of 138.6 km mol−1 for the N−H group on the left side of MIF-1 and badly overestimates the 26.4 and 14.5 km mol−1 DFT intensities in trialanine for which the N−H group is in an α position to both a carbonyl and a CCH3 group. None of the calibration set amino acids have this type of structure; therefore, they are not directly transferable to trialanine. CO Stretches. Glycylglycine has two CO stretching intensities with DFT values of 260.8 and 277.7 km mol−1, in excellent agreement with the 298.2 km mol−1 transferred value. The two CO trialanine DFT intensities, 404.4 and 369.8 km mol−1, are somewhat higher. The MIF-1 has three CO stretches: a high-frequency one (1776 cm−1−293.5 km mol−1) that actually is very well modeled from the calibration amino acids and two almost degenerate low-frequency bands (1730 cm−1, 228.8 km mol−1 and 1710 cm−1, 453.0 km mol−1), which deviate from the predicted value (298.2 km mol−1) quite a bit. One of these vibrations overestimates the predicted value, and the other underestimates it; therefore, the sum of the two values tends to cancel these deviations. The average value of these two vibrations, 341.4 km mol−1, is not that much higher than the average transferred value of 298.2 km mol−1. Examining the L matrix elements of these two vibrations indicates that these vibrations are correlated as the two carbonyls move simultaneously in both normal coordinates. Figure 4 illustrates their relative displacements in MIF-1. In the lower-frequency vibrational mode (1710 cm−1), the carbonyl groups vibrate in the same phase, while for the higherfrequency (1730 cm−1) one, they vibrate with opposite phases. Due to the geometry of this molecule, the dipole moment derivatives of each carbonyl add up for the lower-frequency vibration, resulting in the stronger intensity of 453.0 km mol−1,

Scheme 5. Directions of the Charge, Charge Transfer, and Dipolar Polarization Contributions to the Dipole Moment Derivative Vectors of the NH2 Bend of the Calibration Amino Acids

5.0 km mol−1, mostly owing to a substantially smaller equilibrium charge contribution. Miller et al.33 have also reported several weak N−H stretching intensities for dimethylamine and pyrrole, especially when describing the saturated stretches, which is consistent with the intensities reported here. Resonance structures for the unsaturated ring result in an acidic hydrogen in contrast to the more neutral hydrogen bonded to nitrogen in the saturated ring, accounting for this intensity difference. The DFT results support this interpretation as the hydrogen bonded to nitrogen is more positively charged for the unsaturated ring compound. All of these N−H stretches follow the polarity changes shown in Scheme 6. Scheme 6. Directions of the Charge, Charge Transfer, and Dipolar Polarization Contributions to the Dipole Moment Derivative Vectors of the N−H Stretch of the Calibration Amino Acids

Using Dynamic Atomic Contributions as Building Blocks. The DACs to the intensities calculated for the above characteristic vibrational groups are presented in Table 3. Note the similarities of the DACs for the atoms of characteristic group intensities. Using these values and the group classification in Figure 3, an average of the points belonging to each atom within a vibrational group was taken as the parametrized DACs. These results are shown in Table 3. With these averages, one can determine an average characteristic group intensity, for example, (H) hydroxyl + (O) hydroxyl, 57.9 + 11.2 = 69.1 km mol−1 for the O−H stretch. These characteristic group values can be seen in Table 3. It is important to highlight that our assignment of atomic groups is not arbitrary at all but based on the separation of the vibrations into groups according to Figure 3. This means that the atoms are classified based on CCTDP behavior such as charge transfer and polarization and in this way can be called characteristic vibrations. Assuming the hypothesis upon which this work is based, that is, the DAC contributions of the respective characteristic vibrations are transferrable, we can potentially use these average values as building blocks to make intensity estimates for larger molecules. Initially to test the use of these building blocks, we transferred our average values in order to predict the infrared spectra of three small peptides: glycylglycine, trialanine, and the melanocyte-inhibiting factor (MIF-1). Glycylglycine was I


J

a

199.8

194.4

11.2 16.6

92.3

187.2

2.5 3.7

2.7 7.5

55.8 55.2

10.0 8.2

Ser

8.3 12.6

99.8

199.6

2.7 3.8

2.7 7.7

66.6

11.6

Cis

11.8 20.2

119.4

242.7

1.9 2.3

2.9 5.0

67.5

11.0

Met

4.3 10.0 5.0 18.8 1.7 0.9 14.9 15.2 231.6 203.4 114.0 97.0 14.3 38.3 40.8 24.5

61.2

12.2

Asn

2.0 3.6 5.3 16.8 0.91 2.1 13.2 13.0 182.3 241.7 88.3 114.3 7.1 19.3 43.6 29.4

54.7

9.4

Gln

These molecules have two groups. bAS = antisymmetric stretch. cSS = Symmetric stretch.

11.9 24.5

1.2 2

1.1 2.1

10.0 24.7

2.4 3.3

2.6 4.9

99.5

59.8

67.6

94.4

10.4

11.1

(O) hydroxyl (O) hydroxyla (O) hydroxyl phenol (H) hydroxyl (H) hydroxyla (H) hydroxyl phenol (H) N−H unsat str (N) N−H unsat str (N) N−H sat str (H) N−H sat str (N) NH2 ASb (H) NH2 ASb (N) NH2 AS amide (H) NH2 AS amide (N) NH2 SSc (H) NH2 SSc (N) NH2 SS amide (H) NH2 SS amide (C) carbonyl (C) carbonyla (O) carbonyl (O) carbonyla (N) NH2 bend (H) NH2 bend (N) NH2 bend amide (H) NH2 bend amide

Ala

Gly

atomic type

5.9 12.9

116.0

233.7

1.4 0.9

1.3 3.3

51.3 13.7

55.5

10.7

His

191.3 156.5 94.7 73.6 14.5 36.5

1.7 0.9

3.1 10.7

65.9 56.4

11.2 10.8

Asp

175.4 170.6 85.5 87.1 6.2 13.5

1.24 0.9

1.32 3.1

60.3 53.5

11.0 9.8

Glu

6.4 14.3

111.1

223.8

1.5 1.2

1.1 3.6

54.7

11.3

Phe

6.0 12.2

116.7

229.2

1.7 1.5

1.3 3.8

7.6 18.6

80.7

162.7

0.5 0.2

1.8 1.2

55.9 12.8

61.4

10.0 48.3 45.3

11.2

Trp

10.8

Tyr

86.8

170.7

1.5 3.8

52.4

10.2

Pro

Table 3. Values for Atomic Types (km mol−1) for the Description of the Characteristic Vibrations of the 14 Calibration Amino Acids

(N) (H) (N) (H)

NH2 NH2 NH2 NH2

bend bend bend amide bend amide

(O) carbonyl

(H) N−H unsat str (N) N−H unsat str (N) N−H sat str (H) N−H sat str (N) NH2 ASb (H) NH2 ASb (N) NH2 AS amide (H) NH2 AS amide (N) NH2 SSc (H) NH2 SSc (N) NH2 SS amide (H) NH2 SS amide (C) carbonyl

(H) hydroxyl

(O) hydroxyl

atom type

9.3 20.3 42.2 26.9

98.4

53.6 13.3 1.5 3.8 2.3 5.2 5.2 17.8 1.5 1.7 14.1 14.1 199.8

57.9

11.2

average value

The Journal of Physical Chemistry A Article


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NH2 Bends. The DFT NH2 bending intensities for the three peptides are all surprisingly close to one another even though MIF-1 has an amide NH2 group and the others do not. The MIF-1 intensity of 129.0 km mol−1 is close to the 96.0 km mol−1 DAC estimate from the amide groups of asparagine and glutamine. However, the transferred value of 49.9 km mol−1 for the nonamide NH2 bends is much lower than the 106.8 and 131.6 km mol−1 DFT values for glycylglycine and trialanine. The mechanical weights of these vibrations are practically the same in both the amino acids and the peptides, as are the AIM charges and dipoles. Therefore, the derivatives of the atomic charge and dipole must be responsible for the observed difference between the predicted and calculated intensities. A CCTDP analysis was carried out for glycylglycine, confirming this conclusion as its charge transfer and dipolar polarization contributions are substantially larger than those for most of the amino acids. It should be noted that only asparagine and aspartic acid of the calibration amino acids have two carbonyl groups within three C−C bonds of one another, as do all three peptide molecules. These are the only calibration amino acids with charge transfer and polarization contributions similar to those of glycylglycine. Average values of their DACs are 37.4 km mol−1 for hydrogen and 14.4 km mol−1 for nitrogen. Their NH2 transferred value of 89.2 km mol−1 is in good agreement with the glycylglycine and trialanine DFT intensities.

Figure 4. Mechanical weights of the oxygen atom of each carbonyl and the total oxygen mechanical weight (e2 amu−1) to the total dipole moment derivatives for the two lower-frequency vibrations in MIF-1. R1 = CH2−CO−NH2, R2 = CH−CH−(CH3)2, and R3 = pyrrolidine.

while for the higher-frequency normal coordinate, the dipole moment derivatives are partially canceled, resulting in a weaker intensity of 228.8 km mol−1. This effect becomes quite clear in Figure 4 as the displacements are accompanied by the mechanical weights35 of the oxygen atoms of the carbonyl atoms, ∑σ=x,y,z (∂νj)/(∂Qk)2, of eqs 3 and 4. The mechanical weight quantifies how much an atom is displaced in a vibration as a high value indicates a large motion. The values presented in Figure 4 represent the net displacement of each oxygen atom in each carbonyl vibration and their resulting movement for the represented normal coordinates. The ratio of this total movement, 0.579 e2 amu−1/0.274 e2 amu−1 is 2.1, close to the ratio between the two intensities (453.0 km mol−1/228.8 km mol−1), 2.0. The above analysis suggests that superior intensity estimates could be obtained from DAC dipole moment derivatives rather than the intensity contributions as the derivatives contain directional information lacking for the intensity parameters.

■

CONCLUSIONS Figure 5a−c shows theoretical spectra of glycylglycine, trialanine, and MIF-1, respectively. In each individual image, there is a DFT spectrum calculated by Gaussian09 and a

Figure 5. Analytical DFT and DAC transference approximation infrared spectra of (a) glycylglycine, (b) trialanine, and (c) MIF-1. The red lines represent the DFT intensities calculated analytically with Gaussian09 and the black lines the transferred DAC intensities from the 14 calibration amino acids. The spectra were simulated by the GABEDIT program with a Lorentzian spectral line shape at 300 K using a 20 cm−1 half width. All other fitting functions parameters were chosen by default. K


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During the 1970s, an empirical procedure to quantitatively estimate the infrared intensities of small molecules was proposed by Person and co-workers.37,38 The fluorine atomic polar tensors (APTs) obtained from the experimental intensities of the CH3F molecule were transferred to all of the terminal atoms of SF6, UF6, and the UF5 intermediate species. The APTs of the central atoms were determined by the tensor neutrality constraint. The intensity estimates determined from this transference procedure were fundamental in determining the experimental UF5 geometry. However, the tensor neutrality constraint can only be used to determine one APT; therefore, this method is not applicable to molecules with more than one nonterminal atom. DAC transference is not limited to theoretically calculated parameters. It can be obtained from polar tensors determined from experimental intensities and normal coordinates calculated from experimental frequencies. Indeed, the transference of the DAC intensity and dipole moment derivative parameters appears to provide a promising path to infrared intensity determinations.

predicted spectrum from the DAC transferred values in Table 4 through the Gabedit program.36 Table 4. DFT Frequencies (cm−1), DFT Analytical Intensities, and Transferred DAC Intensities (km mol−1) for the Test Polypeptides vibration O−H str N−H unsat str NH2 ASa NH2 SSb CO str CO str NH2 bend O−H str NH2 AS N−H unsat str N−H unsat str NH2 SS CO str CO str CO str NH2 bend NH2 AS amide NH2 SS amide N−H unsat str N−H sat str N−H unsat str CO str CO str CO str NH2 bend amide a

DFT frequency

DFT intensity

Glycylglycine 3759 3602 3591 3501 1812 1744 1639 Trialanine 3758 3585 3577 3564 3485 1819 1720 1709 1673 MIF-1 3718 3590 3586 3558 3530 1776 1730 1710 1626

transferred DAC

91.4 76.9 11.9 8.7 260.8 277.7 106.8

69.1 66.9 12.7 4.9 298.2 298.2 49.9

84.3 11.0 26.4 14.5 10.8 404.4 369.8 339.3 131.6

69.1 12.7 66.9 66.9 4.9 298.2 298.2 298.2 49.9

53.9 61.1 65.1 8.5 138.6 293.5 228.8 453.0 129.0

40.8 42.3 66.9 5.3 66.9 298.2 298.2 298.2 96.0

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: (19) 37883106. Fax: (19) 37883023. Author Contributions ‡

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Arnaldo F. Silva, Leonardo J. Duarte, and Roy E. Bruns contributed equally. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS A.F.S. thanks FAPESP (Fundaçaõ de Amparo à Pesquisa do Estado de São Paulo, Grant 2014/21241-9) for a postdoc research fellowship, and R.E.B. thanks CNPq for a research fellowship. We are also grateful to FAPESP for partial financial support of this work (Grant 09/09678-4). L.J.D. thanks FAPESP (Fundaçaõ de Amparo à Pesquisa do Estado de São Paulo, Grant 2016/07411-4) for an undergraduate research scholarship.

AS = antisymmetric stretch. bSS = Symmetric stretch.

Note that only the intensities were obtained by these two different methods as the frequencies used in both spectra are also obtained by DFT. All of the carbonyl intensities are nicely reproduced by the DAC transferred intensity parameters. Even though the individual 1710 and 1730 cm−1 transferred values for MIF-1 showed large discrepancies, they are not apparent in the overlapped bands. The underestimated transferred NH 2 bending intensity of glycylglycine is clearly visible but not very apparent for the trialanine and MIF-1 overlapped bands. The OH, NH2, and NH stretching simulated bands match pretty well except for the overlapped NH2 and NH stretching bands of trialanine. It is important to highlight that this is the first time a CCTDP analysis was carried out for peptides and that MIF-1 is a rather large molecule, containing 34 atoms. The DAC transference results can be improved in two important ways. Intensities are proportional to squares of dipole moment derivatives. Better intensity estimates will be obtained by transferring vector parameters rather than scalars as done here. Of course, this would be a substantially more complex procedure but could be worth the effort. Also, calibration sets can be refined to obtain better results. Here, the calibration set was restricted to amino acids as they form peptides.

■

REFERENCES

(1) Fileti, E. E.; Chaban, V. V. The scaled-charge additive force field for amino acid based ionic liquids. Chem. Phys. Lett. 2014, 616-617, 205−211. (2) Miller, M. S.; Lay, W. K.; Elcock, A. H. J. Osmotic Pressure simulations of amino acids and peptides highlight potential routes to protein force field parameterization. J. Phys. Chem. B 2016, 120, 8217. (3) Cheng, A. C.; Frankel, A. D. Ab initio interaction energies of hydrogen-bonded amino acid side chain[bond]nucleic acid base interactions. J. Am. Chem. Soc. 2004, 126, 434−435. (4) Tummanapelli, A. K.; Vasudevan, S. Ab initio molecular dynamics simulations of amino acids in aqueous solutions: Estimating pKa values from metadynamics sampling. J. Phys. Chem. B 2015, 119, 12249− 12255. (5) Chang, J.; Lenhoff, A. M.; Sandler, S. I. Solvation free energy of amino acids and side-chain analogues. J. Phys. Chem. B 2007, 111, 2098−2106. (6) Mu, Y.; Kosov, D. S.; Stock, G. Conformational dynamics of trialanine in water. 2. Comparison of AMBER, CHARMM, GROMOS, and OPLS force fields to NMR and infrared experiments. J. Phys. Chem. B 2003, 107, 5064−5073.

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QTAIM-Based Characteristic Group Infrared Intensities of Amino Acids

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