Quantum Theory of Atoms in Molecules ChargeâCharge Transfer

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Quantum Theory of Atoms in Molecules Charge-Charge TransferDipolar Polarization Classification of Infrared Intensities Leonardo José Duarte, Wagner Eduardo Richter, Arnaldo F. Silva, and Roy Edward Bruns J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b08031 • Publication Date (Web): 02 Oct 2017 Downloaded from http://pubs.acs.org on October 4, 2017

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The Journal of Physical Chemistry

Quantum Theory of Atoms in Molecules Charge-charge Transfer-dipolar Polarization Classification of Infrared Intensities Leonardo J. Duarte1, Wagner E. Richter2,Arnaldo F. Silva3and Roy E. Bruns*1 1

Chemistry Institute, University of Campinas, CP 6154, Campinas, SP, Brazil. 13.083– 970. 2

Department of Chemical Engineering, Technological Federal University of Parana, Ponta Grossa, PR, 84016-210 and 3

Manchester Institute of Biotechnology, University of Manchester, 131 Princess Street, Manchester M1 7DN, Great Britain

*

Corresponding author:

Prof. Dr. Roy Edward Bruns - [email protected]

Abstract Fundamental infrared vibrational transition intensities of gas-phase molecules are sensitive probes of changes in electronic structure accompanying small molecular distortions. Models containing charge, charge transfer and dipolar polarization effects are necessary for a successful classification of the C-H, C-F and C-Cl stretching and bending intensities. C-H stretching and in-plane bending vibrations involving sp3 carbon atoms have small equilibrium charge contributions and are accurately modeled by the charge transfer- counterpolarization contribution and its interaction with equilibrium charge movement. Large C-F and C=O stretching intensities have dominant equilibrium charge movement contributions compared to their charge transfer-dipolar polarization ones and are accurately estimated by equilibrium charge and the interaction contribution. The C-F and C-Cl bending modes have charge and charge transfer-dipolar polarization contribution sums that are of similar size but opposite sign to their interaction values resulting in small intensities. Experimental in-plane C-H bends have 1 ACS Paragon Plus Environment


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small average intensities of 12.6±10.4 km mol-1 owing to negligible charge contributions and charge transfer-counterpolarization cancellations, whereas their average out-of-plane experimental intensities are much larger, 65.7±20.0 km mol-1,as charge transfer is zero and only dipolar polarization takes place. The C-F bending intensities have large charge contributions but very small intensities. Their average experimental out-of-plane intensity of 9.9±12.6 km mol-1 arises from the cancellation of large charge contributions by dipolar polarization contributions. The experimental average in-plane C-F bending intensities, 5.8±7.3 km mol-1 is also small owing to charge and charge transfer-counterpolarization sums being cancelled by their interaction contributions. Models containing only atomic charges and their fluxes are incapable of describing electronic structure changes for simple molecular distortions that are of interest in classifying infrared intensities. One can expect dipolar polarization effects to also be important for larger distortions of chemical interest.

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1. Introduction Infrared fundamental intensities of gas phase molecules provide a wealth of experimental data directly related to changes in electronic structures as molecules are distorted from their equilibrium geometries. Infrared bands of all the normal modes of about 60 molecules have been measured with relatively low resolution spectrometers and reported in the literature some time ago1. Recently, using high resolution spectrometers, the Pacific Northwest National Laboratory has published a library of gasphased infrared spectra for about 500 molecules2. Although infrared intensities arise from small amplitude vibrations their information could be relevant for larger molecular distortions. These data could then be used to improve force fields attempting to model electronic structure changes for molecular distortions of chemical interest. As such a characterization of electronic structure changes for different types of molecular vibrations would be useful. A majority of the attempts towards this end have been made using the Equilibrium

Charge–Charge

Flux

(ECCF)3,

Charge–Charge

Flux–Overlap

(CCFO)4andModified Charge–Charge Flux–Overlap (CCFOM) models5. In the last ten years a Charge–Charge Transfer–Dipolar Polarization (CCTDP)6 model, previously called Charge-Charge Flux-Dipole Flux (CCFDF), was developed within the physics of the Quantum Theory of Atoms in Molecules (QTAIM)7. The main difference between this model and previous ones is the inclusion of atomic dipoles in addition to atomic charges to account for polarization effects. Atomic dipoles along with atomic charges in electronic structure models have been shown to be necessary to quantitatively account for the CH stretching and bending mode infrared intensities in hydrocarbon molecules as well as the ground state and excited states of CO8and 9. These calculated intensities are found to be predominantly determined by intramolecular atomic charge transfer and changes in atomic dipoles to account for polarization effects as the atoms are displaced from their equilibrium positions, i.e. charge flux and dipole flux in the CCFDF terminology. Displacement of static atomic charges plays a secondary role in determining the intensities of the hydrocarbons. For almost all CH stretching and bending modes, except the perpendicular and out-of-plane bending vibrations of linear and planar molecules, charge transfer (CT) in one direction is compensated by dipolar polarization (DP) in the opposite direction.



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Even though this cancelling phenomenon occurs for most hydrocarbon vibrations their net dipole moment changes are substantially larger than the ones from equilibrium charge (C) movement. Counterpolarization does not take place for the out-of-plane bending vibrations of planar molecules and perpendicular vibrations of linear molecules for which the charge transfer contribution is zero.10,11. For these vibrations charge and dipolar polarization are sufficient to describe the electronic structure changes taking place. In this paper we demonstrate the utility of the QTAIM charge-charge transferdipolar polarization model for characterizing different kinds of electronic structure changes for different types of vibrations. This is done applying the model to a group of 29 molecules including the difluoro-and dichloroethylenes, the fluorochloromethanes and the X2CY (X=F,Cl;Y=O,S) molecules whose theoretical intensities have already been reported by our group12. Five hydrocarbons, methane, ethylene, acetylene, cyclopropane and allene previously investigated8 using the CCTDP model are included for comparison purposes. In all 152 vibrations are investigated. Intensities of all the active normal modes of these molecules have been measured and where possible accuracy and precision have been estimated using measurements on isotopomers containing deuterium atoms instead of hydrogen. Atomic polar tensors (APT) have been determined13 from their experimental intensities and frequencies. These values provide references for the quality of the quantum chemical results that are used to obtain the CCTDP parameters.

2. Theoretical background: Charge-charge transfer-dipolar polarization contributions to intensities. The integrated infrared fundamental intensities are proportional to the squares of the dipole moment derivatives with respect to the normal coordinates.14

= = 1 … .3 − 6. (1) 3 The dipole moment derivative Cartesian components can be partitioned into three contributions12 owing to equilibrium charge (C), charge transfer (CT) and dipolar polarization (DP) contributions, 4 ACS Paragon Plus Environment

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= + + = !, #, $ . (2) () () () The first term can be interpreted as the contribution to the dipole moment derivative owing to the movements of static equilibrium atomic charges. The second and third terms account for contributions from intramolecular atomic charge transfer and dipolar polarization. In Ref. 12 the CT and DP contributions were called charge flux and dipole flux, respectively. As such the fundamental intensities, for dipole moment changes occurring along only one Cartesian axis, can be expressed as:   Nπ  ∂pσ  A j =   3c 2  ∂Q j 

 ∂p + 2 σ  ∂Q j 

2

   +  ∂pσ    (C )  ∂Q j

  ∂pσ     ∂Q j  (C ) 

2

  ∂p  + σ    (CT )  ∂Q j

  ∂p  + 2 σ    (DP )  ∂Q j

2

  ∂p  + 2 σ   ∂Q j  (DP ) 

  ∂pσ      (CT )  ∂Q j

  ∂pσ     ∂Q j  (C ) 

    (CT )

   .(3)     (DP ) 

The first three terms are charge, charge transfer and dipolar polarization contributions to the intensities, whereas the last three terms correspond to interactions between these dipole moment derivative contributions. One can combine the terms with the differential changes in the electronic density into a charge transfer-dipolar polarization contribution  ∂p A j ,(CTDP ) =  σ  ∂Q j 

2

  ∂p  + σ    (CT )  ∂Q j

2

  ∂p  + 2 σ   ∂Q j  ( DP ) 

  ∂pσ      (CT )  ∂Q j

  . (4)   (DP )

Each of the first two terms have large positive values and often their sum is almost completely cancelled by the large negative values of the charge transfer-dipolar polarization interaction. Often these much smaller net values are seen to be the result of atomic charge transfer within the molecule that is accompanied by dipolar polarizations in opposite directions to one another. The two interaction terms involving the equilibrium charge factor can be given as:



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 ∂p A j , (CxCT , DP ) = 2 σ  ∂Q j 

   ∂pσ      ∂Q j  (C )  

  ∂p  + σ    (CT )  ∂Q j

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     (5)   (DP ) 

and interpreted as an interaction between equilibrium atomic charge movements and the sum of differential changes to the electronic densities of these atoms. So for the jth normal mode

A j = A j ,(C ) + A j ,(CTDP ) + A j ,(CxCT ,DP )

(6)

where A(C ) , A(CTDP) and A(CxCT, DP) are the charge, charge-transfer-dipolar polarization and the interaction contribution. Of course these equations are valid for vibrations with dipole moment changes along more than one Cartesian axis.

3. Calculations Almost all of the CCTDP parameters reported here were obtained from the charge, charge flux and dipole flux results reported in Refs. 6 and 10. The values had been calculated using the GAUSSIAN0315, PLACZEK16 and MORPHY9817 programs. The QCISD electron correlation treatment level and the cc-pVTZ, 6-31G(2d,2p) and 631G(3d,3p) basis sets were used for almost all molecules. The CCl2CS,CCl2CO and F2CS molecules were treated with the 4-31G and Dunning/Huzinaga full double zeta (D95) basis sets in ref 12 to reduce computational cost. Furthermore our CCTDP contributions were shown to depend heavily on correlation methods or basis set variations (ref 8). The CCTDP parameters for the benzene and hexafluorobenzene vibrations, not given in Refs. 6 and 10, have been included here18.All the calculated intensities reproduce the experimental intensities by 11.4 km mol-1. This error can be compared with experimental values ranging from zero to 493 km mol-1 and having an average of 59.5 km mol-1.Furthermore an rms error of only 5.0 km mol-1 is found between the intensities calculated directly from the molecular wave function and the values obtained by the CCTDP model. The focus here is on differentiating the electronic structure changes that accompany vibrations using the CCTDP model applied


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to the characteristic group intensities of the CH, CF and CCl stretching and bending vibrations.

4. Results 4.1.CH stretching and bending modes. Table S1 contains the charge and charge transfer-dipolar polarization contributions as well as their charge-differential interaction contributions along with the total calculated intensity values of the CH stretching vibrations. The sizes of these contributions are depicted in Figure 1.As can be seen there the charge contributions, with an average value of 2.5 km mol-1, are usually substantially smaller than the A(CTDP) ones that have an average of 16.8 km mol-1. As such the A(CTDP) term and its interaction with the charge contribution can recover much of the total intensity values. This is shown in Figure 2 where there are only a few small deviations from the line representing exact agreement between the A(CTDP) and A(CxCT,DP) sums and the total calculated intensities for the CH stretches. The charge contributions are less than 2 km mol-1 for all these molecules, except for C2H2 that has a 25.2 km mol-1 charge contribution and contributions ranging between 2.2 and 9.5km mol-1 for the CH stretches of propyne,CH2F2, CHF3, CH2Cl2 and CHCl3. Acetylene and propyne have acidic hydrogens as they are bonded to sp hybridized carbon atoms and one would also expect higher charge contributions for the hydrogen and carbon atoms in methane molecules with multiple fluorine and chlorine substituents. Interestingly all the CH stretching modes for the difluoro- and dichloroethylenes have very small charge contributions of less than 2.4 km mol-1. Removing from consideration the CH stretching vibrations of the sp C-H bonds, the A(CTDP) and A(CxCT,DP) sum estimate the CH stretching intensities for the other molecules studied here with only a 2.5 km mol-1 error. These calculated intensities range from zero to 62 km mol-1 with an average value of 18.4 km mol-1.It should be mentioned that all the CH stretching vibrations have individual charge transfer and dipolar polarization contributions to the dipole moment derivatives that are of opposite sign, i.e. they follow a charge transfer – counterpolarization model. This can be verified in Ref.10 where all the charge transfer – dipolar polarization interaction terms are large and of negative sign (last term in Eq. 4). 7 ACS Paragon Plus Environment


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The in-plane sp3CH bending vibrations also tend to have larger A(CTDP) contributions(average of 7.9 km mol-1) compared with those owing to the displacement of the equilibrium hydrogen charges (average of 4.6 km mol-1) as can be seen in Table S2 and Figure S1. Figure 2also contains points representing the sum of the A(CTDP) and A(CxCT,DP) interaction contributions for the CH bends against their total intensities. This sum shows excellent agreement with the total intensities for all the sp3 CH bending vibrations except for the Q8 asymmetric CH bend of CH2F2 and Q2 and Q8 CH bends of CH2Cl2. The A(CTDP) and A(CxCTDP) sum estimates the sp3 CH bends with an rms error of 3.8 km mol-1 whereas this error is 9.2 km mol-1for the sp2 CH bends. The largest discrepancy occurs for the sp CH perpendicular bend of propyne. These values can be compared with the total calculated intensities that range from zero to 106 km mol-1. Besides the larger discrepancies for the sp acetylene and propyne CH bends Figure 2 shows smaller ones for four sp2(ν3 and ν9 of 1,1-C2H2F2 and cis-C2H2F2)CH bends. The

CH

out-of-plane

bending

vibrations

have

zero

charge

transfer

contributions10,11. As such only dipolar polarization effects contribute to the total intensity. Values of the charge, A(C), dipolar polarization, A(DP) and their interaction contributions, A(CxDP), are given at the bottom of Table S2. The A(DP) average contribution for the out-of-plane CH bends of 51.4 km mol-1 is about ten times larger than the charge value of 5.6 km mol-1.Also this A(DP) average for the out-of-plane bends is much larger than the average in-plane A(CTDP)contribution of 7.9 km mol-1. This can be seen in Figure 3 where in-plane and out-of-plane results for CH bends are shown for all planar molecules. All the out-of-plane CH bending intensities are estimated to be much larger than the in-plane ones by the CCTDP model as can be seen in Table S2. This occurs for the in-plane bends because the charge transfer – dipolar polarizations effects are of opposite sign and their intensity contributions cancel one another leading to small A(CTDP) values as shown in Figure 3. This cancellation does not take place for the out-of-plane CH bending vibrations that have much larger A(DP) contributions. These results are strongly supported by experimental evidence. For the bending vibrations in Table S2 the experimental CH bending intensity average for the out of plane modes is 65.7±20.0 km mol-1, more than five times the in-plane value of 12.6±10.4 km mol-1. As an example the larger out-of-plane CH bending experimental intensity for ethylene, 82.1±2.5 km mol-1, compared to its in-plane bends, 0.3 ± 0.0 and 10.1 ± 0.2 km mol-1, has long been a subject of discussion in the spectroscopic 8 ACS Paragon Plus Environment

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community4,19,20. A similar situation holds for benzene for which the measured out-ofplane CH bending intensity is more than 10 times larger than the in-plane one, 86.4 and 3.6km mol-1, respectively21-23. In Table S2 small A(CTDP)and large A(DP)contributions differentiate these in-plane and out-of-plane intensities as can be seen in Figure 3. The A(CTDP) values for the inplane CH bends in ethylene are 3.1 for the 1443 cm-1Q12and 1.4km mol-1for the 810 cm1

Q10 bands compared with an A(DP) value of 64.5 km mol-1 for the 949 cm-1 Q7 out-of-

plane bend. The low in-plane A(CTDP) values are the results of charge transfercounterpolarization cancellation for which the dipole moment change owing to charge transfer is opposite in direction to dipolar polarization although both have similar magnitudes. However the out-of–plane mode has a 64.5 km mol-1 dipolar polarization contribution but zero charge transfer so no such cancellation takes place. As the charge contribution for the out-of-plane vibration is only 2.0 km mol-1 models contemplating only atomic charges are not capable of describing this vibration. Atomic dipole changes are necessary to account for the large polarization effect. Small A(CTDP) contributions for both in-plane bending vibrations do not necessarily imply that their electronic density rearrangements are similar. The Q10 vibration has small individual charge transfer and polarization contributions (second and third terms of Eq. (3)), 14.1 and 6.8 km mol-1, respectively. Their small sum of 20.9 km mol-1 is mostly cancelled by their negative interaction term of -19.5 km mol-1(last term of Eq. (3)) resulting in the small 1.4 km mol-1 A(CTDP) value. This sum is very large for Q12, 1233.6 km mol-1, whereas the charge transfer –dipolar polarization interaction term is -1230.5 km mol-1 for an A(CTDP) value of 3.1 km mol-1. For both these vibrations and many other stretching and bending modes the charge transfer-counterpolarization mechanism is predicted by models including both atomic charges and atomic dipoles for modeling electronic structure behavior. The above discussion shows that it is very important to model electronic density with accurate atomic charges and atomic dipoles as many times the A(CTDP) values are differences of large but similar-sized values24. This explains why very high quality wave functions are necessary for calculating accurate infrared fundamental intensities. The existence of the charge transfer-counterpolarization effect for the in-plane CH bend of benzene also explains its low A(CTDP) contribution of 3.5 km mol-1 that is 9 ACS Paragon Plus Environment


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about thirty times smaller than the out-of-plane value of 106.2 km mol-1 21. (See Figure 3 and Table S2). This owes to a charge transfer-counterpolarization effect for the inplane mode for which the dipole moment change from charge transfer is +0.18 e.amu-½ and from dipolar polarization -0.24 e.amu-½. As a consequence these dipole moment changes cancel one another. This results in a small value of 3.5 km mol-1 for A(CTDP).In contrast the out-ofplane C-H bend has a zero charge transfer contribution and a 0.33 e amu-½ dipolar polarization contribution. So the A(DP) contribution is substantially larger, 106.1 km mol-1.These theoretical results are in good agreement with the large out-ofplane experimental CH bending intensity of benzene, 86.4 km mol-1 and the much smaller in-plane one, 3.6 km mol-1. Years ago researchers21-23 have explained the higher out-of-plane intensity of benzene relative to the in-plane one using the bond moment model modified by including a re-hybridization effect. Assuming that a re-hybridization effect only occurs for the out-of-plane mode a positively charged hydrogen atom moving out of the benzene plane has a dipole moment change reinforced by re-hybridization of the carbon atoms taking place by an introduction of s character into the pπ orbitals. As such electron density is displaced in a direction opposite to that of the moving hydrogen atoms. No such reinforcement was assumed to occur for the in-plane change in dipole moment. The QCISD/cc-pVTZ CCTDP model predicts a zero charge contribution owing to an almost neutral hydrogen atom and a large 106.2 km mol-1 dipolar polarization effect for the out-of-plane mode in contrast to the small 3.5 km mol-1 contribution for the in-plane one. So this CCTDP model attributes the higher out-of-plane benzene experimental intensity of 86.4 km mol-1to zero charge transfer whereas the charge transfercounterpolarization effect results in the low in-plane experimental intensity of 3.6 km mol-1. It should be mentioned that the earlier charge –charge flux models could not explain this intensity difference. The Q8 CH bend for CH2Cl2 has one of the largest A(CTDP) contributions in Table S2, 89.0 km mol-1. Although it has nonzero charge transfer and dipolar polarization contributions the charge transfer dipole moment change vector is quite a bit larger than the polarization one that has an opposite direction.

4.2.CF and CCl stretching modes.


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As might be expected the CF stretching mode intensities are dominated by charge contributions. Their average value of 200.0 km mol-1 in Table S3 is more than ten times larger than the average value of the A(CTDP) values, 14.9 km mol-1. Figure 4 shows the predominant charge and charge – differential interaction contributions relative to the small ACTDP) ones. Figure 5 contains a graph of the A(C) and A(CxCT,CP) sums against the total intensities for the fluoromethanes, fluorochloromethanes, F2CO, F2CS and the difluoroethylenes. Excellent agreement between these values can be seen with few exceptions. The discrepancy for the ν2mode of CHF3 owes to a 55.6 km mol1

A(CTDP) contribution although A(C) is dominant, 311.3 km mol-1. However ν4 of F2CS

and ν10 of cis-C2H2F2 have A(CTDP) values, 47.6 and 59.7 km mol-1, which are larger than their charge contributions. For all these CF modes the charge and interaction sum estimates the total CF stretching intensities with an rms error of 23.3 km mol-1 for intensities ranging from 3.7 to 470.9 km mol-1 and averaging 201.7 km mol-1. Table S4 contains the CCTDP information on the intensities of the CCl stretching modes that have an average value of 104.7 km mol-1, about half the CF stretching average. The averages of the A(C) and A(CTDP) contributions are very similar, 33.6 and 40.7 km mol-1. However these CCl stretching modes follow three very different CCTDP patterns. The Q4 of cis-C2H2Cl2, Q3 of CH2Cl2, Q2 of CHCl3, Q2 of CClF3, Q8 of CCl2F2 and Q2 and Q4 of CCl3F intensities (bold face in Table S4) have much larger charge contributions compared to their A(CTDP) ones and are estimated quite well by the A(C)+A(CxCT,DP) sum with only a rms error of 12.6 km mol-1 compared to an average calculated intensity of 97.2 km mol-1. The Q10cis-C2H2Cl2, Q11 trans-C2H2Cl2, Q2 and Q4Cl2CS, Q2 Cl2CO, Q9 CH2Cl2, Q5 CHCl3 and Q3 CCl4 intensities (bold face in Table S4) with A(CTDP) contributions much larger than their charge contributions are estimated by a A(CTDP) and A(CxCT,DP)sum with a 10.3 km mol-1error for an average intensity of 96.7km mol-1. For this reason the CCl stretching results appear in both Figures 1 and 5. Finally three CCl stretching modes, Q4 of Cl2CO, Q3 of CH3Cl and Q2 of CCl2F2have very similar A(C) and A(CTDP) sizes and do not follow either of the above two patterns. Figure S2 shows a bar graph with CCTDP contributions to the CCl stretching vibrations. Included in Figure 5 are recent results for the C=O stretching intensities of fifteen carbonyl compounds.25 Their CCTDP parameters indicate that the same kind of electronic structure change occurs for the C=O and C-F stretching vibrations, 11 ACS Paragon Plus Environment


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dominating charge and interaction contributions. The largest discrepancies occur for HClCO and HBrCO. Their low symmetry results in dipole moment changes in two Cartesian coordinate directions whereas all the other vibrations in Figure 2 have one directional changes owing to molecular symmetry.

4.3.CF and CCl bending modes. Charge and charge transfer-dipolar polarization intensity contributions for the CF bending modes are given in S5. Besides the A(CxCT,DP) interaction term the sums of A(C) and A(CTDP) contributions are also given. The CF bending modes have much smaller intensities than the CF stretches with values ranging from about zero to only 65 km mol1

. Their average value is 10.3 km mol-1, about 20 times smaller than that of the CF

stretching intensities. This can be understood examining the A(C), A(CTDP) and A(CxCT,DP)contributions. As shown in the graph of Figures6 and S3, the A(C) and A(CTDP)sums have about the same sizes but opposite signs compared with their interaction values. Even though these sum and interactions have relatively large magnitudes, with averages of 127.9 and -117.6 km mol-1, respectively, they cancel each other resulting in small net intensities. The largest intensities occur for ν3 and ν4 of CHF3, ν11 of cis-C2H2F2,ν12 of trans-C2H2F2, ν10 of 1,1-C2H2F2andν6 of F2CO. All other calculated intensities are less than 10 km mol-1. As for the CH out-of-plane bends the charge transfer contribution is zero for the out-of-plane CF bends and the charge transfer-counterpolarization annihilation effect does not take place. So the average A(DP)contribution for the out-of-plane bends in Table S5 is 147.7 km mol-1 that is much larger than the A(CTDP) values for the in-plane bends, 18.2 km mol-1. In contrast to the CH bends the dipolar polarization contribution to the dipole moment derivative has an opposite sign to the charge contribution for the CF bends. Since the negatively charged fluorine atoms are displaced in an opposite direction to the accumulation of electron density owing to polarization for the out-ofplane bend there is a cancelling effect and small dipole moment changes result. Earlier works21-23 attributed the polarization effect to the sp2 carbon atoms. In terms of the intensity contributions, the negative A(CXCT,DP) terms cancel the sums of A(C) and A(CTDP)to a large extent as shown in Figure 7 resulting in small out-of-plane intensity values that are of comparable size to the in-plane ones. This is confirmed


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experimentally as the average in-plane CF intensity is 5.8±7.3 km mol-1 and the out-ofplane average is 9.9±12.6 km mol-1. The calculated C6F6 out-of-plane value, 6.2 km mol-1, is small as is the in-plane ν18 of 1.6 km mol-1 given in Table S5. The experimental values are 3.6 and 2.0 km mol1

, respectively19. This small out-of-plane intensity value for C6F6contrasts with 86.4 km

mol-1 for the corresponding CH vibration in benzene. Experimental infrared intensities have not been reported for tetrafluoroethylene but our group has just calculated them at the QCISD/cc-pVTZ level. As for benzene the in-plane and out-of-plane intensities are both small, 4.7 and 4.4 km mol-1, respectively. Consistent with these calculations the observed out-of-plane CH bending intensities in trans-C2H2F2, (56.7 km mol-1)26 and Small intensity values are found for all the CF bends shown in Figure 7. The average experimental in-plane CF intensity is 5.8±7.3 km mol-1 and the out-of-plane average is 9.9±12.6 km mol-1for1,1 C2H2F2 (60.3 km mol-1)27 are much larger than their CF counterparts (12.7 and 0.3 km mol-1, respectively). The simple bond moment – dipolar polarization model also holds for the out-ofplane modes of F2CO and H2CO. The experimental out of plane F2CO value28 of 30.6 km mol-1 is in good agreement with the QCISD/cc-vPTZ value of 35.8 km mol-1 but three times larger than this experimental value29 for H2CO, 9.9 km mol-1. The small H2CO intensity occurs because the negatively charged oxygen atom is displaced in the opposite direction to the dipolar polarization. The F2CO value is higher owing to an exceptionally high charge contribution of 608 km mol-1as can be seen in Figure 7. Displacements of three very negatively charged atoms gives rise to this exceptionally high charge contribution. Only the CF stretching intensity of CF4 has a higher charge contribution of all the intensities studied in this report. The CCl bending modes also have very small intensities with a calculated average of 2.4 km mol-1 compared to the CCl stretching mode average of 104.7 km mol1

. Again A(C) and A(CTDP) sums and the A(CxCT,DP) contributions tend to cancel one

another as indicated in Figure 6. The largest calculated intensity occurs for Q3 of CCl2F2, 11.5 km mol-1 followed by 8.0 and 5.8 km mol-1 for Q12 of trans-C2H2Cl2 andQ11 of cis-C2H2Cl2. All the other CCl calculated intensities for the bending modes are less than 1 km mol-1. As found for the CH and CF bending vibrations, the average



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() contribution for the out-of-plane bends, 15.2 km mol-1is also larger than the () average of 2.8 km mol-1, for the in-plane CCl bending modes. 5. Concluding remarks Changes in molecular electronic density as the molecule vibrates can be described as the movements of static equilibrium atomic charge densities and differential changes to these densities that are approximated by intramolecular charge transfer and dipolar polarization effects. The inclusion of atomic dipoles along with atomic charges obtained from QTAIM allows a characterization of the natures of the electronic density changes occurring for different kinds of molecular vibrations. The CH stretches and bends have dominant charge transfer-dipolar polarization contributions, the CF and CO stretches have dominant charge contributions and the CF and CCl bends have charge and charge transfer-dipolar polarization contribution sums that are mostly cancelled by the charge-differential interaction contributions. This successful classification has not been achieved previously using models with only static atomic charge and charge flux parameters30. The charge transfer-counterpolarization phenomenon occurs in about 90% of all the

vibrations

studied

here.

The

most

recurring

instances

in

which

the

counterpolarization effect does not take place is for the out-of-plane bending modes, where symmetry imposes a zero charge transfer constraint. Changes in atomic dipoles as molecules are distorted from equilibrium must be included in models for accurate intensity estimates of these vibrations. One would expect the charge transfercounterpolarization behavior to also be important for large amplitude changes in chemical bond lengths and angles. In fact the almost null dipole moment of carbon monoxide has been attributed to the charge transfer-counterpolarization effect31,32. This small moment has been difficult to explain in light of the large electronegativity difference between the carbon and oxygen atoms. We hope this report will stimulate the use of models including changes in atomic dipoles as well as charges for describing electronic structure changes for molecular geometry distortions.


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6. Supporting Information (SI)

Bar graph with the charge, charge transfer-dipolar polarization and the charge differential interaction contributions for the CH in-plane bending vibrations (Figure S1). Bar graph with the charge, charge transfer-dipolar polarization and the charge differential interaction contributions for the CCl stretching vibrations (Figure S2.). Bar graph with the charge, charge transfer-dipolar polarization and the charge - differential interaction contributions for the CF in-plane bending vibrations (Figure S3). Tables with all the data used throughout the paper (Table S1-Table S6).

7. Acknowledgements A. F. S. and L. J. D. thank São Paulo’s FAPESP and CAPES for the award of postdoctoral grant number 2014/21241-9 and undergrad fellowship 2016/07411-4, and R. E. B. acknowledges FAPESP for funding through the award 2009/09678 and Brazil’s CNPq for research fellowship, 304518/2014-0.

8. References (1) Richter, W. E.; Duarte, L. J.; Silva, A. F.; Bruns, R. E. Review of Experimental GAPT and Infrared Atomic Charges in Molecules. J. Braz. Chem. Soc. 2016, 27, 979 - 991.

(2) Sharpe, S.W.; Johnson, T. J.;Sams, R. L.; Chu, P. M.; Rhoderick, G. C.; Johnson,

P.

A.

Gas-Phase

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Infrared

Spectroscopy. Appl. Spectrosc. 2004, 58, 1452 – 1461.

(3) Decius, J. C.An effective atomic charge model for infrared intensities.J. Mol. Spectrosc., 1975, 57, 348.

(4) King, W. T.; Mast, G. B.Infrared intensities, polar tensors, and atomic population densities in molecules.J. Phys. Chem., 1976, 80, 2521 - 2525.

(5) Gussoni, M.; Ramos, M. N.; Castiglioni,C.; Zerbi, G.Ab initio counterpart of infrared atomic charges.Chem. Phys. Lett., 1987, 142, 515 - 518.

(6) Haiduke, R. L. A.; R. E. BrunsAn Atomic Charge−Charge Flux−Dipole Flux Atom-in-Molecule Decomposition for Molecular Dipole-Moment



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Derivatives and Infrared Fundamental Intensities. J. Phys. Chem. A, 2005, 109, 2680-2688.

(7) Bader, R. F. W. in Atoms in Molecules. A Quantum Theory. Clarendon Press, Oxford, 1990.

(8) Silva, A. F.; Richter, W. E.; Meneses, H. G. C.; Bruns, R. E. Atomic charge transfer-counter polarization effects determine infrared CH intensities of hydrocarbons: a quantum theory of atoms in molecules model. Phys. Chem. Chem. Phys. 2014, 16, 23224 - 23232.

(9) Terrabuio, L. A.; Da Silva, N. A.; Haiduke, R. L. A.; Matta, C. F. Real space atomic decomposition of fundamental properties of carbon monoxide in the ground and the two lowest lying excited electronic states. Mol. Phys. 2017, 115, 1955-1965. (10) Dinur, U.;Hagler, A. T. Determination of atomic point charges and point dipoles from the Cartesian derivatives of the molecular dipole moment and second moments, and from energy second derivatives of planar dimers. I. Theory.J. Chem. Phys. 1989, 91, 2949 - 2959. (11) Dinur, U.; Hagler, A. T.Determination of atomic point charges and point dipoles from the Cartesian derivatives of the molecular dipole moment and second moments, and from energy second derivatives of planar dimers. II.Applications to model systems.J. Chem. Phys. 1989, 91, 2959 - 2971.

(12)

Silva, A. F.; Richter, W. E.;Meneses, H. G. C.;Faria, S. H. D. M.; Bruns,

R. E. How Accessible Is Atomic Charge Information from Infrared Intensities? A QTAIM/CCFDF Interpretation. J. Phys. Chem. A 2012, 116, 8238 - 8249.

(13) Person, W. B.; Newton, J. H. Dipole moment derivatives and infrared intensities. I. Polar tensors. J. Chem. Phys., 1974, 61, 1040 - 1050. (14) Overend J., in Infrared Spectroscopy and Molecular Structure, ed. M. Davies, Elsevier, Amsterdam, 1963.

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Frisch; M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M.

A.; Cheeseman, J. R.; Montgomery, Jr., J. A.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M., et al. Gaussian 03, Revision D.02, Gaussian, Inc., Wallingford CT, 2004.

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Silva, Jr., J. V., Vidal, L. N.; Vazquez, P. A. M.; Bruns, R. E.Coupled

cluster and configuration interaction quantum calculations of infrared fundamental intensities. Int. J. Quantum Chem. 2010, 110, 2029 - 2036.


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MORPHY98, a program written by P. L. A. Popelier with a contribution

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Silva Jr, J. V.; Oliveira, A. E.; Hase, Y.; Bruns, R. E. Quantum Theory

Atoms in Molecules Charge−Charge Flux−Dipole Flux Models for the Infrared Intensities of Benzene and Hexafluorobenzene. J. Phys. Chem. A

2009, 113, 7972 - 1978. (19)

Eggers, Jr., D. F.Anomalous Infrared Intensity in Ethylene. J. Chem.

Phys. 1955, 23, 221-222.

(20) Golike, R. C.; Mills, I.M.; Person, W.B.; Crawford, Jr., B.Vibrational Intensities. VI. Ethylene and Its Deuteroisotopes. J. Chem. Phys. 1956, 25, 1266 - 1276. (21) Spedding, H.; Whiffen, D. H. Intensities in the infra-red spectrum of benzene. Proc. R. Soc. London Ser. A 1956, 238, 245-255.

(22) Steele, D.;Whiffen, D. H.Infrared Absorption Intensities of Hexafluorobenzene. J. Chem. Phys. 1958, 29, 1194. (23) Steele, D.; Wheatley, W. J.Studies in vibrational absorption intensities: Vibronic effects in hexafluorobenzene and benzene. J. Mol. Spectrosc. 1969, 32, 265-275.

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Gomes, T. C. F.; Silva, Jr. J. V.; Vidal, L. N.; Vazquez, P. A. M.; Bruns,

R. E.ChelpG and QTAIM atomic charge and dipole models for the infrared fundamental intensities of the fluorochloromethanes. Theor. Chem. Account.

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infrared intensities of carbonyl stretching vibrations. Phys. Chem. Chem. Phys. 2016, 18, 17575 - 17585.

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Kagel, R. O.; Powell, D. L.; Overend, J.; Ramos, M. N.; Bassi, A. B. M.

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(29) Nakanaga, T.; Kondo, S.; Saëki, S.Infrared band intensities of formaldehyde and formaldehyde‐d2 J. Chem. Phys. 1982, 76, 3860 - 3866. (30) Richter, W. E.;Silva, A. F.; Bruns, R. E. Atomic polarizations necessary for coherent infrared intensity modeling with theoretical calculations. The Journal of Chemical PhysicsJ. Chem. Phys.2017, 146, 134107.

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9. Figure Captions Figure 1. Bar graph with the charge, charge transfer-dipolar polarization and chargedifferential interaction contributions for the CH stretching vibrations. Figure 2. Graph of the sum of the charge transfer-dipolar polarization and chargedifferentialinteraction intensity contributions vs. the total calculated intensity for CH stretches and bends and some CCl stretches (km mol-1). Figure 3. Bar graph with the charge, charge transfer-dipolar polarization and the charge - differential interaction contributions for the in-plane and out-of-plane CH bending vibrations of planar molecules. Figure 4. Bar graph with the charge, charge transfer-dipolar polarization and the charge - differential interaction contributions for the CF stretching vibrations. Figure 5. Graph of the sum of the charge and the charge - differential interaction intensity contributions vs. the total calculated intensity for CF, CCl and CO stretches (km mol-1). Figure 6. Graph of the sum of the charge and charge transfer-dipolar polarization intensity contributions vs. the charge - differential interaction intensity contribution for the CF and CCl bending vibrations (km mol-1). Figure 7. Bar graph with the charge, charge transfer-dipolar polarization and the charge - differential interaction contributions for the in-plane and out-of-plane CF bending vibrations of planar molecules.


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TOC GRAPHIC



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Figure 1. Bar graph with the charge, charge transfer-dipolar polarization and charge-differential interaction contributions for the CH stretching vibrations. 651x516mm (120 x 120 DPI)

ACS Paragon Plus Environment

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Figure 2. Graph of the sum of the charge transfer-dipolar polarization and charge- differential interaction intensity contributions vs. the total calculated intensity for CH stretches and bends and some CCl stretches (km mol-1). 289x202mm (150 x 150 DPI)



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Figure 3. Bar graph with the charge, charge transfer-dipolar polarization and the charge - differential interaction contributions for the in-plane and out-of-plane CH bending vibrations of planar molecules. 419x457mm (120 x 120 DPI)


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Figure 4. Bar graph with the charge, charge transfer-dipolar polarization and the charge - differential interaction contributions for the CF stretching vibrations. 695x452mm (120 x 120 DPI)



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Figure 5. Graph of the sum of the charge and the charge - differential interaction intensity contributions vs. the total calculated intensity for CF, CCl and CO stretches (km mol-1). 289x202mm (150 x 150 DPI)


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Figure 6. Graph of the sum of the charge and charge transfer-dipolar polarization intensity contributions vs. the charge - differential interaction intensity contribution for the CF and CCl bending vibrations (km mol-1). 289x202mm (150 x 150 DPI)



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Figure 7. Bar graph with the charge, charge transfer-dipolar polarization and the charge - differential interaction contributions for the in-plane and out-of-plane CF bending vibrations of planar molecules. 579x469mm (120 x 120 DPI)


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Quantum Theory of Atoms in Molecules ChargeâCharge Transfer

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