Fast Quantum Chemical Simulations of Infrared Spectra of Organic

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A: Spectroscopy, Molecular Structure, and Quantum Chemistry

Fast Quantum Chemical Simulations of Infrared Spectra of Organic Compounds with the B97-3c Composite Method Sergey Aleksandrovich Katsyuba, Elena E. Zvereva, and Stefan Grimme J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.9b01688 • Publication Date (Web): 08 Apr 2019 Downloaded from http://pubs.acs.org on April 8, 2019

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The Journal of Physical Chemistry

Fast Quantum Chemical Simulations of Infrared Spectra of Organic Compounds with the B97-3c Composite Method

Sergey A. Katsyuba a,*, Elena E. Zverevaa and Stefan Grimmeb

aArbuzov

Institute of Organic and Physical Chemistry, FRC Kazan Scientific Centre of RAS,

Arbuzov st., 8, Kazan, 420088, Russia. bMulliken

Center for Theoretical Chemistry, Institut für Physikalische und Theoretische

Chemie der Universität Bonn, Beringstr. 4, 53115 Bonn, Germany.

ABSTRACT. The ability of the quantum chemical computations to reproduce spectral positions and relative intensities of infrared (IR) bands for experimental vibrational spectra of organic molecules is assessed. The efficient B97-3c density functional approximation,

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routinely applicable to hundreds of atoms on a single processor, has been applied to simulation of IR spectra for species containing up to 216 atoms. The results demonstrate that B97-3c, being much faster than the well recognized hybrid functional B3LYP, offers similarly good quantitative performance in comparison to experimental data for relative IR intensities and fundamental frequencies (  2200 cm-1) for isolated molecules comprising three to twenty one first- or second-row atoms.

Introduction. Infrared (IR) spectroscopy is widely used in structural studies of organic molecules and, especially, of various materials. Quantum chemical simulation of IR spectra and comparison of simulated spectra with their experimental counterparts is a powerful tool for interpreting experimental spectra, particularly for large molecules with low or no symmetry. As correlated ab initio methods are inapplicable to the vast majority of such species, density functional theory (DFT) is typically used for the spectra simulations of practically interesting systems. DFT approximations, especially combined with scaling techniques,1,2,3,4 provide a reasonable accuracy for fundamental frequencies5,6,7,8,9,10,11 and IR intensities12,13,14 of the gas-phase species of small and medium size. In particular, reasonably accurate and fast simulations of the gas-phase IR spectra are provided by the hybrid B3LYP functional in combination with moderate-size AO basis sets.14,15


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Nevertheless, even at this level, the IR spectra simulations for moderately large systems, e.g., comprising about 100-200 atoms, require large computational resources and involve very long computation times, which makes them problematic for practical spectrochemists. Very recently a revised version of the well-established B97-D density functional approximation with general applicability for chemical properties of large systems was proposed.16 The new composite scheme (termed B97-3c) can be routinely applied to hundreds of atoms on a single processor and yields excellent molecular and condensed phase geometries, similar to most hybrid functionals evaluated in a larger basis set expansion.17,18 The present work is focused on the assessment of the ability of B97-3c to replace the more “expensive” B3LYP method in computations of the vibrational frequencies and IR intensities for organic molecules. We compare the DFT computations with available gas-phase experiments and high-level correlated ab initio computations for isolated molecules. As in our previous work,10,15 we assess the quality of a computational method on how well it reproduces the relative intensities, because relative, rather than absolute band intensities are usually of interest for spectra simulation and interpretation. The hybrid DFT functional B3LYP, which originally was developed with a focus on IR spectra simulations,19 was earlier assessed as one of the best approaches to simulations of vibrational spectra for small and medium-size molecules (from one to twelve first- or second-row atoms) in the gas phase.9,10,15 Here we study a set of forty seven test molecules ranging in size from three to 21 first- or second-row atoms. Finally, the


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computational efficiency of B97-3c and B3LYP treatments is assessed by examples of molecular systems comprising up to 216 first-row atoms.

Computations All calculations were carried out using the Turbomole-7.2 program package.20 Following full geometry optimisations at each level of theory, harmonic vibrational frequencies and IR intensities were calculated analytically for the DFT methods employed in this study, corresponding to the B97-3c generalized gradient approximation (GGA) functional16 and Becke’s three-parameter hybrid exchange functional21 in combination with the Lee-YangParr’s correlation functional22 (B3LYP) with the D3 London dispersion correction in the Becke-Johnson sampling scheme (indicated by “-D3” appended to the functional name).23,24 B3LYP-D3 calculations were carried out with the 6-31+G*25,26,27,28 doublezeta basis set and Sadlej’s polarized triple zeta basis sets, optimized for electric properties (pVTZ29,30,31,32,33,34 and Z3PolX35), while the polarized valence-triple-zeta basis set mTZVP16 was used in B97-3c computations. Note the B97-3c applies the same D3(BJ) dispersion correction as in B3LYP-D3 but additionally a short-range bond length correction potential as well as a specific adjustment of the electronic parameters in the B97 Taylor expansion. Infrared intensities were computed in the double harmonic approximation, ignoring cubic and higher force constants and omitting second and higher order dipole moment and polarizability derivatives. To minimize the influence of this neglect of the anharmonicity effects on a comparison of the computed and experimental


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(anharmonic) intensities, the bands of the most anharmonic CH stretching modes were excluded. In the comparison both the computed and the corresponding experimental spectra were normalized by setting the intensity of the strongest band to unity. Therefore we compared the computed IR intensity ratio from a given level of theory Ik /Imax (where Ik is the IR intensity of the k-th vibration mode, Imax is the IR intensity of strongest band in the region of   ca. 2200 cm-1) with the same IR intensity ratio obtained either experimentally or by means of high-level reference ab initio methods. The harmonic frequencies obtained using both the ab initio and the B97-3c or B3LYP-D3 computations were compared directly without any frequency scaling. The correlation between experimental and theoretical frequencies was based on a manual normal mode assignment of individual bands. To minimize the influence of the anharmonicity effects on a comparison of the computed (harmonic) and experimental frequencies of the most anharmonic vibrations involving CH bendings (usually appearing in the spectral region of ~1000-1500 cm-1) the frequencies obtained with the B97-3c method and falling in this interval were scaled using empirical equation scaled = A∙computed + B (vide infra). In case of B3LYP-D3/6-31+G* computations the same purpose was achieved through application of so called scaled quantum mechanics (SQM) technique,1,8 that is the scaling of the quantum-chemical harmonic force field. The calculated force fields were transformed to redundant set of individual internal coordinates8 and the scaling procedure was applied: Fij (scaled)= (sisj)1/2 Fij, where si and sj are scaling factors for internal coordinates i and j,


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respectively. Transferable scaling factors, employed for this purpose, were taken from Refs.8,9

Results and discussion Assessment of “gas-phase” infrared intensities As shown elsewhere,36,37 the high-level correlated ab initio methods, QCISD38 and CCSD(T)39 with large basis sets yield IR intensities in good mutual agreement. Larger deviations from the experimental values found for the both methods should be attributed to the double harmonic approximation used in the computations and the experimental uncertainties, which typically amount to at least 10%. To avoid these interfering factors in our previous study,15 we preferred to use as reference IR intensities computed for pyrrole, thiophene, furan, uracile, and pyrimidine by the high-level correlated ab initio method CCSD(T). For this test set further referred to as a test set (i) B3LYP-D3/6-31+G* performed excellently with a correlation coefficient R = 0.9958; and a small standard deviation, SD = 0.023 for the relative intensities. The B97-3c method provides even marginally better results: R = 0.9967; SD = 0.021 (Table 1). TABLE 1: Assessment of computed relative infrared intensities vs. experimental or ab

initio results for the test sets (i-v) and 1h-pyrrolo[3,2-h]quinoline (PQ).a The correlation coefficient R and standard deviation (SD) are given. Performance

Test set

PQ


6

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measure, method

R, B97-3c

(i)

(ii)

(iii)

(iv)

(v)

All

In-

Out-of-

modes

plane

plane

modes

modes

0.9959

0.9956

0.9845

0.9683

0.9884

0.9027

0.9557

0.8040

R, B3LYP-D3 0.9958

0.9993

0.9849

0.9897

0.9908

0.9228

0.9735

0.8214

b

c

c

c

b

b

b

b

0.021

0.046

0.071

0.083

0.049

0.084

0.055

0.130

0.017c

0.069c

0.048c

0.046b

0.072b

0.044b

0.104b

SD, B97-3c

SD, B3LYP- 0.023b D3 a

Only those modes for which experimental intensities had been available were

considered. Total number of data included in the analysis and other details are given in Tables S1-S6 (ESI). b With 6-31+G* basis set. c With Z3PolX basis set.

In our previous assessment10 of MP2 and hybrid density functionals, we compared the relative intensities computed at these levels of theory with the experimental relative intensities measured in the gas-phase IR spectra of C2H4, H2CO, CH2F2 molecules, further referred to as as a test set (ii), and C2D4, CH2=C=CH2, CD2=C=CD2, C2H4O, C2D4O, CD2O, CH3CH=O, (CH3)2C=O, CH3CN, CD3CN, CH3NC, CS2, SCO, COCl2, CD2F2, CH2Cl2, further referred to as as a test set (iii). B3LYP computations with various AO basis sets were in good agreement with the experimental data. According to our present calculations B97-3c yields almost equally good results (Table 1): R = 0.9956 and SD = 0.046 vs R = 0.9993 and SD = 0.017 for the best combination B3LYP-D3/Z3PolX in


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case of test set (ii); R = 0.9845 and SD = 0.071 vs R = 0.9849 and SD = 0.069 for the best combination B3LYP-D3/Z3PolX in case of test set (iii). Intensities of IR bands for the most representative test set (iv) were taken from the gasphase spectra of the following molecules: ethane,40 ethane-D6,40 propane,41 propaneD2,41

propane-D6,41

propene,42

methylacetylene,43

methylacetylene-D,43

methylacetylene-D3,43 cyclobutene,44 dimethylformamide,45 benzene,46 cyclohexane,47 cyclohexane-D12,47 toluene,48 toluene-D8,48 p-xylol,48 hexafluorobenzene.49 The B97-3c results obtained for this set are a bit inferior relative to the best combination B3LYP/Z3PolX (Table 1), mainly because of a larger B97-3c deviation for the relative intensity of two bands for out-of-plane vibrations at 694/729 cm-1 in the IR spectrum of toluene: 0.9 vs experimental value of 0.3 (Table S4). The corresponding B3LYP/Z3PolX value of 0.515 or 0.3 (B3LYP-D3/6-31+G*) better matches the experiment. Nevertheless, with the exception of this drawback, the spectrum simulated with the use of B97-3c matches the experimental spectrum as well as the spectrum produced by B3LYP/631+G* computations (Figure 1).


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A

B

C

1600 1400 1200 1000

800

-1

600 , cm

Figure 1. IR spectra of toluene. A – “experimental” spectrum, which represents tabulated frequencies and intensities from Ref.48 plotted with a Lorentzian broadening (f.w.h.m. = 10 cm-1), B – B3LYP-D3/6-31+G*, and C – B97-3c spectra are based on frequencies and intensities from Table S4 (ESI). In general, in the overwhelming majority of cases, the B97-3c simulations provide very reasonable results qualitatively coinciding with the corresponding experimental data and the B3LYP computations (e.g., Figures 2 and 3).


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A

B

C

1600 1400 1200 1000

800

-1

600 , cm

Figure 2. IR spectra of para-xylol. A – “experimental” spectrum, which represents tabulated frequencies and intensities from Ref.48 plotted with a Lorentzian broadening (f.w.h.m. = 10 cm-1), B – B3LYP-D3/6-31+G*, and C – B97-3c spectra are based on frequencies and intensities from Table S4 (ESI).


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A #

B #

C # 1600 1400 1200 1000 800

600

-1

400 , cm

Figure 3. IR spectra of hexafluorobenzene. A – “experimental” spectrum, which represents tabulated frequencies and intensities from Ref.49 plotted with a Lorentzian broadening (f.w.h.m. = 10 cm-1), B – B3LYP-D3/6-31+G*, and C – B97-3c spectra are based on frequencies and intensities from Table S4 (ESI). # - very weak bands.

The molecules pyridine, 1,4-dioxane and 1,4-dioxane-D8 forming test set (v) have not been analysed in our previous papers.10,15 According to the current data, IR intensities of the bands of these molecules computed both at B3LYP-D3/6-31+G* and B97-3c levels are in a very good agreement with their experimental counterparts (Table 1). B97-3c results are slightly inferior to B3LYP-D3/6-31+G*, but nevertheless reproduce all


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qualitative features of experimental intensity distribution in the gas phase spectra50,51 of all three molecules. Typical spectra as examples are given in Figures 4 and 5.

A

B

C

1600 1400 1200 1000

800

-1

600 , cm

Figure 4. IR spectra of pyridine. A – “experimental” spectrum, which represents tabulated frequencies and intensities from Ref.50 plotted with a Lorentzian broadening (f.w.h.m. = 10 cm-1), B – B3LYP-D3/6-31+G*, and C – B97-3c spectra are based on frequencies and intensities from Table S5 (ESI).


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A

B

C 1600

1400

1200

1000

800

-1

600 , cm

Figure 5. IR spectra of dioxane. A – “experimental” spectrum, which represents tabulated frequencies and intensities from Ref.51 plotted with a Lorentzian broadening (f.w.h.m. = 10 cm-1), B – B3LYP-D3/6-31+G*, and C – B97-3c spectra are based on frequencies and intensities from Table S5 (ESI). In addition, 1H-pyrrolo[3,2-h]quinoline (PQ) was included as a benchmark (Figure 6, Table S6, ESI). Though the IR intensities for this molecule were measured52 in an Ar matrix instead of the gas phase, the authors of Ref.52 claimed that transfer of PQ from the gas to Ar matrix resulted in only minor intensity variations. Six different DFT functionals were tested52 for their ability to reproduce measured IR intensities for PQ, which to our knowledge is the largest system with available quantitative experimental intensity


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information. Here, B3LYP/6-311++G** yields the best results: R = 0.9557, SD = 0.054.52 Surprisingly, B3LYP computations with the triple-zeta basis sets Z3PolX and Sadlej’s pVTZ, which provide the best results for test sets (ii-iv), were less satisfactory for PQ: R = 0.7445, SD = 0.119 for Z3PolX and R = 0.7585, SD = 0.183 for pVTZ.52 The more economical B3LYP/6-31+G* level performs reasonably well: R = 0.9228, SD = 0.072.52 This corroborates our recommendation15 of the hybrid B3LYP functional in combination with the 6-31+G* basis set as a good choice for accurate and cost-effective IR spectral simulations. Our present computations with the B97-3c GGA functional, however, yield results of comparable quality: R = 0.9027, SD = 0.084 (see also Figure 6). The lower accuracy observed with both functionals for PQ relative to test sets (ii-v) can be assigned to problems with intensities calculated for the out-of-plane vibrations, which are reproduced less well than for the in-plane modes (Table 1). These results, as well as a rather poor reproduction of experimental IR intensities of the out-of-plane vibrations of toluene (vide supra) by both B3LYP and especially by B97-3c computations, suggest that DFT predictions for IR bands of out-of-plane vibrations of planar aromatic molecules should be taken with some caution. As suggested by a reviewer, we also conducted semiempirical PM6 calculations for PQ and got qualitatively wrong results for the intensities of the prototypical bands between 400 and 1600 cm-1.


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A

B

C

1600 1400 1200 1000

800

-1

600 , cm

Figure 6. Structure and IR spectra of 1H-pyrrolo[3,2-h]quinoline (PQ). A – “experimental” spectrum, which represents tabulated frequencies and intensities from Ref.52 plotted with a Lorentzian broadening (f.w.h.m. = 10 cm-1), B – B3LYP-D3/6-31+G* (without scaling), and C – B97-3c spectra are based on frequencies and intensities from Table S6 (ESI).

Complete tables of the numeric results for the test sets (i) - (v) and PQ are provided as ESI (Tables S1 - S6, respectively). In conclusion the present data show that differences in quality of IR intensity computations by hybrid B3LYP and GGA B97-3c functionals are practically negligible.


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Assessment of vibrational frequencies of isolated molecules. Clearly, a well-founded assignment of experimental IR bands should be based on a good prediction of not only the intensities but also the vibrational frequencies. For test set (i) B3LYP-D3 computations with the 6-31+G* basis set (Table S1) yield excellent results (Figure S1). The present B97-3c computations produce almost equally good frequencies (Figure S1), which are only slightly underestimated relative to both CCSD(T) and B3LYP results (Table S1). This general good agreement of harmonic frequencies calculated at different levels of theoretical approximations suggests that the main source of more substantial deviations of frequencies, computed with the use of both B3LYP10,15 and B973c functionals, from the corresponding experimental values (Tables S2-S6) is the anharmonicity of the latter. In case of B3LYP/6-31G* and B3LYP/6-31+G* computations an agreement between the computed and experimental vibrational frequencies was improved through the scaling of the quantum chemical harmonic force constants (SQM technique).9,15 Transferable scaling factors are not available for the B97-3c functional which hampers the application of the SQM approach in this case. Nevertheless, the accuracy of the calculated frequencies can be improved by simple frequency scaling. For this purpose we fit computed frequencies of the most anharmonic vibrations involving CH, CH2 and CH3 moieties of molecules from test set (iv) to their experimental counterparts registered in the interval of ca. 1000 – 1500 cm-1, using the empirical relation scaled = A∙computed + B.


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Deuterated species were excluded from the fit as anharmonicity effects for vibrations of deuterated and protonated molecules could be different. The values A = 0.9415 and B = 52 cm-1 provide a quite satisfactory correlation of the scaled and experimental frequencies (Figure S2 B) comparable to the accuracy obtained by the SQM technique in combination with B3LYP computations (Figure S2 A). To check transferability of the obtained empirical scaling factors A and B, we applied them to the correction of computed vibrational frequencies (~1000 cm-1    ~1500 cm1)

of molecules from test sets (ii, iii, v) and PQ, not included in the fit. An improved match

between experimental and calculated frequencies after the scaling of the latter (Figure 7, Tables S2, S3, S5 and S6) suggests a good transferability of the scaling factors. Thus, B97-3c seems to provide the quantitative and a cost effective prediction of both IR intensities, and vibrational frequencies. 2000

2000 1800

-1

1600 Calculated frequencies, cm

-1

1400

B97-3c, scaled R=0.9990 SD=14.949 N=126

1800

B97-3c R=0.9989 SD=16.161 N=126

1600 Calculated frequencies, cm

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1200 1000 800 600 400

1400 1200 1000 800 600 400 200

200

0

0 0

200

400

600

800 1000 1200 1400 1600 1800 2000

0

200

400

-1

Experimental frequencies, cm

A

600

800 1000 1200 1400 1600 1800 2000 -1

Experimental frequencies, cm

B

Figure 7. Correlation plot of calculated harmonic frequencies calculated for the test sets (ii, iii, v) and PQ with the use of B97-3c before (A) and after scaling of frequencies in the


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interval of ca. 1000 – 1500 cm-1 (B) vs. experimental anharmonic frequencies; R, correlation coefficient; SD, standard deviation; N, total number of data included in the analysis. See Tables S2, S3, S5 and S6 for details (ESI). Assessment of the efficiency of B97-3c and B3LYP computations of IR spectra. As shown both in our present study and elsewhere15 the hybrid DFT functional B3LYP, combined with the double-zeta basis set 6-31+G* and SQM techniques, performs excellently for the calculations of relative infrared intensities and frequencies for the bands with   2200 cm-1. Computations at this level of theory are very economical and can be conducted on a PC or laptop computer for medium-size molecules. The B97-3c GGA functional offers an even higher efficiency, which is demonstrated by the example of the 21-atomic PQ molecule: the speed-up by B97-3c is ca. 1.8 compared to B3LYP-D3/631+G*

computations.

This

advantage

increases

for

larger

systems:

for

5-

hydroxymethylfurfural (HMF) explicitly solvated by ten molecules of tetrahydrofuran (Figure S1 in ESI) comprising 145 atoms, B97-3c turned out to be ten times faster than B3LYP. For a cluster of 18 dimethylformamide molecules, comprising 216 atoms, the speed-up of B97-3c relative to B3LYP/6-31+G* amounts to ca. 12. The wall time required for these computations carried out in parallel on 14 processors amounts to only about 17 hours and almost 9 days for B97-3c and B3LYP, respectively.

Conclusions


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The results presented here demonstrate that the novel DFT composite GGA functional B97-3c offers good quantitative performance for the calculations of relative intensities and frequencies for vibrational bands with   ~2200 cm-1 in infrared spectra of organic molecules. B97-3c treatment allows reasonably accurate simulation of IR spectra of systems comprising more than two hundred atoms within a day, which is suitable for application in everyday spectrochemical practice. We have shown recently15 that B3LYP/6-31+G*, combined with the SQM technique, performs well in calculations of IR spectra of isolated molecules, while producing unsatisfactory results for the solution spectra of the same species. Neither larger basis sets nor implicit continuum solvation treatment of the media effects improve the agreement of the simulated spectra with the condensed-phase experimental data. At the same time, there is a growing evidence that explicit treatment of intermolecular interactions allows to reproduce experimental IR spectra of crystals (see for example, Ref.53) or solutions (see for example, Ref.54 and Refs cited herein) that were not reproduced by calculations of isolated molecules. Explicit modeling of media effects necessarily results in a substantial increase of system size and, hence, of the invested computational resources and time. Thus, even application of hybrid DFT functionals could become problematic at this level of approximation. The present study demonstrates that the novel B97-3c method is so fast that explicit quantum chemical modeling of IR spectra of condensed-phase systems seems to become feasible in a standard, non-periodic cluster approach. We hope that the quantitative analysis described herein should facilitate


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further studies on the media effects in computational IR spectroscopy and ultimately it could aid the design of practical approaches to reliable IR spectra simulations for both gas- and condensed-phase systems.

Supporting Information Available. Table S1. Computed vibrational frequencies and relative IR intensities vs. high-level ab initio results for test set (i). Table S2. B97-3c computed frequencies and relative IR intensities vs. experimental results for test set (ii). Table S3. B97-3c computed frequencies and relative IR intensities vs. experimental results for test set (iii). Table S4. B97-3c computed relative IR intensities and frequencies

vs. experimental results and B3LYP computations for test set (iv). Table S5. B97-3c computed relative IR intensities and frequencies vs. experimental results and B3LYP-D3 computations for test set (v). Figure S1. Correlation plot of experimental and calculated frequencies for the test set (i). Figure S2. Correlation plot of experimental and calculated frequencies for the test set (iv). Table S6. B97-3c computed relative IR intensities and frequencies vs. experimental results for PQ. Figure S3. HMF solvated by 10 molecules of THF. This information is available free of charge via the Internet at http://pubs.acs.org.


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Corresponding Author * [email protected]; [email protected]


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TOC Graphic


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Edition; John Wiley & Sons, Ltd: West Sussex, England, 2004. (4) Arenas, J.F., Centeno, S.P., Marcos, J.P., Otero, J.C., Soto, J. A method to improve the agreement between calculated and observed vibrational frequencies after scaling of a quantum mechanical force field. J. Chem. Phys. 2000, 113, 8472-8477. (5) Rauhut, G.; Pulay, P. Transferable Scaling Factors for Density Functional Derived Vibrational Force Fields. J. Phys. Chem. 1995, 99, 3093-3100. (6) Rauhut, G.; Pulay, P. Identification of Isomers from Calculated Vibrational Spectra. A Density Functional Study of Tetrachlorinated Dibenzodioxins. J. Am. Chem. Soc. 1995,

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