Isotopically-Labeled Solid-State Vibrational Mode Energies And Intensities In Crystal09 – A Simple How-To

The generation of isotopically-substituted molecular crystal spectra has become a point of interest, which means blog post. To be clear, this is for cases where isotopic substitution does not affect the crystal geometry – the crystal cell does not change significantly upon deuteration (and for those who believe isotopic substitution never leads to significant changes in the solid, I refer you Zhou, Kye, and Harbison’s article on Isotopomeric Polymprphism and their work on 4-methylpyridine pentachlorophenol, which changes dramatically upon deuteration. I beat on this point because blindly assuming of the crystal cell geometry in such cases will produce spectra noticeably different than measured. It’s NOT the calculation’s fault!).

The generation of isotopically-substituted spectra and intensities in Crystal09 is trivial provided that you KEEP THE FREQINFO.DAT FILE. In fact, you need keep ONLY the FREQINFO.DAT to generate these spectra, which greatly reduces file transfer loads and allows for the scripted calculation of new vibrational spectra and thermodynamic data post-frequency calculation.

As my example system, I’m using the dispersion-corrected crystal cell of alpha-HMX (I have it handy, it’s a small system, and having anything about HMX on your website is proven to increase traffic) at the B3LYP/6-31G(d,p) level of theory. Original input file (the one where the original normal mode analysis is performed) is below:

Test - alpha-HMX 6-31Gdp set DFT/B3LYP FREQ
CRYSTAL
0 0 0
43
15.14 23.89 5.913 124.3
14
6      1.016493675797E-01 -4.109909899348E-02 -3.351438244488E-03
6     -6.539109813231E-02 -6.180633576707E-02 -1.110575784790E-02
1      9.149797846691E-02 -4.382919469310E-02 -1.860042940246E-01
1      1.558888705857E-01 -6.829708099502E-02  4.595161229829E-02
1     -5.138242817334E-02 -5.844587273099E-02 -1.920922064181E-01
1     -9.781600273101E-02 -1.015710562102E-01  2.063738273292E-02
7      1.992579327285E-02 -5.951921578598E-02  1.040704228546E-01
7      1.232154652110E-01  1.634305404407E-02  5.951841980010E-02
7      2.220759010770E-02 -7.142100857312E-02  3.299259852838E-01
7      2.054067942916E-01  2.817244373261E-02  1.473285310628E-01
8     -4.761487685316E-02 -8.656669456613E-02  4.192568497756E-01
8      9.327421157186E-02 -6.479426971916E-02  4.286363161888E-01
8      2.563441491059E-01 -1.128705054032E-02  1.760581823035E-01
8      2.225071782791E-01  7.736574474011E-02  1.903699942346E-01
FREQCALC
INTENS
END
END
8 4
0 0 6 2.0 1.0
 5484.671700         0.1831100000E-02
 825.2349500         0.1395010000E-01
 188.0469600         0.6844510000E-01
 52.96450000         0.2327143000    
 16.89757000         0.4701930000    
 5.799635300         0.3585209000  
0 1 3 6.0 1.0
 15.53961600        -0.1107775000         0.7087430000E-01
 3.599933600        -0.1480263000         0.3397528000    
 1.013761800          1.130767000         0.7271586000    
0 1 1 0.0 1.0
 0.2700058000          1.000000000          1.000000000
0 3 1 0.0 1.0
 0.800000000          1.00000000    
7 4
0 0 6 2.0 1.0
       4173.51100         0.183480000E-02
       627.457900         0.139950000E-01
       142.902100         0.685870000E-01
       40.2343300         0.232241000    
       12.8202100         0.469070000    
       4.39043700         0.360455000    
0 1 3 5.0 1.0
       11.6263580        -0.114961000         0.675800000E-01
       2.71628000        -0.169118000         0.323907000    
      0.772218000          1.14585200         0.740895000    
0 1 1 0.0 1.0
      0.212031300          1.00000000          1.00000000    
0 3 1 0.0 1.0
 0.800000000          1.00000000    
6 4
0 0 6 2.0 1.0
    .3047524880D+04   .1834737130D-02
    .4573695180D+03   .1403732280D-01
    .1039486850D+03   .6884262220D-01
    .2921015530D+02   .2321844430D+00
    .9286662960D+01   .4679413480D+00
    .3163926960D+01   .3623119850D+00
0 1 3 4.0 1.0
    .7868272350D+01  -.1193324200D+00   .6899906660D-01
    .1881288540D+01  -.1608541520D+00   .3164239610D+00
    .5442492580D+00   .1143456440D+01   .7443082910D+00
0 1 1 0.0 1.0
    .1687144782D+00   .1000000000D+01   .1000000000D+01
0 3 1 0.0 1.0
    .8000000000D+00   .1000000000D+01
1 3
0 0 3 1.0 1.0
    .1873113696D+02   .3349460434D-01
    .2825394365D+01   .2347269535D+00
    .6401216923D+00   .8137573262D+00
0 0 1 0.0 1.0
    .1612777588D+00   .1000000000D+01
0 2 1 0.0 1.0
    .1100000000D+01   .1000000000D+01
99 0
END
DFT
B3LYP
XLGRID
END
EXCHSIZE
10654700
BIPOSIZE
10654700
TOLINTEG
8 8 8 8 16
SCFDIR
MAXCYCLE
100
TOLDEE
11
GRIMME
1.05 20. 25.
4
1 0.14 1.001
6 1.75 1.452 
7 1.23 1.397
8 0.70 1.342
SHRINK
8 8
LEVSHIFT
5 0
FMIXING
50
END
END

Upon completion of this run, you need only the FREQINFO.DAT file, the last set of coordinates from the .OUT file (for atom counting purposes) and an input file which is modified from the original only in the specification of the ISOTOPES section and which includes a RESTART.

Question – how does one deal with isotopically-labeling atoms when it breaks the space group symmetry? If I isotopically label Atom 1 in the asymmetric unit, what happens to the other N symmetry-related atoms?

Answer – Crystal09, in its infinite wisdom, does not consider the asymmetric unit in the isotopic substitution scheme. If you’ve 14 atoms in the asymmetric unit (the symmetry-unique atoms you provide in the input file)…

14
6      1.016493675797E-01 -4.109909899348E-02 -3.351438244488E-03
6     -6.539109813231E-02 -6.180633576707E-02 -1.110575784790E-02
...
8      2.563441491059E-01 -1.128705054032E-02  1.760581823035E-01
8      2.225071782791E-01  7.736574474011E-02  1.903699942346E-01

and 56 atoms in the full unit cell…

ATOMS IN THE ASYMMETRIC UNIT   14 - ATOMS IN THE UNIT CELL:   56
     ATOM              X/A                 Y/B                 Z/C    
 *******************************************************************************
   1 T   6 C    -1.460999048177E-01  1.393970283287E-01  6.390170683069E-02
   2 F   6 C     1.393970283287E-01 -1.460999048177E-01 -5.719883034171E-02
   3 F   6 C     3.071988303417E-01  1.860982931693E-01  1.106029716713E-01
   4 F   6 C     1.860982931693E-01  3.071988303417E-01  3.960999048177E-01
...
  53 T   8 O     4.522856069554E-02  3.355114277736E-01  1.095029287847E-01
  54 F   8 O     3.355114277736E-01  4.522856069554E-02 -4.902429172538E-01
  55 F   8 O    -2.597570827462E-01  1.404970712153E-01 -8.551142777356E-02
  56 F   8 O     1.404970712153E-01 -2.597570827462E-01  2.047714393045E-01

your ISOTOPES section relies on the numbering of the atoms in the “56 atom” list.

The input file below will calculate an isotopically-labeled vibrational spectrum for 8 of the hydrogen atoms that ends up breaking the unit cell symmetry (which will be more obvious from the produced mode energies). Again, the atom numbers come from the “ATOMS IN THE ASYMMETRIC UNIT” part of the original optimization by which you performed the original normal mode analysis (hopefully).

Test - alpha-HMX 6-31Gdp set DFT/B3LYP FREQ - Isotopic Substitution
CRYSTAL
0 0 0
43
15.14 23.89 5.913 124.3
14
6      1.016493675797E-01 -4.109909899348E-02 -3.351438244488E-03
6     -6.539109813231E-02 -6.180633576707E-02 -1.110575784790E-02
1      9.149797846691E-02 -4.382919469310E-02 -1.860042940246E-01
1      1.558888705857E-01 -6.829708099502E-02  4.595161229829E-02
1     -5.138242817334E-02 -5.844587273099E-02 -1.920922064181E-01
1     -9.781600273101E-02 -1.015710562102E-01  2.063738273292E-02
7      1.992579327285E-02 -5.951921578598E-02  1.040704228546E-01
7      1.232154652110E-01  1.634305404407E-02  5.951841980010E-02
7      2.220759010770E-02 -7.142100857312E-02  3.299259852838E-01
7      2.054067942916E-01  2.817244373261E-02  1.473285310628E-01
8     -4.761487685316E-02 -8.656669456613E-02  4.192568497756E-01
8      9.327421157186E-02 -6.479426971916E-02  4.286363161888E-01
8      2.563441491059E-01 -1.128705054032E-02  1.760581823035E-01
8      2.225071782791E-01  7.736574474011E-02  1.903699942346E-01
FREQCALC
RESTART
ISOTOPES
8
9  2
10 2
11 2
13 2
14 2
15 2
16 2
18 2
INTENS
END
END
8 4
0 0 6 2.0 1.0
 5484.671700         0.1831100000E-02
 825.2349500         0.1395010000E-01
 188.0469600         0.6844510000E-01
 52.96450000         0.2327143000    
 16.89757000         0.4701930000    
 5.799635300         0.3585209000  
0 1 3 6.0 1.0
 15.53961600        -0.1107775000         0.7087430000E-01
 3.599933600        -0.1480263000         0.3397528000    
 1.013761800          1.130767000         0.7271586000    
0 1 1 0.0 1.0
 0.2700058000          1.000000000          1.000000000
0 3 1 0.0 1.0
 0.800000000          1.00000000    
7 4
0 0 6 2.0 1.0
       4173.51100         0.183480000E-02
       627.457900         0.139950000E-01
       142.902100         0.685870000E-01
       40.2343300         0.232241000    
       12.8202100         0.469070000    
       4.39043700         0.360455000    
0 1 3 5.0 1.0
       11.6263580        -0.114961000         0.675800000E-01
       2.71628000        -0.169118000         0.323907000    
      0.772218000          1.14585200         0.740895000    
0 1 1 0.0 1.0
      0.212031300          1.00000000          1.00000000    
0 3 1 0.0 1.0
 0.800000000          1.00000000    
6 4
0 0 6 2.0 1.0
    .3047524880D+04   .1834737130D-02
    .4573695180D+03   .1403732280D-01
    .1039486850D+03   .6884262220D-01
    .2921015530D+02   .2321844430D+00
    .9286662960D+01   .4679413480D+00
    .3163926960D+01   .3623119850D+00
0 1 3 4.0 1.0
    .7868272350D+01  -.1193324200D+00   .6899906660D-01
    .1881288540D+01  -.1608541520D+00   .3164239610D+00
    .5442492580D+00   .1143456440D+01   .7443082910D+00
0 1 1 0.0 1.0
    .1687144782D+00   .1000000000D+01   .1000000000D+01
0 3 1 0.0 1.0
    .8000000000D+00   .1000000000D+01
1 3
0 0 3 1.0 1.0
    .1873113696D+02   .3349460434D-01
    .2825394365D+01   .2347269535D+00
    .6401216923D+00   .8137573262D+00
0 0 1 0.0 1.0
    .1612777588D+00   .1000000000D+01
0 2 1 0.0 1.0
    .1100000000D+01   .1000000000D+01
99 0
END
DFT
B3LYP
XLGRID
END
EXCHSIZE
10654700
BIPOSIZE
10654700
TOLINTEG
8 8 8 8 16
SCFDIR
MAXCYCLE
100
TOLDEE
11
GRIMME
1.05 20. 25.
4
1 0.14 1.001
6 1.75 1.452 
7 1.23 1.397
8 0.70 1.342
SHRINK
8 8
LEVSHIFT
5 0
FMIXING
50
END
END

The difference is in the FREQCALC section, which calls RESTART (to use the FREQINFO.DAT file), ISOTOPES (obvious), the total number of atoms that are having their isotopes changed (8), then the list, containing the atom number and the new mass (here, 2 for deuterium).

The proof is in the high-frequency region, where the last 16 modes (H-atom motion) in the non-deuterated form…

 HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH

    MODES         EIGV          FREQUENCIES     IRREP  IR   INTENS    RAMAN
             (HARTREE**2)   (CM**-1)     (THZ)             (KM/MOL)
...
  153- 153    0.2003E-03   3106.1384   93.1197  (A2 )   I (     0.00)   A
  154- 154    0.2003E-03   3106.5054   93.1307  (B1 )   A (     0.02)   A
  155- 155    0.2004E-03   3106.5586   93.1323  (A1 )   A (     0.23)   A
  156- 156    0.2004E-03   3106.8420   93.1408  (B2 )   A (     0.48)   A
  157- 157    0.2017E-03   3117.1664   93.4503  (B2 )   A (     1.13)   A
  158- 158    0.2018E-03   3117.4901   93.4600  (B1 )   A (     2.33)   A
  159- 159    0.2021E-03   3120.2876   93.5439  (A1 )   A (   115.24)   A
  160- 160    0.2022E-03   3120.7805   93.5586  (A2 )   I (     0.00)   A
  161- 161    0.2131E-03   3203.6552   96.0432  (A1 )   A (    44.59)   A
  162- 162    0.2131E-03   3203.6581   96.0433  (B2 )   A (   115.98)   A
  163- 163    0.2132E-03   3204.6505   96.0730  (B1 )   A (    15.30)   A
  164- 164    0.2132E-03   3204.8874   96.0801  (A2 )   I (     0.00)   A
  165- 165    0.2157E-03   3223.4669   96.6371  (A1 )   A (    44.98)   A
  166- 166    0.2157E-03   3223.5803   96.6405  (B2 )   A (    27.02)   A
  167- 167    0.2158E-03   3223.8536   96.6487  (B1 )   A (    35.26)   A
  168- 168    0.2158E-03   3224.3355   96.6631  (A2 )   I (     0.00)   A

change to the following last 16 modes (H/D-atom motion) upon deuteration. Note the mode energies split and the mode symmetries go from (A1,A2,B1,B2) to (A). Also note your IR mode intensities change, giving you the complete picture upon isotopic substitution.

 HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH

    MODES         EIGV          FREQUENCIES     IRREP  IR   INTENS    RAMAN
             (HARTREE**2)   (CM**-1)     (THZ)             (KM/MOL)
...
  153- 153    0.1074E-03   2274.8942   68.1996  (A  )   A (     1.07)   A
  154- 154    0.1075E-03   2275.5949   68.2206  (A  )   A (     3.75)   A
  155- 155    0.1075E-03   2275.7008   68.2238  (A  )   A (     2.93)   A
  156- 156    0.1099E-03   2300.7446   68.9746  (A  )   A (     4.68)   A
  157- 157    0.1148E-03   2351.7846   70.5047  (A  )   A (    11.32)   A
  158- 158    0.1183E-03   2387.0269   71.5613  (A  )   A (    36.17)   A
  159- 159    0.1183E-03   2387.2610   71.5683  (A  )   A (    16.04)   A
  160- 160    0.1184E-03   2387.6687   71.5805  (A  )   A (     3.73)   A
  161- 161    0.2006E-03   3108.6223   93.1942  (A  )   A (     0.93)   A
  162- 162    0.2009E-03   3110.5061   93.2506  (A  )   A (    12.43)   A
  163- 163    0.2009E-03   3110.7567   93.2581  (A  )   A (    13.67)   A
  164- 164    0.2039E-03   3134.0133   93.9554  (A  )   A (    40.48)   A
  165- 165    0.2147E-03   3215.5160   96.3987  (A  )   A (    19.38)   A
  166- 166    0.2157E-03   3223.4291   96.6360  (A  )   A (    35.29)   A
  167- 167    0.2157E-03   3223.5925   96.6409  (A  )   A (    29.50)   A
  168- 168    0.2158E-03   3223.8729   96.6493  (A  )   A (     8.37)   A

Terahertz Spectroscopic Investigation Of S-(+)-Ketamine Hydrochloride And Vibrational Assignment By Density Functional Theory, “Function Follows Functional Follows Formalism”

Accepted in the Journal of Physical Chemistry A, with my fingers crossed for pulling off the rare double-header in an upcoming print edition of the journal (having missed it by three intermediate articles with the Cs2B12H12 and HMX papers back in 2006 (you’d keep track, too). A fortuitous overlap of scheduled defense dates between P. Hakey, Ph.D. and M. Hudson, A.B.D.). A brief summary of interesting points from this study is provided below, including what I think is a useful point about how to most easily interpret AND represent solid-state vibrational spectra for publications.

1. AS USUAL, YOU CANNOT USE GAS-PHASE CALCULATIONS TO ASSIGN SOLID-STATE TERAHERTZ SPECTRA. It will take a phenomenal piece of data and one helluvan interpretation to convince me otherwise. As a more subtle point (for those attempting an even worse job of vibrational mode assignment), if the molecule exists in its protonated form in the solid-state, do not use the neutral form for your gas-phase calculation (this is a point that came up as part of an MDMA re-assignment published (and posted here) previously).

2. It is very difficult to find what I would consider to be “complete data sets” for molecules and solids being studied by spectroscopic and computational methods. For many molecular solids, the influences of thermal motion are not important to providing a proper vibrational analysis by solid-state density functional theory methods. Heating a crystal may make spectral lines broader, but phase changes and unusual spectral features do not often result when heating a sample from cryogenic (say, liquid nitrogen) to room temperature. Yes, there are thousands of cases where this is not true, but several fold more cases where it is. We are fortunate to live in a temperature regime where characterization is reasonably straightforward and yet we can modify a system to observe its subtle changes under standard laboratory conditions. The THz spectrum of S-(+)-Ketamine Hydrochloride gets a bit cleaner upon cooling, which makes the assignment easier. As the ultimate goal is to be able to characterize these systems in a person’s pocket instead of their liquid nitrogen thermos, the limited observed change to the spectrum upon cooling is important to note.

3. Crystal06 vs. DMol3 – This paper contains what is hoped to be a level, pragmatic discussion about the strengths and weaknesses of computational tools available to terahertz spectroscopists for use in their efforts to assign spectra. This type of discussion is, as a computational chemist using tools and not developing tools, a touchy subject to present on not because of the finger-pointing of limitations with software, but because the Crystal06 team and Accelrys (through Delley’s initial DMol3 code) clearly are doing things that the vast majority of their users (myself included) could in no way do by themselves. The analysis for the theory-minded terahertz spectroscopist is presented comparing two metrics – speed and functionality (specifically, infra-red intensity prediction). What is observed as the baseline is that both DMol3 and Crystal06 make available density functionals and basis sets that, when used at high levels of theory and rigorous convergence criteria, produce simulated terahertz spectra with vibrational mode energies that are in good (if not very good) agreement with each other. For the terahertz spectroscopist, Crystal06 provides as output (although this is system size- and basis set size-dependent) rigorous infrared intensity predictions for vibrational modes, inseparable from mode energy as “the most important” pieces of information for mode assignments. While DMol3 does not produce infrared intensities (the many previous terahertz papers I’ve worked on employed difference-dipole calculations that are, at best, a guesstimate), DMol3 produces very good mode energy predictions in 1/6th to (I’ve seen it happen) 1/10th the time of a comparable Crystal06 calculation. This is the reason DMol3 has been the go-to program for all of the neutron scattering spectroscopy papers cited on this blog (where intensity is determined by normal mode eigenvectors, which are provided by both (and any self-respecting quantum chemical code) programs).

Now, it should be noted that this difference in functionality has NOTHING to do with formalism. Both codes are excellent for what they are intended to do. To the general assignment-minded spectroscopist (the target audience of the Discussion in the paper), any major problem with Crystal06 likely originates with the time to run calculations (and, quite frankly, the time it takes to run a calculation is the worst possible reason for not running a calculation if you need that data. Don’t blame the theory, blame the deadline). In my past exchanges with George Fitzgerald of Accelrys, the issue of DMol3 infrared intensities came up as a feature request that would greatly improve the (this) user experience and Dr. Fitzgerald is very interested (of course) in making a great code that much better. Neither code will be disappearing from my toolbox anytime soon.

4. The Periodicity Of The Molecular Solid Doesn’t Care What The Space Group Is – One of the more significant problems facing the assignment-minded spectroscopist is the physical description of molecular motion in a vibrational mode. In the simplest motions involving the most weakly interacting molecules, translational and rotational motions are often quite easy to pick out and state as such. When the molecules are very weakly interacting, often the intramolecular vibrational modes are easy to identify as well, as they are largely unchanged from their gas-phase descriptions. In ionic solids or strongly hydrogen-bonded systems, it is often much harder to separate out individual molecular motions from “group modes” involving the in- and out-of-phase motions of multiple molecules. In the unit cells of molecular solids, it can be the case that these group modes appear, by inspection, to be extremely complicated, sometimes too involved to easily describe in the confines of a table in a journal article.

S-(+)-Ketamine Hydrochloride is one such example where a great simplification in vibrational mode description comes from thinking, well, “outside the box.” The image below shows two cells and the surrounding molecules of S-(+)-Ketamine Hydrochloride. As it is difficult to see why the mode descriptions are complex from just an image, assume that I am right in this statement of complexity. Part of this complexity comes from the fact that the two molecules in the unit cell are not strongly interacting, instead packed together by van der Waals and dispersion forces more than anything else. The key to a greatly simplified assignment comes from the realization that the most polar fragments of these molecules are aligned on the edges of the unit cell.

An alternate view of molecular vibrational motion comes from considering not the contents of the defined unit cell but the hydrogen-bonding and ionic bonding arrangement that exists between pairs of molecules between unit cells. The colorized image below shows two distinct chains (red and blue) that, when the predicted vibrational modes are animated, become trivial to characterize as the relative motions of a hydrogen/ionic-bonded chain. Rotational motions appear as spinning motions of the chains, translational motions as either chain sliding motions or chain breathing modes. It appears as a larger macromolecule undergoing very “molecular” vibrations. In optical vibrational spectroscopy, selection rules and the unit cell arrangement do not produce in- and out-of-phase motions of the red and blue chains, as only one “chain” exists in the periodicity of the unit cell. In neutron scattering spectroscopy, these relative motions between red and blue would appear in the phonon region. This same discussion was had, in part, in a previous post on the solid-state terahertz assignment of ephedrine (with a nicer picture).

So, look at the cell contents, then see if there’s more structure than crystal packing would indicate. It greatly simplifies the assignment (which, in turn. greatly simplifies the reader’s digestion of the vibrational motions).

Patrick M. Hakey, Damian G. Allis, Matthew R. Hudson, Wayne Ouellette, and Timothy M. Korter

Department of Chemistry, Syracuse University, Syracuse, New York 13244-4100

Abstract: The terahertz (THz) spectrum of (S)-(+)-ketamine hydrochloride has been investigated from 10 to 100 cm-1 (0.3-3.0 THz) at both liquid-nitrogen (78 K) and room (294 K) temperatures. Complete solid-state density functional theory structural analyses and normal-mode analyses are performed using a single hybrid density functional (B3LYP) and three generalized gradient approximation density functionals (BLYP, PBE, PW91). An assignment of the eight features present in the well-resolved cryogenic spectrum is provided based upon solid-state predictions at a PW91/6-31G(d,p) level of theory. The simulations predict that a total of 13 infrared- active vibrational modes contribute to the THz spectrum with 26.4% of the spectral intensity originating from external lattice vibrations.

pubs.acs.org/journal/jpcafh
www.somewhereville.com/?p=29
www.somewhereville.com/?p=26
www.somewhereville.com/?p=126
en.wikipedia.org/wiki/Density_functional_theory
en.wikipedia.org/wiki/Ketamine
www.crystal.unito.it
accelrys.com/products/materials-studio/quantum-and-catalysis-software.html
en.wikipedia.org/wiki/Time_domain_terahertz_spectroscopy
en.wikipedia.org/wiki/Computational_chemistry
accelrys.com
en.wikipedia.org/wiki/Inelastic_neutron_scattering
en.wikipedia.org/wiki/Vibrational_spectroscopy
www.somewhereville.com/?p=680

Investigation of Crystalline 2-Pyridone Using Terahertz Spectroscopy and Solid-State Density Functional Theory

Accepted in Chemical Physics Letters. A solid-state density functional theory (DFT) follow-up to the solution-phase 2-pyridone (2PD) study published by Motley and Korter previously. Much of the work-up for this paper was straightforward, run-of-the-mill calculation and correlation (on the theory side, anyway). The most difficult part of the analysis was the identification of the easiest way to present the normal mode analysis of the 2PD crystal cell.

In terahertz (THz) spectroscopy, one observes the lowest-frequency vibrational motions of molecules (if the molecule has low-lying vibrational modes, of course). In the solid-state (such as molecular crystals), one observes both low-lying molecular vibrational motions (if they exist) and the relative motions between molecules in the unit cell. The boilerplate separation of internal (intramolecular) and external (between-molecule) modes is performed (and presented) as follows:

A crystal unit cell containing M molecules with N atoms contains 3N-6M internal modes (those modes associated with intramolecular motions), 6M-3 external modes (those modes associated with relative motions between the M molecules, such as rotations and translations), and three acoustic modes.

Some molecules simply do not absorb in the THz region, so all assignments are for external motions (and one simply identifies molecules sliding along axes or spinning around their centers of mass in their lattice site). Some molecules are very strongly bound to neighboring molecules in their lattice sites, which results in significant changes to the mode energies of low-lying vibrational modes (these are far more complicated systems to perform assignments of and a few of these cases are being prepared for future publications). Some molecules are strongly bound in very localized ways in their crystal cell to neighboring molecules and are very weakly bound to other neighbors in other ways. In 2PD, chains of molecules are strongly bound through hydrogen bonding along the crystal c-axis (see the figure below) and only weakly interacting between chains. In the figure below, the blue and red chains are strongly coupled in-chain (hydrogen-bonding) and only weakly coupled (dispersion and van der Waals forces) between chains.

The assignment of the 2PD solid is simplified by two important facts. First, the two chains (red and blue) are related by symmetry (the unit cell contains two anti-parallel 2PD chains). Second, the chains are very weakly interacting.

What point 1 means is that the chains, if in isolation, would undergo the same vibrational motions at the same energies (as if the chains were simply chiral molecules).

What point 2 means is that these chains are, because they interact very weakly, approaching a limit where there can, in fact, be considered isolated chains so that the unit cell will contain vibrational motions that involve the two chains undergoing the same motion in-phase with respect to reach other (in-phase here meaning that, for instance, both of your lungs are expanding at the same time) and out-of-phase with respect each other (the hypothetical case where the left and right lobes are out-of-sync with one another).

For instance, if both chains are sliding along the crystal c-axis in a vibrational mode, that makes the mode the in-phase acoustic translation in c (because the whole cell is sliding in one direction). If the two chains are sliding in opposite directions with respect to each other, this makes the mode the optical translation in c (the center of mass of the cell stays put while the chains undergo out-of-phase motions).

This simplification for the 2PD assignment (and other solid-state molecular chains) turned out to be the mode assignment based on the treatment of not the in-cell contents of atoms and molecular fragments (if we kept ourselves to only viewing what is happening in the cell, for instance), but instead the relative motions of the chains, which requires ever-so-slightly thinking outside of the box.

Tanieka L. Motley, Damian G. Allis, and Timothy M. Korter*

Department of Chemistry, Syracuse University, Syracuse, NY 13244-4100

Crystalline 2-pyridone has been investigated using terahertz vibrational spectroscopy in the range of 10 to 90 cm-1 (0.3 to 2.7 THz). Solid-state density functional theory (B3LYP, BP, and PW91 with the 6-311G(d,p) basis set) was used to simulate and assign both observed terahertz spectral features and a previously published far-infrared spectrum up to 400 cm-1. The PW91 functional was found to provide the best combination of crystal structure and vibrational frequency reproduction. Observed spectral features below 150 cm-1 are assigned to intermolecular movements of the 2-pyridone chains within the unit cell. The use of independent intramolecular and intermolecular frequency scalars is proposed.

www.sciencedirect.com/science/journal/00092614
dx.doi.org/10.1016/j.cplett.2008.09.021
en.wikipedia.org/wiki/2-Pyridone
en.wikipedia.org/wiki/Density_functional_theory
en.wikipedia.org/wiki/Terahertz
en.wikipedia.org/wiki/Vibrational_spectroscopy
en.wikipedia.org/wiki/Hydrogen_bonds
en.wikipedia.org/wiki/Van_der_Waals_force
en.wikipedia.org/wiki/Chirality_(chemistry)
en.wikipedia.org/wiki/Phonon