Commensurate Urea Inclusion Crystals With The Guest (E,E)-1,4-Diiodo-1,3-Butadiene

Published in Crystal Growth & Design (Cryst. Growth Des., 2013, 13 (9), pp. 3852-3855) earlier this year. The theory work is less impressive than the successful crystal growth, with initial solid-state efforts in Crystal09 only very recently now producing good results (leaving the molecular calculations to Gaussian09 in this paper). The procedure leading to the observed crystal structure of this inclusion complex is a significant step in the direction of testing the theory proposed in Bond Alternation In Infinite Periodic Polyacetylene: Dynamical Treatment Of The Anharmonic Potential published earlier this year in J. Mol. Struct.

2013dec20_DIBD_UIC

Caption: Two views along the ba and ca crystal axes of the (E,E)‐1,4-Diiodo-1,3-Butadiene : Urea Inclusion Complex.

Amanda F. Lashua, Tiffany M. Smith, Hegui Hu, Lihui Wei, Damian G. Allis, Michael B. Sponsler, and Bruce S. Hudson

Abstract: The urea inclusion compound (UIC) with (E,E)-1,4-diiodo-1,3-butadiene (DIBD) as a guest (DIBD:UIC) has been prepared and crystallographically characterized at 90 and 298 K as a rare example of a commensurate, fully ordered UIC. The crystal shows nearly hexagonal channels in the monoclinic space group P21/n. The DIBD guest molecules are arranged end-to-end with the nonbonding iodine atoms in the van der Waals contact. The guest structure is compared with that for DIBD at 90 K and with computations for the periodic UIC and isolated DIBD molecule.

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