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

Wednesday, November 21st, 2012

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

Running (Only) A Single-Point Energy Calculation In Crystal06/09, Proper Input Format For Long-Range Dispersion Contributions In Crystal09, And Removing The MPICH2 Content From The Output File In Pcrystal

Saturday, May 29th, 2010

Now enjoying the benefits of dispersion-corrected solid-state density functional theory (and a proper MPICH2 implementation for infrared intensity calculations, although this now a problem for reasons to be addressed in an upcoming post) in Crystal09, three issues in recent calculations caused me to think hard enough about keyword formats and job runs that I have opted to post briefly about what to do in case google and bing are your preferred methods of manual searching.

1. How To Run Only A Single-Point Energy Calculation In Crystal06/Crystal09

This had never come up before and, by the time I needed to find an input file to see what do to, the first google search provided Civalleri’s Total Energy Calculation page that currently has broken links to .zip files. There is quite a bit about the different geometry optimization approaches in the manual, but a search for “single-point” provides no information about what to do for only single-point energy calculations.

The solution, it should be obvious after, is simply to not include the geometry optimization section in the input file. What would otherwise be the following (with arbitrary geometry optimization-like info between [COORDINATES] and [BASIS SETS]…

[COORDINATES]
OPTGEOM
TOLDEG
0.000005
TOLDEX
0.000020
END
END
[BASIS SETS]

becomes…

[COORDINATES]
[BASIS SETS]

One problem solved by simply not having any optimization parameters (again, makes sense and is now google-able).

2. Proper GRIMME Input Format For Long-Range Dispersion Contributions In Crystal09

This is another example where one’s first efforts in translating the manual into calculations may lead to considerable confusion until the proper format is finally identified (by which time you’ve run many pruned-down input tests).

GRIMME
1.05 20. 25.
1.05 20. 25. s6 (scaling factor) d (steepness) Rcut (cutoff radius)
5
1  0.14 1.001 Hydrogen Conventional Atomic number , C6 , Rvdw
6  1.75 1.452 Carbon Conventional Atomic number , C6 , Rvdw
7  1.23 1.397 Nitrogen Conventional Atomic number , C6 , Rvdw
8  0.70 1.342 Oxygen Conventional Atomic number , C6 , Rvdw
17 5.07 1.639 Chlorine Conventional Atomic number , C6 ,'Rvdw

I’m not even sure where the final ,’Rvdw comes from. Your .out file may terminate with the following error (or something similar)…

rank 7 in job 8  korterquad_51438   caused collective abort of all ranks
  exit status of rank 7: killed by signal 9

And the ERROR.peN file with any content will show the following, clearly pointing to a GRIMME-specific error…

 ERROR **** GRIMME_INPUT **** ELEMENT NOT DEFINED:           1

The problem is the additional content within the manual pages for the GRIMME keyword that require pruning (or, at least, some identifier to show what is and what is not needed). The proper GRIMME section above is properly provided in the INPUT file as…

GRIMME
1.05 20. 25.
5
1  0.14 1.001
6  1.75 1.452
7  1.23 1.397
8  0.70 1.342
17 5.07 1.639

Where (see page 88 of the Crystal09 manual)…

GRIMME <- keyword is called
1.05 20. 25. <- scaling factor, steepness, cutoff distance
5 <- number of elements in the list (not the total number of atoms)
1  0.14 1.001 <- atomic number, dispersion coefficient, van der Waals radius
...

When all is properly run, the bottom of your output file will look something like the following:

 CYC  43 ETOT(AU) -5.784662098123E+03 DETOT  1.18E-11 tst  8.17E-15 PX  6.73E-08

 == SCF ENDED - CONVERGENCE ON ENERGY      E(AU) -5.7846620981229E+03 CYCLES  43

 ENERGY EXPRESSION=HARTREE+FOCK EXCH*0.20000+(BECKE  EXCH)*0.80000+LYP    CORR

 TOTAL ENERGY(DFT)(AU)( 43) -5.7846620981229E+03 DE 1.2E-11 tester 8.2E-15
 TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT EDFT        TELAPSE     4705.82 TCPU     4651.41

 *******************************************************************************

 GRIMME DISPERSION ENERGY CORRECTION

 SCALE FACTOR (S6):     1.0500

 GRIMME DISPERSION ENERGY (AU) -1.9723347118951E-01
 TOTAL ENERGY + DISP (AU) -5.7848593315941E+03

 *******************************************************************************

The Crystal09 manual refers you to Table 1 of the Stefan Grimme paper, “Semiempirical GGA-type density functional constructed with a long-range dispersion correction” (Journal of Computational Chemistry, Volume 27, Issue 15, Pages 1787 – 1799), which I’ve put together into the proper format below. Be sure to (1) delete the elements in parentheses ( -> get rid of the (H) <- ), (2) remove those atoms you do not need, (3) be sure to change the “number of elements” number for your structure, and (4) get and reference the Grimme paper so you have the proper C6 parameters and van der Waals radii accounted for (you’ll be the right nitwit if I mis-copied something and you ran with it (although I trust my input), and you should have the reference regardless).

( H)   1   0.14 1.001
(Li)   3   1.61 0.825
(Na)  11   5.71 1.144
( K)  19  10.80 1.485
(Rb)  37  24.67 1.628
(Be)   4   1.61 1.408
(Mg)  12   5.71 1.364
(Ca)  20  10.80 1.474
(Sr)  38  24.67 1.606
( B)   5   3.13 1.485
(Al)  13  10.79 1.639
(Ga)  31  16.99 1.650
(In)  49  37.32 1.672
( C)   6   1.75 1.452
(Si)  14   9.23 1.716
(Ge)  32  17.10 1.727
(Sn)  50  38.71 1.804
( N)   7   1.23 1.397
( P)  15   7.84 1.705
(As)  33  16.37 1.760
(Sb)  51  38.44 1.881
( O)   8   0.70 1.342
( S)  16   5.57 1.683
(Se)  34  12.64 1.771
(Te)  52  31.74 1.892
( F)   9   0.75 1.287
(Cl)  17   5.07 1.639
(Br)  35  12.47 1.749
( I)  53  31.50 1.892
(He)   2   0.08 1.012
(Ne)  10   0.63 1.243
(Ar)  18   4.61 1.595
(Kr)  36  12.01 1.727
(Xe)  54  29.99 1.881
Y-Cd      24.67 1.639
Sc-Zn     10.80 1.562

Note that the d-block is identical for each row (so no atom numbers provided).

3. Removing The MPICH2 Content From The Output File In Pcrystal(/09)

This final issue does not occur in Pcrystal(/06) but does in Pcrystal(/09), with the reason being (I assume) the new use of MPICH2 in Pcrystal(/09) instead of MPICH in Pcrystal(/06).  The problem comes from running the following set of commands at the terminal window in MPICH2:

mpiexec -machinefile machine -np N /path/to/Pcrystal &>FILENAME.out &

Embedded within the FILENAME.out file will be all flavors of MPI-specific output, perhaps such as the following (in this case errors, but it happens in proper output as well):

application called MPI_Abort(MPI_COMM_WORLD, 1) - process 4
application called MPI_Abort(MPI_COMM_WORLD, 1) - process 7
rank 7 in job 9  korterquad_51438   caused collective abort of all ranks
 exit status of rank 7: return code 1 
rank 4 in job 9  korterquad_51438   caused collective abort of all ranks
 exit status of rank 4: killed by signal 9 

or…

mpiexec_machine (handle_stdin_input 1089): stdin problem; if pgm is run in background...
mpiexec_machine (handle_stdin_input 1090):     e.g.: mpiexec -n 4 a.out < /dev/null &

The solution is to break up the mpiexec output from the Pcrystal output, performed by directing the mpiexec-specific content to, in this case, /dev/null (because it is not necessary except for diagnostic purposes).

mpiexec -machinefile machine -np N /path/to/Pcrystal < /dev/null &>FILENAME.out &

Which removes all traces of mpi-specific output from FILENAME.out.

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

Sunday, February 21st, 2010

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

The Vibrational Spectrum Of Parabanic Acid By Inelastic Neutron Scattering Spectroscopy And Simulation By Solid-State DFT

Sunday, February 21st, 2010

Available as an ASAP in The Journal of Physical Chemistry A. As a general rule in computational chemistry, the smaller the molecule, the harder it is to get right. As a brief summary, parabanic acid has several interesting properties of significance to computational chemists as both a model for other systems containing similar sub-structures and as a complicated little molecule in its own right.

1. The solid-state spectrum requires solid-state modeling. This should be of no surprise (see the figure below for the difference in solid-state (top) and isolated-molecule (bottom)). This task was undertaken with both DMol3 and Crystal06, with DMol3 calculations responsible for the majority of the analysis of this system (as has always been the case in the neutron studies reported on this site).

2. The agreement in the hydrogen-bonded N-H…O vibrations is, starting from the crystal structure, in poor agreement with experiment. You’ll note the region between 750 and 900 cm-1 is a little too high (and for clarification, the simulated spectrum is in red below). According to the kitchen sink that Matt threw at the structure, the problem is not the same anharmonicity one would acknowledge by Dr. Walnut’s “catalytic handwaving” approach to spectrum assignment (Dr. Walnut does not engage in this behavior, rather endeavors to find it in others where it should not be).

3. The local geometry of the hydrogen-bonding network in this molecular solid leads to notable changes in parabanic acid structure that, in turn, leads to the different behavior of the N-H…O vibrational motions. There is one potentially inflammatory comment in the Conclusions section that results from this identification. The parabanic acid molecule is, at its sub-structure, a set of three constrained peptide linkages that under go subtle but vibrationally-observable changes to their geometry because of crystal packing and intermolecular hydrogen bond formation. This means that the isolated molecule and solid-state forms are different and that peptide groups are influenced by neighboring interactions.

So, why should one care? Suppose one is parameterizing a biomolecular force field (CHARMM, AMBER, GROMOS, etc.) using bond lengths, bond angles, etc., for the amino acid geometry and vibrational data for some aspect of the force constant analysis. The structural data for these force fields often originates with solid-state studies (diffraction results). This means, to those very concerned with structural accuracy, that a geometry we know to be influenced by solid-state interactions is being used as the basis for molecular dynamics calculations that will NOT be used in their solid-state forms. Coupled with the different spectral properties due to intermolecular interactions, the description being used as the basis for the biomolecular force field likely being used in solution (solvent box approaches) is based on data in a phase where the structure and dynamics are altered from their less conformationally-restricted counterpart (in this case, solid-state).

A subtle point, but that’s where applied theoreticians do some of their best work.

Matthew R. Hudson, Damian G. Allis, and Bruce S. Hudson

Department of Chemistry, 1-014 Center for Science and Technology, Syracuse University, Syracuse, New York 13244-4100

Abstract: The incoherent inelastic neutron scattering spectrum of parabanic acid was measured and simulated using solid-state density functional theory (DFT). This molecule was previously the subject of low-temperature X-ray and neutron diffraction studies. While the simulated spectra from several density functionals account for relative intensities and factor group splitting regardless of functional choice, the hydrogen-bending vibrational energies for the out-of-plane modes are poorly described by all methods. The disagreement between calculated and observed out-of-plane hydrogen bending mode energies is examined along with geometry optimization differences of bond lengths, bond angles, and hydrogen-bonding interactions for different functionals. Neutron diffraction suggests nearly symmetric hydrogen atom positions in the crystalline solid for both heavy-atom and N-H bond distances but different hydrogen-bonding angles. The spectroscopic results suggest a significant factor group splitting for the out-of-plane bending motions associated with the hydrogen atoms (N-H) for both the symmetric and asymmetric bending modes, as is also supported by DFT simulations. The differences between the quality of the crystallographic and spectroscopic simulations by isolated-molecule DFT, cluster-based DFT (that account for only the hydrogen-bonding interactions around a single molecule), and solid-state DFT are considered in detail, with parabanic acid serving as an excellent case study due to its small size and the availability of high-quality structure data. These calculations show that hydrogen bonding results in a change in the bond distances and bond angles of parabanic acid from the free molecule values.

pubs.acs.org/doi/abs/10.1021/jp9114095
pubs.acs.org/journal/jpcafh
en.wikipedia.org/wiki/Computational_chemistry
accelrys.com/products/materials-studio/quantum-and-catalysis-software.html
www.crystal.unito.it
en.wikipedia.org/wiki/Anharmonicity
chemistry.syr.edu/faculty/walnut.html
en.wikipedia.org/wiki/Hydrogen_bond
en.wikipedia.org/wiki/Peptide
en.wikipedia.org/wiki/Force_field_%28chemistry%29
www.charmm.org
ambermd.org
gromacs.org
en.wikipedia.org/wiki/Molecular_dynamics

Examination of Phencyclidine Hydrochloride via Cryogenic Terahertz Spectroscopy, Solid-State Density Functional Theory, and X-Ray Diffraction

Wednesday, September 30th, 2009

“I’m high on life… and PCP.” – Mitch Hedberg

In press, in the Journal of Physical Chemistry A. If the current rosters of pending manuscripts and calculations are any indication, this PCP paper will mark the near end of my use of DMol3 for the prediction (and experimental assignment) of terahertz (THz) spectra (that said, it is still an excellent tool for neutron scattering spectroscopy and is part of several upcoming papers).

While the DMol3 vibrational energy (frequency) predictions are generally in good agreement with experiment (among several density functionals, including the BLYP, BOP,VWN-BP, and BP generalized gradient approximation density functionals), the use of the difference-dipole method for the calculation of infrared intensities has shown itself to be of questionable applicability when the systems being simulated are charged (either molecular salts (such as PCP.HCl) or zwitterions (such as the many amino acid crystal structures)). The previously posted ephedrine paper (in ChemPhysChem) is most interesting from a methodological perspective for the phenomenal agreement in both mode energies AND predicted intensities obtained using Crystal06, another solid-state density functional theory program (that has implemented hybrid density functionals, Gaussian-type basis sets, cell parameter optimization and, of course, a more theoretically sound prediction of infrared intensities by way of Born charges). The Crystal06 calculations take, on average, an order of magnitude longer to run than the comparable DMol3 calculations, but the slight additional gain in accuracy for good density functionals, the much greater uniformity of mode energy predictions across multiple density functionals (when multiple density functionals are tested), and the proper calculation of infrared intensities all lead to Crystal06 being the new standard for THz simulations.

After a discussion with a crystallographer about what theoreticians trust and what they don’t in a diffraction experiment, the topic of interatomic separation agreement between theory and experiment came up in the PCP.HCl analysis performed here (wasn’t Wayne). As the position of hydrogen atoms in an X-ray diffraction experiment are categorically one of those pieces of information solid-state theoreticians do NOT trust when presented with a cif file, I reproduce a snippet from the paper considering this difference below (and, generally, one will not find comparisons of crystallographically-determined hydrogen positions and calculated hydrogen positions in any of the THz or inelastic neutron scattering spectroscopy papers found on this blog).

The average calculated distance between the proton and the Cl- ion is 2.0148 Angstroms, an underestimation of nearly 0.13 Angstroms when compared to the experimental data. This deviation is likely strongly tied to the uncertainly in the proton position as determined by the X-ray diffraction experiment and is, therefore, not used as a proper metric of agreement between theory and experiment. The distance from the nitrogen atom to the Cl- ion has been determined to be an average of 3.0795 Angstroms, which is within 0.002 Angstroms of the experimentally determined bond length. This proper comparison of heavy atom positions between theory and experiment indicates that this interatomic separation has been very well predicted by the calculations.

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

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

The terahertz (THz) spectrum of phencyclidine hydrochloride from 7.0 – 100.0 cm-1 has been measured at cryogenic (78 K) temperature. The complete structural analysis and vibrational assignment of the compound have been performed employing solid-state density functional theory utilizing eight generalized gradient approximation density functionals and both solid-state and isolated-molecule methods. The structural results and the simulated spectra display the substantial improvement obtained by using solid-state simulations to accurately assign and interpret solid-state THz spectra. A complete assignment of the spectral features in the measured THz spectrum has been completed at a VWN-BP/DNP level of theory, with the VWN-BP density functional providing the best-fit solid-state simulation of the experimentally observed spectrum. The cryogenic THz spectrum contains eight spectral features that, at the VWN-BP/DNP level, consist of fifteen infrared-active vibrational modes. Of the calculated modes, external crystal vibrations are predicted to account for 42% of the total spectral intensity.

en.wikipedia.org/wiki/Mitch_Hedberg
pubs.acs.org/journal/jpcafh
en.wikipedia.org/wiki/Phencyclidine
accelrys.com/products/materials-studio/modules/dmol3.html
en.wikipedia.org/wiki/Terahertz_radiation
en.wikipedia.org/wiki/Density_functional_theory
en.wikipedia.org/wiki/Density_functional_theory#Approximations_.28Exchange-correlation_functionals.29
en.wikipedia.org/wiki/Zwitterions
en.wikipedia.org/wiki/Amino_acid
www.somewhereville.com/?p=680
www3.interscience.wiley.com/journal/122540399/abstract
www.crystal.unito.it
en.wikipedia.org/wiki/Basis_set_(chemistry)
en.wikipedia.org/wiki/X-ray_scattering_techniques
en.wikipedia.org/wiki/Inelastic_neutron_scattering
chemistry.syr.edu
www.syr.edu

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