From owner-chemistry@ccl.net Mon Jun 5 09:29:00 2017 From: "Alcides Simao alsimao(!)gmail.com" To: CCL Subject: CCL:G: Anharmonic Infrared Spectroscopy Message-Id: <-52824-170604170255-21190-yTDPXkmqpIK+dcal+YkyIQ/a\server.ccl.net> X-Original-From: Alcides Simao Content-Type: multipart/alternative; boundary="94eb2c0be38666fca9055128b5f9" Date: Sun, 04 Jun 2017 21:02:36 +0000 MIME-Version: 1.0 Sent to CCL by: Alcides Simao [alsimao-.-gmail.com] --94eb2c0be38666fca9055128b5f9 Content-Type: text/plain; charset="UTF-8" Content-Transfer-Encoding: quoted-printable Welcome to the strange world of DFT implementation in quantum chemistry packages. There isn't but one single implementation of B3LYP, but rather several, differing essentially at the way the LDA correlation function is defined. By default, Gaussian uses the Vosko-Wilk-Nusair (VWN) - III implementation, whereas other software, like ORCA, uses both the -III and -V implementations - in other words, B3LYP and B3LYP/G-G. So, differences in the way these correlation functions are written may very well induce differences in both intensity and wavenumber. But there are other special issues to take into account - how is the numerical derivation carried out (methodology). This has a huge impact in the precision - and validity - of the calculation. There are a couple of discussions around regarding this issues. As for the basis set effect - the smaller it is, the more simplistic the system is described, which in turn ends up with more similar results (despite the use of (an)harmonicity) So, you could see if ORCA reproduces your results OR you can increase the accuracy of your calculation and see if by using more tight criterias if the phenomena is still reproducible. Still, I'm a bit baffled at your results. Perhaps someone can offer a more detailed explanation to this phenomena - of which I am extremely curious to understand, too! Best regards! Alcides ---------- Forwarded message --------- > From: Jens Spanget-Larsen spanget**ruc.dk Date: domingo, 4/06/2017 =C3=A0s 19:51 Subject: CCL:G: Anharmonic Infrared Spectroscopy To: Simao, Alcides Dear CCL! When I perform Gaussian calculations with the option freq=3Danharm, I frequently get strange results (Gaussian 09, Revision D.01). Below is a portion of the results of a b3lyp/6-311++G(d,p) calculation on a planar, aromatic, C2v symmetrical hydrocarbon. The anharmonic results are obviously ridiculous. With smaller basis sets, the results tend to be more realistic. Any explanations? Yours, Jens >--< =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D Anharmonic Infrared Spectroscopy =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D Fundamental Bands ----------------- Mode(Quanta) E(harm) E(anharm) I(harm) I(anharm) 1(1) 3476.017 3200.902 43.37436356 538.05352307 2(1) 3202.964 3109.532 0.01728522 255.35137878 3(1) 3200.221 3033.726 8.04709323 191.91610101 4(1) 3175.408 3220.259 4.37202654 2730.70615470 5(1) 2205.565 2153.406 1.97473796 11.71516009 6(1) 1604.309 1584.143 6.91156654 634.57714516 7(1) 1432.153 1374.467 3.54182113 12790.38891389 8(1) 1263.675 1263.359 0.79105395 139.40836060 9(1) 1112.643 1056.598 5.36740074 1394.13686552 10(1) 1010.305 1031.530 0.00269831 47.10463873 11(1) 717.365 793.822 1.28159522 103894.31384900 12(1) 697.978 1794.196 67.17706473 1444.46852987 13(1) 505.134 1553.018 6.40712425 16868.05994564 14(1) 465.540 608.353 2.04849136 24943.02416835 15(1) 115.463 594.923 0.77231918 6377.20573512 16(1) 930.354 -1253.748 0.00000000 0.00000039 17(1) 653.549 -2649.903 0.00000000 0.00000067 18(1) 621.501 -20992.872 0.00000000 0.01789241 19(1) 355.466 -1676.263 0.00000000 0.00001474 20(1) 156.168 -1653.479 0.00000000 0.00002682 21(1) 990.196 7085.310 0.11097137 176674.25100856 22(1) 925.704 -2638.620 16.28434626 228593.72377779 23(1) 811.788 1939.226 41.57436680 251187.21629870 24(1) 701.424 1649.690 14.23131322 *************** 25(1) 650.217 -656.428 106.61652268 433910.83299326 26(1) 493.743 16521.965 0.05960240 *************** 27(1) 378.821 -1503.535 5.22048529 779479.83775810 28(1) 121.625 -1543.939 2.61491704 76301.87107925 ....... ....... ------------------------------------------------------ JENS SPANGET-LARSEN Office: +45 4674 2710 <+45%2046%2074%2027%2010> Dept. of Science Fax: +45 4674 3011 <+45%2046%2074%2030%2011> Roskilde University Mobile: +45 2320 6246 <+45%2023%2020%2062%2046> P.O.Box 260 E-Mail: spanget||ruc.dk DK-4000 Roskilde, Denmark Web: thiele.ruc.dk/~spanget ------------------------------------------------------ --=20 Alcides Pinto Sim=C3=A3o, AMRSC, PhD. Student University of Coimbra Office: +351 239 852 080 / Fax: +351 239 827 703 Departamento de Qu=C3=ADmica da Universidade de Coimbra, 3004-535 COIMBRA, PORTUGAL Website: http://www.qui.uc.pt/ This e-mail message may contain confidential or legally privileged information and is intended only for the use of the intended recipient(s). Any unauthorized disclosure, dissemination, distribution, copying or the taking of any action in reliance on the information herein is prohibited. E-mails are not secure and cannot be guaranteed to be error free as they can be intercepted, amended, or contain viruses. Anyone who communicates with us by e-mail is deemed to have accepted these risks. University of Coimbra is not responsible for errors or omissions in this message and denies any responsibility for any damage arising from the use of e-mail. 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malgorzata.biczysko^-^sns.it" To: CCL Subject: CCL:G: Anharmonic Infrared Spectroscopy Message-Id: <-52825-170605074930-31121-QAooQ84a8tchHjkmE0PvWw||server.ccl.net> X-Original-From: Malgorzata Biczysko Content-Type: multipart/alternative; boundary="94eb2c1cccaa084f0505513518a6" Date: Mon, 5 Jun 2017 19:49:21 +0800 MIME-Version: 1.0 Sent to CCL by: Malgorzata Biczysko [malgorzata.biczysko-#-sns.it] --94eb2c1cccaa084f0505513518a6 Content-Type: text/plain; charset="UTF-8" Content-Transfer-Encoding: quoted-printable Dear Jens SPANGET-LARSEN, there can be few problems, maybe all of them together. 1. Generation of anharmonic force-field and dipole moment derivatives. To get reliable results FF need to be generated for at least "tight" optimized structure, and using at least int=3Dultrafine grid for DFT. If not, numerical errors m= ay lead to completely un-reliable results, like negative frequencies, huge corrections to energies etc. 2. Anharmonic resonances, in particular for intensities (1-1 resonances) That is most likely the case of modes 2 and 3 which have very similar harmonic wavenumbers, but just off the default threshold (2cm-1) . Solution is to change resonance criteria, for instance by using keyword Resonances=3D(DFreq11=3DXX) xx=3D5 or 10 can be a good choice there also ot= her options related to the magnitude of force constants (i.e Res11F3=3D0.0,Res11F4=3D0.0) 3. Coupling with low-freqency large amplitude motions (LAM) (i.e methyl rotation) This can be overcome by excluding LAM from VPT2 treatment, that is well tested and reliable procedure it can be done by using the keywords: DataMod=3DSkipPT2=3DModes RedDim=3DInactive=3D1 mode number You can note that several procedures, in particular for anharmonic resonances, including 1-1, have been modified to be more robust in their default version in G16. But, most importantly there is a large number of keywords which allow to set up GVPT2 computations accordingly to the system, i.e. not using VPT2 for floppy modes etc. However, first "must" is reliable generation of force constants, so the warnings in this part need to be also checked. Hope it helps, Best wishes, Malgorzata 2017-06-05 4:53 GMT+08:00 Robert Molt r.molt.chemical.physics-x-gmail.com < owner-chemistry|,|ccl.net>: > Is it plausible that there are degeneracies in the vibrational/rotational > spectrum, leading to the divergences you observe? This would be the most > obvious explanation for why the numbers blow up for any finite-order > perturbation theory. Perhaps you have coupled methyl groups? > > > With smaller basis sets, oftentimes the divergences in finite order > perturbation theory are "masked" (I've seen this with cc-pvdz vs. > aug-cc-pVDZ), simply because you have not yet encountered the denominator > problem. It's a "better" answer for wrong reasons. > > On 6/4/17 4:38 AM, Jens Spanget-Larsen spanget**ruc.dk wrote: > > Dear CCL! > When I perform Gaussian calculations with the option freq=3Danharm, I > frequently get strange results (Gaussian 09, Revision D.01). Below is a > portion of the results of a b3lyp/6-311++G(d,p) calculation on a planar, > aromatic, C2v symmetrical hydrocarbon. The anharmonic results are obvious= ly > ridiculous. With smaller basis sets, the results tend to be more realisti= c. > Any explanations? > > Yours, Jens >--< > > > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D > Anharmonic Infrared Spectroscopy > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D > > > > Fundamental Bands > ----------------- > Mode(Quanta) E(harm) E(anharm) I(harm) I(anharm) > 1(1) 3476.017 3200.902 43.37436356 538.0535230= 7 > 2(1) 3202.964 3109.532 0.01728522 255.3513787= 8 > 3(1) 3200.221 3033.726 8.04709323 191.9161010= 1 > 4(1) 3175.408 3220.259 4.37202654 2730.7061547= 0 > 5(1) 2205.565 2153.406 1.97473796 11.7151600= 9 > 6(1) 1604.309 1584.143 6.91156654 634.5771451= 6 > 7(1) 1432.153 1374.467 3.54182113 12790.3889138= 9 > 8(1) 1263.675 1263.359 0.79105395 139.4083606= 0 > 9(1) 1112.643 1056.598 5.36740074 1394.1368655= 2 > 10(1) 1010.305 1031.530 0.00269831 47.1046387= 3 > 11(1) 717.365 793.822 1.28159522 103894.3138490= 0 > 12(1) 697.978 1794.196 67.17706473 1444.4685298= 7 > 13(1) 505.134 1553.018 6.40712425 16868.0599456= 4 > 14(1) 465.540 608.353 2.04849136 24943.0241683= 5 > 15(1) 115.463 594.923 0.77231918 6377.2057351= 2 > 16(1) 930.354 -1253.748 0.00000000 0.0000003= 9 > 17(1) 653.549 -2649.903 0.00000000 0.0000006= 7 > 18(1) 621.501 -20992.872 0.00000000 0.0178924= 1 > 19(1) 355.466 -1676.263 0.00000000 0.0000147= 4 > 20(1) 156.168 -1653.479 0.00000000 0.0000268= 2 > 21(1) 990.196 7085.310 0.11097137 176674.2510085= 6 > 22(1) 925.704 -2638.620 16.28434626 228593.7237777= 9 > 23(1) 811.788 1939.226 41.57436680 251187.2162987= 0 > 24(1) 701.424 1649.690 14.23131322 **************= * > 25(1) 650.217 -656.428 106.61652268 433910.8329932= 6 > 26(1) 493.743 16521.965 0.05960240 **************= * > 27(1) 378.821 -1503.535 5.22048529 779479.8377581= 0 > 28(1) 121.625 -1543.939 2.61491704 76301.8710792= 5 > ....... > > ....... > > > > ------------------------------------------------------ > > JENS SPANGET-LARSEN Office: +45 4674 2710 > <+45%2046%2074%2027%2010> > > Dept. of Science Fax: +45 4674 3011 > <+45%2046%2074%2030%2011> > > Roskilde University Mobile: +45 2320 6246 > <+45%2023%2020%2062%2046> > > P.O.Box 260 E-Mail: spanget||ruc.dk > > DK-4000 Roskilde, Denmark Web: thiele.ruc.dk/~spanget > > > ------------------------------------------------------ > > > --=20 Prof. Malgorzata Biczysko International Centre for Quantum and Molecular Structures, 1/F Building E, Shanghai University, 99 Shangda Road, Shanghai, 200444 China e-mail: biczysko|,|shu.edu.cn http://icqms.shu.edu.cn =E4=B8=8A=E6=B5=B7=E5=A4=A7=E5=AD=A6=E9=87=8F=E5=AD=90=E4=B8=8E=E5=88=86=E5= =AD=90=E7=BB=93=E6=9E=84=E5=9B=BD=E9=99=85=E4=B8=AD=E5=BF=83 =E4=B8=8A=E6=B5=B7=E5=B8=82=E5=AE=9D=E5=B1=B1=E5=8C=BA=E4=B8=8A=E5=A4=A7=E8= =B7=AF99=E5=8F=B7E=E6=A5=BC1=E6=A5=BC --94eb2c1cccaa084f0505513518a6 Content-Type: text/html; charset="UTF-8" Content-Transfer-Encoding: quoted-printable
Dear Jens SPANGET-LARSEN,
there can be few problems, maybe all of them together.

1. Generati= on of anharmonic force-field and dipole moment derivatives.

To get r= eliable results FF need to be generated for at least "tight" opti= mized structure,
and using at least int=3Dultrafine grid for DFT. If not= , numerical errors may lead to completely un-reliable results,
like nega= tive frequencies, huge corrections to energies etc.

2. Anharmonic re= sonances, in particular for intensities (1-1 resonances)

That is most likely the case of modes 2 and 3 which have very similar=20 harmonic wavenumbers, but just off the default threshold (2cm-1) .
Solut= ion is to change resonance criteria, for instance by using keyword
Reso= nances=3D(DFreq11=3DXX) xx=3D5 or 10 can be a good choice there also other options related to the magnitude of force constants (i.e Res11F3=3D0.0,Res11F4=3D0.0)

3. C= oupling with low-freqency large amplitude motions (LAM) (i.e methyl rotatio= n)

This can be overcome by excluding LAM from VPT2 treatment, that i= s well tested and reliable procedure
it can be done by using the keyword= s:

DataMod=3DSkipPT2=3DModes RedDim=3DInactive=3D1

mode numbe= r

You can note that several procedures, in particular for anharmonic=20 resonances, including 1-1, have been modified to be more robust
in=20 their default version in G16. But, most importantly there is a large=20 number of keywords which allow to set up GVPT2 computations accordingly=20 to the system,
i.e. not using VPT2 for floppy modes etc.

However= , first "must" is reliable generation of force constants, so the = warnings in this part need to be also checked.

Hope it helps,
Best wishes,

Malgorzata

2017-06-05 4:53 GMT+08:00 Robert Molt r.molt.chemical.physics-x-g= mail.com <owner-chemistry|,|ccl.net>:
=20 =20 =20

Is it plausible that there are degeneracies in the vibrational/rotational spectrum, leading to the divergences you observe? This would be the most obvious explanation for why the numbers blow up for any finite-order perturbation theory. Perhaps you have coupled methyl groups?


With smaller basis sets, oftentimes the divergences in finite order perturbation theory are "masked" (I've seen this = with cc-pvdz vs. aug-cc-pVDZ), simply because you have not yet encountered the denominator problem. It's a "better" an= swer for wrong reasons.


On 6/4/17 4:= 38 AM, Jens Spanget-Larsen spanget**ruc.dk wrote= :
=20 =20

Dear CCL!
When I perform Gaussian calculations with the option freq=3Danharm, I frequently get strange results (Gaussian 09, Revision D.01). Below is a portion of the results of a b3lyp/6-311++G(d,p) calculation on a planar, aromatic, C2v symmetrical hydrocarbon. The anharmonic results are obviously ridiculous. With smaller basis sets, the results tend to be more realistic. Any explanations?

Yours, Jens >--<

=C2=A0

=C2=A0=C2=A0=C2=A0=C2=A0 =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D
=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0 Anharmonic Infrared Spectroscopy
=C2=A0=C2=A0=C2=A0=C2=A0 =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D

=C2=A0

=C2=A0Fundamental Bands
=C2=A0-----------------
=C2=A0=C2=A0=C2=A0 Mode(Quanta)=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2= =A0 E(harm)=C2=A0=C2=A0 E(anharm)=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 I(harm)=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 I(anharm)
=C2=A0=C2=A0=C2=A0=C2=A0 1(1)=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0= =C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 3476.017=C2=A0=C2=A0 3200.902=C2= =A0=C2=A0=C2=A0=C2=A0 43.37436356=C2=A0=C2=A0=C2=A0 538.05352307
=C2=A0=C2=A0=C2=A0=C2=A0 2(1)=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0= =C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 3202.964=C2=A0=C2=A0 3109.532=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0 0.01728522=C2=A0=C2=A0=C2=A0 255.35137878
=C2=A0=C2=A0=C2=A0=C2=A0 3(1)=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0= =C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 3200.221=C2=A0=C2=A0 3033.726=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0 8.04709323=C2=A0=C2=A0=C2=A0 191.91610101
=C2=A0=C2=A0=C2=A0=C2=A0 4(1)=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0= =C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 3175.408=C2=A0=C2=A0 3220.259=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0 4.37202654=C2=A0=C2=A0 2730.70615470
=C2=A0=C2=A0=C2=A0=C2=A0 5(1)=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0= =C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 2205.565=C2=A0=C2=A0 2153.406=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0 1.97473796=C2=A0=C2=A0=C2=A0=C2=A0 11.71516009
=C2=A0=C2=A0=C2=A0=C2=A0 6(1)=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0= =C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 1604.309=C2=A0=C2=A0 1584.143=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0 6.91156654=C2=A0=C2=A0=C2=A0 634.57714516
=C2=A0=C2=A0=C2=A0=C2=A0 7(1)=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0= =C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 1432.153=C2=A0=C2=A0 1374.467=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0 3.54182113=C2=A0 12790.38891389
=C2=A0=C2=A0=C2=A0=C2=A0 8(1)=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0= =C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 1263.675=C2=A0=C2=A0 1263.359=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0 0.79105395=C2=A0=C2=A0=C2=A0 139.40836060
=C2=A0=C2=A0=C2=A0=C2=A0 9(1)=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0= =C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 1112.643=C2=A0=C2=A0 1056.598=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0 5.36740074=C2=A0=C2=A0 1394.13686552
=C2=A0=C2=A0=C2=A0 10(1)=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 1010.305=C2=A0=C2=A0 1031.530=C2=A0= =C2=A0=C2=A0=C2=A0=C2=A0 0.00269831=C2=A0=C2=A0=C2=A0=C2=A0 47.10463873
=C2=A0=C2=A0=C2=A0 11(1)=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 717.365=C2=A0=C2=A0=C2=A0 793= .822=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 1.28159522 103894.31384900
=C2=A0=C2=A0=C2=A0 12(1)=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 697.978=C2=A0=C2=A0 1794.196= =C2=A0=C2=A0=C2=A0=C2=A0 67.17706473=C2=A0=C2=A0 1444.46852987
=C2=A0=C2=A0=C2=A0 13(1)=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 505.134=C2=A0=C2=A0 1553.018= =C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 6.40712425=C2=A0 16868.05994564
=C2=A0=C2=A0=C2=A0 14(1)=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 465.540=C2=A0=C2=A0=C2=A0 608= .353=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 2.04849136=C2=A0 24943.02416835
=C2=A0=C2=A0=C2=A0 15(1)=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 115.463=C2=A0=C2=A0=C2=A0 594= .923=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 0.77231918=C2=A0=C2=A0 6377.20573512
=C2=A0=C2=A0=C2=A0 16(1)=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 930.354=C2=A0 -1253.748=C2=A0= =C2=A0=C2=A0=C2=A0=C2=A0 0.00000000=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 0.00000039
=C2=A0=C2=A0=C2=A0 17(1)=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 653.549=C2=A0 -2649.903=C2=A0= =C2=A0=C2=A0=C2=A0=C2=A0 0.00000000=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 0.00000067
=C2=A0=C2=A0=C2=A0 18(1)=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 621.501 -20992.872=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0 0.00000000=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 0.01789241
=C2=A0=C2=A0=C2=A0 19(1)=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 355.466=C2=A0 -1676.263=C2=A0= =C2=A0=C2=A0=C2=A0=C2=A0 0.00000000=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 0.00001474
=C2=A0=C2=A0=C2=A0 20(1)=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 156.168=C2=A0 -1653.479=C2=A0= =C2=A0=C2=A0=C2=A0=C2=A0 0.00000000=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 0.00002682
=C2=A0=C2=A0=C2=A0 21(1)=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 990.196=C2=A0=C2=A0 7085.310= =C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 0.11097137 176674.25100856
=C2=A0=C2=A0=C2=A0 22(1)=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 925.704=C2=A0 -2638.620=C2=A0= =C2=A0=C2=A0=C2=A0 16.28434626 228593.72377779
=C2=A0=C2=A0=C2=A0 23(1)=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 811.788=C2=A0=C2=A0 1939.226= =C2=A0=C2=A0=C2=A0=C2=A0 41.57436680 251187.21629870
=C2=A0=C2=A0=C2=A0 24(1)=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 701.424=C2=A0=C2=A0 1649.690= =C2=A0=C2=A0=C2=A0=C2=A0 14.23131322 ***************
=C2=A0=C2=A0=C2=A0 25(1)=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 650.217=C2=A0=C2=A0 -656.428= =C2=A0=C2=A0=C2=A0 106.61652268 433910.83299326
=C2=A0=C2=A0=C2=A0 26(1)=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 493.743=C2=A0 16521.965=C2=A0= =C2=A0=C2=A0=C2=A0=C2=A0 0.05960240 ***************
=C2=A0=C2=A0=C2=A0 27(1)=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 378.821=C2=A0 -1503.535=C2=A0= =C2=A0=C2=A0=C2=A0=C2=A0 5.22048529 779479.83775810
=C2=A0=C2=A0=C2=A0 28(1)=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 121.625=C2=A0 -1543.939=C2=A0= =C2=A0=C2=A0=C2=A0=C2=A0 2.61491704=C2=A0 76301.87107925
=C2=A0=C2=A0=C2=A0 .......

=C2=A0=C2=A0=C2=A0 .......

=C2=A0

=C2=A0 --= ----------------------------------------------------

=C2=A0 JENS SPANGET-LARSEN=C2=A0= =C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 Office:=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 =C2=A0+45 4674 2= 710

=C2=A0 Dept. of Science=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 Fax:=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 = +45 4674 3011

=C2=A0 Roskilde University=C2=A0= =C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 Mobile:=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 =C2=A0+45 2320 6= 246

=C2=A0 P.O.Box 260=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 E-Mail:=C2=A0=C2=A0=C2=A0=C2=A0 =C2=A0spanget||ruc.dk

=C2=A0 DK-4000 Roskilde, Denmark=C2=A0=C2=A0Web: thiele.ruc.dk/~spanget

=C2=A0 ------------------------------------------------------=





--
= Prof. Malgorzata Biczysko

International= Centre for Quantum and Molecular Structures,
1/F Building E,
Shangha= i University,
99 Shangda Road, Shanghai, 200444 China
e-mail: biczysko|,|shu.edu.cn

http://icqms.shu.edu= .cn

=E4=B8=8A=E6=B5=B7=E5=A4=A7=E5=AD=A6=E9=87=8F=E5=AD=90=E4=B8=8E=E5=88= =86=E5=AD=90=E7=BB=93=E6=9E=84=E5=9B=BD=E9=99=85=E4=B8=AD=E5=BF=83

=E4=B8=8A= =E6=B5=B7=E5=B8=82=E5=AE=9D=E5=B1=B1=E5=8C=BA=E4=B8=8A=E5=A4=A7=E8=B7=AF99= =E5=8F=B7E=E6=A5=BC1=E6=A5=BC

--94eb2c1cccaa084f0505513518a6-- From owner-chemistry@ccl.net Mon Jun 5 11:40:00 2017 From: "Theo Keane t.keane++sheffield.ac.uk" To: CCL Subject: CCL:G: Anharmonic Infrared Spectroscopy Message-Id: <-52826-170605112536-26702-11TbBJaahTT9k90nA04O4g-*-server.ccl.net> X-Original-From: Theo Keane Content-Type: multipart/alternative; boundary="f403045ec282c73c6f0551381cf8" Date: Mon, 5 Jun 2017 16:25:05 +0100 MIME-Version: 1.0 Sent to CCL by: Theo Keane [t.keane]|[sheffield.ac.uk] --f403045ec282c73c6f0551381cf8 Content-Type: text/plain; charset="UTF-8" Content-Transfer-Encoding: quoted-printable Dear Jens, It would be helpful if you could provide a little more detail about your input file, especially if you've used any additional keywords to tune your GVPT2 calculation. One thing to consider is that anharmonic calculations are exceedingly sensitive to the quality of your integration grid and can be sensitive to convergence criteria. Recall that GVPT2 includes some 4th order derivative terms, so it's best to use int=3Dsuperfine if you can. It's also a good ide= a to employ very tight convergence criteria. (Obviously this will increase the cost of your calculation) This is advocated by Barone and co-workers in PCCP, 2014, 16, 1759 (doi:10.1039/C3CP53413H) You might also want to try excluding low energy vibrational modes (e.g. >100 cm-1) from the perturbative treatment. This is because low energy modes tend to correspond to movements on relatively flat parts of the PES (e.g. the derivatives are small). This means they are quite sensitive to the quality of the grid and the convergence criteria. Hope that helps, Theo On 4 June 2017 at 22:02, Alcides Simao alsimao(!)gmail.com < owner-chemistry]-[ccl.net> wrote: > Welcome to the strange world of DFT implementation in quantum chemistry > packages. > > There isn't but one single implementation of B3LYP, but rather several, > differing essentially at the way the LDA correlation function is defined. > By default, Gaussian uses the Vosko-Wilk-Nusair (VWN) - III > implementation, whereas other software, like ORCA, uses both the -III and > -V implementations - in other words, B3LYP and B3LYP/G-G. > > So, differences in the way these correlation functions are written may > very well induce differences in both intensity and wavenumber. > > But there are other special issues to take into account - how is the > numerical derivation carried out (methodology). This has a huge impact in > the precision - and validity - of the calculation. > > There are a couple of discussions around regarding this issues. As for th= e > basis set effect - the smaller it is, the more simplistic the system is > described, which in turn ends up with more similar results (despite the u= se > of (an)harmonicity) > > So, you could see if ORCA reproduces your results OR you can increase the > accuracy of your calculation and see if by using more tight criterias if > the phenomena is still reproducible. > > Still, I'm a bit baffled at your results. Perhaps someone can offer a mor= e > detailed explanation to this phenomena - of which I am extremely curious = to > understand, too! > > Best regards! > > Alcides > > > ---------- Forwarded message --------- > From: Jens Spanget-Larsen spanget**ruc.dk > Date: domingo, 4/06/2017 =C3=A0s 19:51 > Subject: CCL:G: Anharmonic Infrared Spectroscopy > To: Simao, Alcides > > > Dear CCL! > When I perform Gaussian calculations with the option freq=3Danharm, I > frequently get strange results (Gaussian 09, Revision D.01). Below is a > portion of the results of a b3lyp/6-311++G(d,p) calculation on a planar, > aromatic, C2v symmetrical hydrocarbon. The anharmonic results are obvious= ly > ridiculous. With smaller basis sets, the results tend to be more realisti= c. > Any explanations? > > Yours, Jens >--< > > > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D > Anharmonic Infrared Spectroscopy > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D > > > > Fundamental Bands > ----------------- > Mode(Quanta) E(harm) E(anharm) I(harm) I(anharm) > 1(1) 3476.017 3200.902 43.37436356 538.0535230= 7 > 2(1) 3202.964 3109.532 0.01728522 255.3513787= 8 > 3(1) 3200.221 3033.726 8.04709323 191.9161010= 1 > 4(1) 3175.408 3220.259 4.37202654 2730.7061547= 0 > 5(1) 2205.565 2153.406 1.97473796 11.7151600= 9 > 6(1) 1604.309 1584.143 6.91156654 634.5771451= 6 > 7(1) 1432.153 1374.467 3.54182113 12790.3889138= 9 > 8(1) 1263.675 1263.359 0.79105395 139.4083606= 0 > 9(1) 1112.643 1056.598 5.36740074 1394.1368655= 2 > 10(1) 1010.305 1031.530 0.00269831 47.1046387= 3 > 11(1) 717.365 793.822 1.28159522 103894.3138490= 0 > 12(1) 697.978 1794.196 67.17706473 1444.4685298= 7 > 13(1) 505.134 1553.018 6.40712425 16868.0599456= 4 > 14(1) 465.540 608.353 2.04849136 24943.0241683= 5 > 15(1) 115.463 594.923 0.77231918 6377.2057351= 2 > 16(1) 930.354 -1253.748 0.00000000 0.0000003= 9 > 17(1) 653.549 -2649.903 0.00000000 0.0000006= 7 > 18(1) 621.501 -20992.872 0.00000000 0.0178924= 1 > 19(1) 355.466 -1676.263 0.00000000 0.0000147= 4 > 20(1) 156.168 -1653.479 0.00000000 0.0000268= 2 > 21(1) 990.196 7085.310 0.11097137 176674.2510085= 6 > 22(1) 925.704 -2638.620 16.28434626 228593.7237777= 9 > 23(1) 811.788 1939.226 41.57436680 251187.2162987= 0 > 24(1) 701.424 1649.690 14.23131322 **************= * > 25(1) 650.217 -656.428 106.61652268 433910.8329932= 6 > 26(1) 493.743 16521.965 0.05960240 **************= * > 27(1) 378.821 -1503.535 5.22048529 779479.8377581= 0 > 28(1) 121.625 -1543.939 2.61491704 76301.8710792= 5 > ....... > > ....... > > > > ------------------------------------------------------ > > JENS SPANGET-LARSEN Office: +45 4674 2710 > <+45%2046%2074%2027%2010> > > Dept. of Science Fax: +45 4674 3011 > <+45%2046%2074%2030%2011> > > Roskilde University Mobile: +45 2320 6246 > <+45%2023%2020%2062%2046> > > P.O.Box 260 E-Mail: spanget||ruc.dk > > DK-4000 Roskilde, Denmark Web: thiele.ruc.dk/~spanget > > ------------------------------------------------------ > -- > Alcides Pinto Sim=C3=A3o, AMRSC, PhD. Student > > University of Coimbra Office: +351 239 852 080 <+351%20239%20852%20080> / > Fax: +351 239 827 703 <+351%20239%20827%20703> > Departamento de Qu=C3=ADmica da Universidade de Coimbra, 3004-535 COIMBRA= , > PORTUGAL > Website: http://www.qui.uc.pt/ > > This e-mail message may contain confidential or legally privileged > information and is intended only for the use of the intended recipient(s)= . > Any unauthorized disclosure, dissemination, distribution, copying or the > taking of any action in reliance on the information herein is prohibited. > E-mails are not secure and cannot be guaranteed to be error free as they > can be intercepted, amended, or contain viruses. Anyone who communicates > with us by e-mail is deemed to have accepted these risks. University of > Coimbra is not responsible for errors or omissions in this message and > denies any responsibility for any damage arising from the use of e-mail. > Any opinion and other statement contained in this message and any > attachment are solely those of the author and do not necessarily represen= t > those of the company. > > [image: Follow me on ResearchGate] > > > > --=20 ######################################################## Dr Theo Keane EPSRC Doctoral Prize Fellow Department of Chemistry, Room G8 w: www.theokeane.net The University of Sheffield e: t.keane]-[shef.ac.uk Sheffield S3 7HF, UK t: +44 114 222 9529 ######################################################## --f403045ec282c73c6f0551381cf8 Content-Type: text/html; charset="UTF-8" Content-Transfer-Encoding: quoted-printable
Dear Jens,

It would be helpful if you c= ould provide a little more detail about your input file, especially if you&= #39;ve used any additional keywords to tune your GVPT2 calculation.

One thing to consider is that anharmonic calculations are= exceedingly sensitive to the quality of your integration grid and can be s= ensitive to convergence criteria. Recall that GVPT2 includes some 4th order= derivative terms, so it's best to use int=3Dsuperfine if you can. It&#= 39;s also a good idea to employ very tight convergence criteria. (Obviously= this will increase the cost of your calculation) This is advocated by Baro= ne and co-workers in PCCP, 2014, 16, 1759 (doi:10.1039/C3CP53413H)

You might also want to try excluding low energy vibrationa= l modes (e.g. >100 cm-1) from the perturbative treatment. This is becaus= e low energy modes tend to correspond to movements on relatively flat parts= of the PES (e.g. the derivatives are small). This means they are quite sen= sitive to the quality of the grid and the convergence criteria.
<= br>
Hope that helps,


Theo=


On 4 June 2017 at 22:02, Alcides Simao alsimao(!)gmail.com <owner-chemistry]-[ccl.net> w= rote:
Welcome to the str= ange world of DFT implementation in quantum chemistry packages.

Ther= e isn't but one single implementation of B3LYP, but rather several, dif= fering essentially at the way the LDA correlation function is defined. By d= efault, Gaussian uses the=C2=A0Vosko-Wilk-Nusair=C2=A0(VWN) - III implementation, whereas ot= her software, like ORCA, uses both the -III and -V implementations - in oth= er words, B3LYP and B3LYP/G-G.

So, differences in the way these corr= elation functions are written may very well induce differences in both inte= nsity and wavenumber.

But there are other special issues to take int= o account - how is the numerical derivation carried out (methodology). This= has a huge impact in the precision - and validity - of the calculation.
There are a couple of discussions around regarding this issues. As for= the basis set effect - the smaller it is, the more simplistic the system i= s described, which in turn ends up with more similar results (despite the u= se of (an)harmonicity)

So, you could see if ORCA reproduces your re= sults OR you can increase the accuracy of your calculation and see if by us= ing more tight criterias if the phenomena is still reproducible. =C2=A0
=
Still, I'm a bit baffled at your results. Perhaps someone can offer= a more detailed explanation to this phenomena - of which I am extremely cu= rious to understand, too!

Best regards!

Alcides


---------- For= warded message ---------
From: Jens Spanget-Larsen spanget**ruc.dk <owner-chemistry]-[ccl.net>
Date: d= omingo, 4/06/2017 =C3=A0s 19:51
Subject: CCL:G: Anharmonic Infrared Spec= troscopy
To: Simao, Alcides <alsimao]-[gmail.com>


Dear CCL!
When I perform Gaussian calculations with the option freq=3Danharm, I frequ= ently get strange results (Gaussian 09, Revision D.01). Below is a portion = of the results of a b3lyp/6-311++G(d,p) calculation on a planar, aromatic, = C2v symmetrical hydrocarbon. The anharmonic results are obviously ridiculous. With smaller basis sets, the results ten= d to be more realistic. Any explanations?

Yours, Jens >--<

=C2=A0

=C2=A0=C2=A0=C2=A0=C2=A0 =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D
=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2= =A0 Anharmonic Infrared Spectroscopy
=C2=A0=C2=A0=C2=A0=C2=A0 =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D

=C2=A0

=C2=A0Fundamental Bands
=C2=A0-----------------
=C2=A0=C2=A0=C2=A0 Mode(Quanta)=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 E(harm)= =C2=A0=C2=A0 E(anharm)=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 I(harm)=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 I(anharm)
=C2=A0=C2=A0=C2=A0=C2=A0 1(1)=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 3476.017=C2=A0=C2=A0 3200.902=C2=A0=C2=A0= =C2=A0=C2=A0 43.37436356=C2=A0=C2=A0=C2=A0 538.05352307
=C2=A0=C2=A0=C2=A0=C2=A0 2(1)=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 3202.964=C2=A0=C2=A0 3109.532=C2=A0=C2=A0= =C2=A0=C2=A0=C2=A0 0.01728522=C2=A0=C2=A0=C2=A0 255.35137878
=C2=A0=C2=A0=C2=A0=C2=A0 3(1)=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 3200.221=C2=A0=C2=A0 3033.726=C2=A0=C2=A0= =C2=A0=C2=A0=C2=A0 8.04709323=C2=A0=C2=A0=C2=A0 191.91610101
=C2=A0=C2=A0=C2=A0=C2=A0 4(1)=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 3175.408=C2=A0=C2=A0 3220.259=C2=A0=C2=A0= =C2=A0=C2=A0=C2=A0 4.37202654=C2=A0=C2=A0 2730.70615470
=C2=A0=C2=A0=C2=A0=C2=A0 5(1)=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 2205.565=C2=A0=C2=A0 2153.406=C2=A0=C2=A0= =C2=A0=C2=A0=C2=A0 1.97473796=C2=A0=C2=A0=C2=A0=C2=A0 11.71516009
=C2=A0=C2=A0=C2=A0=C2=A0 6(1)=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 1604.309=C2=A0=C2=A0 1584.143=C2=A0=C2=A0= =C2=A0=C2=A0=C2=A0 6.91156654=C2=A0=C2=A0=C2=A0 634.57714516
=C2=A0=C2=A0=C2=A0=C2=A0 7(1)=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 1432.153=C2=A0=C2=A0 1374.467=C2=A0=C2=A0= =C2=A0=C2=A0=C2=A0 3.54182113=C2=A0 12790.38891389
=C2=A0=C2=A0=C2=A0=C2=A0 8(1)=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 1263.675=C2=A0=C2=A0 1263.359=C2=A0=C2=A0= =C2=A0=C2=A0=C2=A0 0.79105395=C2=A0=C2=A0=C2=A0 139.40836060
=C2=A0=C2=A0=C2=A0=C2=A0 9(1)=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 1112.643=C2=A0=C2=A0 1056.598=C2=A0=C2=A0= =C2=A0=C2=A0=C2=A0 5.36740074=C2=A0=C2=A0 1394.13686552
=C2=A0=C2=A0=C2=A0 10(1)=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0 1010.305=C2=A0=C2=A0 1031.530=C2=A0=C2=A0=C2=A0= =C2=A0=C2=A0 0.00269831=C2=A0=C2=A0=C2=A0=C2=A0 47.10463873
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=C2=A0=C2=A0=C2=A0 .......

=C2=A0=C2=A0=C2=A0 .......

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Alcides Pinto Sim=C3=A3o, AMRSC, PhD. Student

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Dr Theo Keane =C2=A0 =C2=A0= =C2=A0 =C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 EPSRC Doctoral Pri= ze Fellow
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