1. K. V. Jovan Jose and Krishnan Raghavachari
Department of Chemistry, Indiana University, Bloomington, IN 47405, United States
An Efficient Implementation of Molecules-in-Molecules Fragment-Based Method for
Chiroptical Vibrational Spectra of Large Molecules
Abstract
References
Acknowledgments
We thank NSF grant (CHE-1266154) for financial support and the BigRed-II
Supercomputing Facility at Indiana University for computational time.
1. MIM-VCD is a fast, accurate and robust ab initio linear scaling method.
2. MIM2 could reproduce the high level total energies, VCD and ROA spectrum accurately.
3. MIM-VCD and MIM-ROA spectrum show excellent agreement with experimental spectrum.
4. MIM-VCD and MIM-ROA are promissing tool for exploring absolute configuration of molecules
Conclusions and Outlook
1. N. J. Mayhall and K. Raghavachari J. Chem. Theory Comput. 2011, 7, 1336.
2. K. V. Jovan Jose and K. Raghavachari J. Chem. Theory Comput. 2015, 11, 950.
3. K. V. Jovan Jose and K. Raghavachari Mol. Phys. 2015, 113, 3057.
4. K. V. Jovan Jose, D. Beckett, K. Raghavachari J. Chem. Theory Comput. 2015, 11, 4238.
5. K. V. Jovan Jose and K. Raghavachari J. Chem. Theory Comput. 2016, 12, 585.
An accurate first-principles evaluation of chiroptic spectroscopic properties of
large molecules is a challenge in electronic structure theory. The Molecules-in-
Molecules method has been adapted for the accurate evaluation of the infrared
(IR), Raman, vibrational circular dichroism (VCD) and Raman optical activity
(ROA) spectra for large molecules. The relevant higher energy derivatives from
smaller fragments are used to build the property tensors of the parent molecule
in our approach. Further, the fragment tensor components are evaluated in the
global coordinate framework, and the link atom tensor components projected
onto the corresponding host and supporting atoms through the Jacobian
projection method in our rigorous implementation. In this poster, I will be
presenting the details of the theory implementation and performance of the
MIM model for evaluating the IR, Raman, VCD and ROA spectra.
VCD and ROA Spectra of Cryptophane-A
Theory of VCD and ROA Spectroscopy
B3LYP/6-311+G(d,p):HF/6-31G
No. of Atoms=45
No. of Basis Functions=638
Anti-Trans-Anti-Trans-Anti-Trans-Perhydrotriphenylene
MPW1PW91/aug-cc-pVTZ-f
No. of Atoms=48
No. of Basis Functions=1026
𝐻 𝑎𝑏 =
𝜕2
𝐸 𝑇𝑜𝑡𝑎𝑙
𝜕𝑋 𝛼 𝜕𝑋 𝛽
=
𝜕2
𝐸𝑟𝑙
𝜕𝑋 𝛼 𝜕𝑋 𝛽
− ෍
𝐿=1
𝑀
𝐽 𝑇
𝜕2
𝐸 𝑚𝑙
𝜕𝑋 𝛼 𝜕𝑋 𝛽
𝐽 + ෍
𝐿=1
𝑀
𝐽 𝑇
𝜕2
𝐸 𝑚ℎ
𝜕𝑋 𝛼 𝜕𝑋 𝛽
𝐽
VCD Intensity
𝐷0→1(𝑖) = 0 𝜇 𝑒𝑙𝑒 1 2
𝑖 =
𝜕𝜇 𝑒𝑙𝑒
𝐺
𝜕𝑄𝑖
2
ħ
4𝜋𝜈𝑖
𝑄𝑖 = ෍
𝑖
𝑆𝜆𝛼,𝑖 𝑋𝜆𝛼
IR Intensity
𝑃𝛼𝛽,𝑇𝑜𝑡𝑎𝑙
𝜆
=
𝜕2
𝐸 𝑇𝑜𝑡𝑎𝑙
𝜕𝑋𝜆𝛼 𝜕𝐹𝛽
= 𝑃𝛼𝛽,𝑟𝑙
𝜆
− ෍
𝐿=1
𝑀
𝑃𝛼𝛽,𝑚𝑙
𝜆
𝐽 𝑅2; 𝑅1, 𝑅3 + ෍
𝐿=1
𝑀
𝑃𝛼𝛽,𝑚ℎ
𝜆
𝐽 𝑅2; 𝑅1, 𝑅3
𝑀 𝛼𝛽,𝑇𝑜𝑡𝑎𝑙
𝜆
= 𝑀 𝛼𝛽,𝑟𝑙
𝜆
− ෍
𝐿=1
𝑀
𝑀 𝛼𝛽,𝑚𝑙
𝜆
𝐽 𝑅2; 𝑅1, 𝑅3 + ෍
𝐿=1
𝑀
𝑀 𝛼𝛽,𝑚ℎ
𝜆
𝐽 𝑅2; 𝑅1, 𝑅3
Actual vs MIM1-VCD
Actual vs MIM2-VCD
No. of Atoms=126
No. of Basis Functions=1872
Frequency=488nm
@MIM2[B3LYP/6-311++G(d,p):
HF/6-31G]
Experiment-Raman
MIM2-Raman
Experiment-ROA
MIM2-ROA
𝛼 𝛼𝛽 =
2
ħ
෍
𝑗≠0
𝜔𝑗0
𝜔𝑗0
2
− 𝜔2
𝑅𝑒 0 𝜇 𝛼 𝑗 ⋅ 𝑗 𝜇 𝛽 0 = 4 ෍
𝑘
𝜙 𝑘
0
𝜇 𝛼 ൯𝜙 𝑘
′
(𝐹𝛽
𝐺 𝛼𝛽
′
=
−2
ħ
෍
𝑗≠0
𝜔
𝜔𝑗0
2
− 𝜔2
𝐼𝑚 0 𝜇 𝛼 𝑗 ⋅ 𝑗 𝑚 𝛽 0 = −4ħ𝜔 ෍
𝑘
𝐼𝑚 )𝜙 𝑘
′
(𝐹𝛼 ൯𝜙 𝑘
′
(𝐵 𝛽
𝐴 𝛼𝛽𝛾 =
2
ħ
෍
𝑗≠0
𝜔𝑗0
𝜔𝑗0
2
− 𝜔2
𝑅𝑒 0 𝜇 𝛼 𝑗 ⋅ 𝑗 𝜃 𝛽𝛾 0 = 4 ෍
𝑘
𝜙 𝑘
0
𝜃 𝛽𝛾 )𝜙 𝑘
′
(𝐹𝛼
𝐴 𝛼𝛽𝛾,𝑇𝑜𝑡𝑎𝑙
𝜆
= 𝐴 𝛼𝛽𝛾,𝑟𝑙
𝜆
− ෍
𝐿=1
𝑀
𝐴 𝛼𝛽𝛾,𝑚𝑙
𝜆
𝐽 𝑅2; 𝑅1, 𝑅3 + ෍
𝐿=1
𝑀
𝐴 𝛼𝛽𝛾,𝑚ℎ
𝜆
𝐽 𝑅2; 𝑅1, 𝑅3
𝐺 𝛼𝛽,𝑇𝑜𝑡𝑎𝑙
𝜆
= 𝐺 𝛼𝛽,𝑟𝑙
𝜆
− ෍
𝐿=1
𝑀
𝐺 𝛼𝛽,𝑚𝑙
𝜆
𝐽 𝑅2; 𝑅1, 𝑅3 + ෍
𝐿=1
𝑀
𝐺 𝛼𝛽,𝑚ℎ
𝜆
𝐽 𝑅2; 𝑅1, 𝑅3
𝛼 𝛼𝛽,𝑇𝑜𝑡𝑎𝑙
𝜆
= 𝛼 𝛼𝛽,𝑟𝑙
𝜆
− ෍
𝐿=1
𝑀
𝛼 𝛼𝛽,𝑚𝑙
𝜆
𝐽 𝑅2; 𝑅1, 𝑅3 + ෍
𝐿=1
𝑀
𝛼 𝛼𝛽,𝑚ℎ
𝜆
𝐽 𝑅2; 𝑅1, 𝑅3
VCD and ROA Spectra
ROA Intensity
Raman and ROA Spectrum of α-D-Cyclodextrin
@MIM2[B3LYP/6-31+G(d,p):
HF/6 -31G]
No. of Atoms=120
No. of Basis Functions=1872
(+)
T1T1T1
Atomic Forces
Hessian
𝐹𝑎 =
𝜕𝐸 𝑇𝑜𝑡𝑎𝑙
𝜕𝑋 𝛼
=
𝜕2
𝐸𝑟𝑙
𝜕𝑋 𝛼
− ෍
𝐿=1
𝑀
𝜕𝐸 𝑚𝑙
𝜕𝑋 𝛼
𝐽 𝑅2; 𝑅1, 𝑅3 + ෍
𝐿=1
𝑀
𝜕𝐸 𝑚ℎ
𝜕𝑋 𝛼
𝐽 𝑅2; 𝑅1, 𝑅3
𝑅0→1(𝑖) = ħ2
෍
𝛽
෍
𝜆,𝛼
𝜆′,𝛼′
𝑆𝜆𝛼,𝑖 𝑃𝛼𝛽
𝜆
𝑆 𝜆′ 𝛼′,𝑖 𝑀 𝛼′ 𝛽
𝜆′
𝑅 𝑎→𝑏(𝑖) = 𝐼𝑚 𝑎 𝜇 𝑒𝑙𝑒 𝑏 𝑖 ⋅ 𝑏 𝜇 𝑚𝑎𝑔 𝑎
𝑖
𝜕𝑟2,𝑎
𝜕𝑟1,𝑏
= (1 − 𝑔)𝛿 𝑎,𝑏
𝜕𝑟2,𝑎
𝜕𝑟3,𝑏
= (𝑔)𝛿 𝑎,𝑏
Experiment-VCD
MIM2-VCD
Experiment-ROA
MIM2-ROA
Proton Assisted Clustering of (Proline)12
+2
Fasman, G., Ed.; Circular Dichroism and
the Conformational Analysis of
Biomolecules.
Springer: New York, 1996; pp 687.
Energy=-704.10569 a.u.
(+) (−)
∆Energy= 0.124 kcal/mol
MAD in ν(I)=0.32(3.24) cm-1 (esu2 cm2)
Experiment
MIM2-VCD
(−)
Enantiopure Recemic Mixture
Infrared Spectra @MIM2[MPW1PW91/6-311G(d,p):MPW1PW91/6-31G]
MIM1
MIM2
Calibration
Ongoing
Experiment MIM2