.. _tutorial_raman: Raman spectra ================ This tutorial explains :ref:`how to run ` Raman spectra calculations, :ref:`visualize them `. Please also check out the :ref:`theory ` behind the calculations and the current :ref:`limitations ` of our implementations. .. include:: a-mlatom-xacs_notice.rst .. _tutorial_raman_theory: Theory -------- The frequencies of a stationary point can be calculated by diagonalizing its Hessian matrix. The corresponding Raman intensities need polarizability derivatives (first derivatives of polarizability with respect to coordinates): :math:`I_{n} = 45 a_{n}^{2} + 7 \gamma _{n}^{2}` , :math:`a_{n} = (R_{nxx} + R_{nyy} + R_{nzz}) / 3` , :math:`\gamma _{n}^{2} = [(R_{nxx}-R_{nyy})^2 + (R_{nxx}-R_{nzz})^2 + (R_{nyy}-R_{nzz})^2 + 6(R_{nxy}^2 + R_{nxz}^2 + R_{nyz}^2)] / 2` , where :math:`R_{n \mu \nu} = \frac {\partial \alpha_{\mu \nu}} {\partial Q_{n}}`, :math:`\alpha_{\mu \nu}` is the component of polarizability, :math:`Q_{n}` is the :math:`n` th normal coordinate. Usually, we get polarizability with respect to each atomic coordinate, so the above derivatives can be rewritten as: :math:`R_{n \mu \nu} = \sum \limits _{x} \frac {\partial \alpha_{\mu \nu}} {\partial q_{x}} \frac {\partial q_{x}} {\partial Q_{n}}` , where :math:`q_{x}` is the component of atomic coordinates. .. _tutorial_raman_example: Example --------- We present a simple example of calculating Raman intensities of ethanol. The initial geometry can be downloaded here :download:`ethanol_init.xyz `. We need to optimize its geometry first **at the same level** as we intend to calculate Raman spectra. .. warning:: We recommend to use :ref:`UAIQM ` methods for the Raman spectra calculations, example below is just to show that you can also use GFN2-xTB. Example with input file +++++++++++++++++++++++++ First, optimize the geometry of ethanol. .. code-block:: geomopt GFN2-xTB #uaiqm_gfn2xtbstar@cc # if you want to use UAIQM xyzfile=ethanol_init.xyz optxyz=ethanol_opt.xyz After getting the geometry of the optimized ethanol (``ethanol_opt.xyz``) we can calculate its frequencies and Raman intensities. The keyword ``raman`` is needed for such calculations. IR intensities are calculated as well. You can refer to :ref:`frequencies tutorial ` for information of other keywords. .. code-block:: raman GFN2-xTB #uaiqm_gfn2xtbstar@cc # if you want to use UAIQM xyzfile=ethanol_opt.xyz You will find in the MLatom output the vibrational analysis and Raman intensities. .. code-block:: ============================================================================== Vibration analysis for molecule 1 ============================================================================== Multiplicity: 1 Rotational symmetry number: 1 This is a nonlinear molecule Mode Frequencies Reduced masses Force Constants IR intensities Raman intensities (cm^-1) (AMU) (mDyne/A) (km/mol) (A^4/AMU) 1 202.4514 1.1396 0.0275 6.9861 0.0561 2 293.5529 1.0836 0.0550 146.0294 2.1517 3 394.0049 2.8293 0.2588 10.2430 0.1549 4 837.2716 1.0923 0.4512 0.0441 0.0392 5 930.2857 2.0739 1.0575 17.0638 3.4220 6 1040.4667 1.9132 1.2203 33.2100 4.2849 7 1128.2307 2.9052 2.1788 64.1200 4.0781 8 1152.3249 1.5093 1.1808 12.9415 0.5200 9 1239.8816 1.3027 1.1799 85.5492 3.1744 10 1265.1749 1.1070 1.0440 0.7252 6.4292 11 1365.5011 1.2951 1.4228 2.9341 0.8742 12 1404.6911 1.2902 1.5000 17.2619 2.4119 13 1474.2396 1.0536 1.3492 8.6029 5.5777 14 1493.7381 1.0691 1.4054 5.5911 10.6898 15 1495.5801 1.0697 1.4098 3.3431 1.5195 16 2853.0411 1.0966 5.2594 55.5098 58.1244 17 2886.1994 1.0439 5.1236 73.3246 107.4003 18 3046.5584 1.0570 5.7805 7.8562 77.8001 19 3051.4826 1.0946 6.0053 9.7351 39.2472 20 3055.3796 1.0641 5.8528 12.8053 63.1401 21 3568.2629 1.0658 7.9951 75.0869 44.4583 .. _tutorial_raman_visualize: .. include:: tutorial_vibrview.inc .. _tutorial_raman_limitations: Limitations ----------- .. include:: a-mlatom-xacs_notice.rst The Raman spectra are only available when using GFN2-xTB and UAIQM that uses GFN2-xTB as baseline. While GFN2-xTB does not support calculations of polarizability derivatives, they are calculated using PTB (S. Grimme, M. Mueller, A. Hansen, *J. Chem. Phys.* **2023**, *158*, 124111 `DOI: 10.1063/5.0137838 `__). Any questions or suggestions? ----------------------------- If you have further questions, criticism, and suggestions, we would be happy to receive them in English or Chinese via `email `_, `Slack `_ (preferred), or WeChat (please send an email to request to add you to the XACS user support group).