# Tag Info

14

I wrote the following simple Python function that allows one to use any distribution from scipy.stats for peak broadening (the scale parameter determines how broad peaks will be): import numpy as np from scipy.stats import cauchy, norm def broaden_spectrum(x, x0, y0, distribution="gaussian", scale=1.0, fit_points=True, *args, **kwargs)...

13

In the jj-representation, each electron from $i$ to $N$ will have: $\vec{l}_i$ (orbital angular momentum), $\vec{s}_i$ (spin angular momentum), and $\vec{j}_i=\vec{l}_i + \vec{s}_i$ (total angular momentum). In your example we have $N=2$ and both electrons are $p$-type so we have: $$\tag{1} {l}_1=1,~~~~~~~{l}_2=1.$$ Let's also assign the spins for each ...

11

Many thanks to Felipe, the code is very useful! I know this is just a simple editing, but this is how I adjusted part of the code for Raman spectra: import cclib data = cclib.ccopen("molecule.out").parse() x = np.linspace(data.vibfreqs.min() - 100., data.vibfreqs.max() + 100., num=1000) y = broaden_spectrum(x, data.vibfreqs, data.vibramans, ...

11

This is a task suited to single crystal XRD. This does require you to be able to form a crystal of your substance which can be difficult at times but this allows for potentially high accuracy of bond lengths/angles to be determined. In the spirit of this community though, if you do know the bonding structure from something like NMR, you could model the ...

11

A partial list of bond lengths I have determined from IR spectra over my career: \begin{array}{ccc} \rm{Molecule} & \rm{Bond ~Length ~ (picometers)} & \rm{References}\\ \hline \ce{Li_2}(1^1\Sigma_g^+) & 267.298 74(19)& \href{}\textrm{2009 JCP, 2013 PRA} \\ \ce{Li_2}(1^3\Sigma_u^+) & 417.000 6(32)& \href{}\textrm{2011 JMS, 2013 PRA (2)}...

11

tldr; it's related to the excitation energy The lifetime of an excited molecule assuming there are no non-radiative pathways, is related to the Einstein A coefficient: $\left(\frac{dn_2}{dt}\right)_\mathrm{spontaneous} = -A_{21}n_2$ where $n_2$ is the population of the excited-state. I used this reference to get the following equations: J. Braz. Chem. Soc., ...

9

The Einstein A coefficient (as mentioned in Cody's answer) tells you the probability per unit time of spontaneous radiative decay from an excited state to a lower state. The Fermi golden rule (as mentioned in sleepy's answer) also gives a probability per unit time to transition from a specific state, but the destination is usually a group of states in a ...

9

I have a different page on the NIST website (https://cccbdb.nist.gov/vibscale.asp) that gives uncertainties in the scaling factors. I believe many of these were actually established by NIST themselves from the database itself. But many of them are in the paper you cite, in Table 1: As you probably know, one problem is that most quantum chemical methods ...

9

tldr: This is something of an eternal debate. IMHO very small imaginary frequencies can be okay, but it depends on your system and needs. As you might see from the various comments above, there are often different opinions on whether very small imaginary frequencies matter. The truth is, that it depends a bit on the size of the molecule and what you plan to ...

9

I agree with all answers provided so far: you cannot quantitatively deduce bond lengths from infrared spectra. However, see the answer by Nike Dattani about the inverse, predicting IR spectra from theory. IR (and Raman) spectra can be very useful tools to understand properties associated with bond lengths. An example I really like comes from the high ...

8

The expression you are describing is equation (6) from your first link: $$R_j=\frac{3\hbar c\ln(10)1000}{16\pi^2N_A}\int_\text{band j}\frac{\Delta\epsilon}{\omega}d\omega\tag{1}$$ which defines the rotatory strength $R_j$ of a band $j$ as the differential absorption coefficient integrated over that band, with the units changed via a prefactor containing the ...

8

Addendum: While the method described below is commonly used by experimentalists, I was mistaken that IR spectrum could not be used to obtain bond lengths. Nike's answer does a great job explaining how the entire potential energy surface can be determined by fitting using some model calculations. The important thing to learn from all this is that what you can ...

8

Actually, quantum chemistry codes tend to reorient molecules to make calculations more reproducible, since as was already mentioned in a comment above, the use of quadrature makes density functional calculations somewhat dependent on the absolute orientation of the molecule, see e.g. the paper by Gill, Johnson, and Pople. As to the second part of your ...

8

You can use Galore package. Galore is a package which applies Gaussian and Lorentzian broadening to data from ab initio calculations, such as VASP. The two main intended applications are: Gaussian and Lorentzian broadening of electronic density-of-states, with orbital weighting to simulate UPS/XPS/HAXPES measurements. Application of Lorentzian ...

8

Ok, I figured out the answer, so I will go ahead and answer my own question. First, I will provide an overview in bullet points: [Optional] Generate the velocities at evenly spaced frames from the geometries by the equation $\frac{x(t)-x(t-\Delta T)}{n\Delta t}$ where $x(t)$ is the geometry at time $t$. $n$ is the lag between frames form the simulation that ...

8

Since you include the command cphf=RdFreq, Gaussian expects you to have entered a perturbation frequency after the rest of the input. You need to specify a frequency in order to compute dynamic properties. Here is how it would look for your case. Note you can specify the perturbation in a couple different units (nm, au,etc). --Link1-- %chk=go40r.chk %nproc=...

8

Fermi golden rule should give you the transition probability (per time), from which you should be able to estimate the lifetime. You should know of be able to estimate the density of states in the final (ground) state, of course.

7

In general, you should use the $S_1$ state by default, unless you have reasons to suspect that your molecule is anti-Kasha. IMHO satisfying one of the following criteria guarantees that your molecule obeys the Kasha rule (supposing that your calculation is accurate), and you basically need not suspect otherwise: The experimental fluorescence spectrum ...

7

If the peaks shift inconsistently, you will never fix this with scaling factors etc. Consider if you can make a table of peak assignments with relative shifts + maximum peak heights instead. However, you can still present either of your spectra that you have calculated (subtracted or divided) if it helps you visually present an argument. Your calculated ...

7

Strontium aluminate can be doped with europium to give a material with properties like you are expecting. This can be optimized to give maximum fluorescent yield as well, but keep in mind this will likely shift the wavelength. The material must heat and cool in this process since absorption of light will not be 100% efficient and neither will the loss of ...

7

The Hamiltonian Just as for vibrations we have the harmonic oscillator approximation, for rotations we often use the rigid rotor approximation, where bond lengths are fixed. Recall the rigid-rotor Hamiltonian (in this case the kinetic energy operator) for a diatomic, which is often written as follows: \tag{1} \hat{H} = \hat{T} = \frac{J_x^2}{2I_x} + \frac{... 7 The paradox discovered by @HansWurst comes by the assumption that it is possible to treat both minima on the 1D PES separately and define a separate set of normal coordinates for them. 3N normal coordinates are functions of 3N Cartesian coordinates of the bodies in our system. It turns out that for a double-well potential in 1D, which you describe here, the ... 7 Roughly speaking, absorption spectra are obtained by TDDFT calculations on optimized ground-state geometries, while emission spectra are obtained by TDDFT calculations on optimized excited state geometries. These are the results of the Franck-Condon approximation, which says that there is a high probability that a molecule is near its equilibrium geometry, ... 6 I am surprised no-one above mentions the classic textbook example of the IR spectrum of HCl gas, which shows rather beautiful rotational structure superimposed on the vibrational band. The spacing of the rotational peaks, of course gives direct access to the angular momentum and the bond length. I say "directly" and "of course" - but you ... 6 Notice that after you divided the blue spectrum's values by the red spectrum's values, you got something that looks almost exactly like the red spectrum, but with much smaller numerical values. What you may like to do now is to use a peak alignment tool such as the alignsignals function in MATLAB's Signal Processing Toolbox or any of the many tools for ... 6 I agree with Emil Zak's answer that normal mode coordinates from different minima should, in general, be put together with special care. However, relating the two different sets of normal mode origin from different minima (or transition states) is not of nonsense, see SVP model of Hua Guo and Bin Jiang and related theories. To make things short, I will use ... 6 LEVEL Given a well-behaved electronic potential energy curve for a diatomic molecule, LEVEL will "automatically locate and calculate expectation values for all vibration–rotation levels". This means that for any operator \hat{M}, you can calculate the expectation values for each vibrational level v and each associated rotational level J: \...

5

This is a complicated question for which I do not have a full answer. However, here are some thoughts: Excited state relaxation. In solids, the calculation of excited states typically requires the many-body GW approximation for quasi-particle energies and the solution of the Bethe-Salpeter equation for excitonic properties. The calculation of forces, a ...

5

Let $u_{pi\alpha}$ be the displacement of atom $\alpha$ in the basis located in supercell with position $\mathbf{R}_p$ and in Cartesian direction $i$. With this "Cartesian" description of the motion of the atoms, it then becomes very simple to understand whether an atom moves out of plane (zero amplitude $x$ and $y$ components), or in plane (zero ...

5

The Crystallography Open Database is a good database of experimental crystal structures, take a look at their .hkl files which contain structure factors. The Materials Project, a computational database, also calculations X-ray diffraction patterns and absorption patterns (disclosure, I'm on the Materials Project staff). You can also generate your own once ...

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