# Tag Info

20

Phonons are a measure of the curvature of the potential energy surface about a stationary point. In particular, the matrix of force constants is calculated as: $$D_{i\alpha,i^{\prime}\alpha^{\prime}}(\mathbf{R}_p,\mathbf{R}_{p^{\prime}})=\frac{\partial^2 E}{\partial u_{p\alpha i}\partial u_{p^{\prime}\alpha^{\prime}i^{\prime}}},$$ where $E$ is the ...

18

I've never done this myself, and there may be other approaches, but one possible detailed answer seems to be provided by the Gaussian webpage. For stability reasons, you can find this page via the Internet Archive (pdf). In particular, you may want to jump to the sections "Determine the principal axes of inertia" and "Generate coordinates in the rotating ...

14

Phonon calculations tend to be very expensive to run. That being said, for gas phase molecules it is very common and expected that frequency calculations are run to ensure the molecule is not on a saddle point. In general, you can publish anything if it makes it past peer review. Phonon calculations are something you would do if you fear you are on the ...

13

In general it is not justified to published the geometry of a system without performing a phonon calculation. This is where you may end up in the potential energy surface depending on which type of calculation you perform: Geometry optimization. With a geometry optimization, you may end up at a local minimum or at a saddle point of the potential energy ...

13

Assuming that all calculation parameters associated with the electronic structure are properly converged, then obtaining imaginary frequencies can mean one of two things. Physical imaginary frequencies This situation corresponds to obtaining imaginary frequencies on $\mathbf{q}$-points that are included in the $n_1\times n_2\times n_3$ grid that you ...

10

The zero-point energy is of no importance here, since you can always choose your reference energy freely you can energy-shift your hamiltonian by $\frac{1}{2}\hbar\omega$ $$H = \frac{p^2}{2m}+\frac{1}{2}m\omega^2x^2-\frac{1}{2}\hbar\omega,$$ and the physics of the system will stay the same (the wave function will be the same). Since this wavefunction is ...

10

Some people do: In this paper there is a system coupled to a bath of Morse oscillators rather than a bath of harmonic oscillators, but it is not exactly solvable, they used a numerical approach called mctdh. When it is said that the Morse potential is "exactly solvable", what it means is that you can solve the vibrational Schroedinger equation for ...

10

This depends on what you are studying. For molecular systems without periodicity, the simplest approach is to carry out a vibrational frequency analysis and confirm that there are no imaginary modes. It is considered standard to carry out a vibrational frequency analysis for all investigated structures, provided the number of investigated systems is not ...

9

If you index the molecule and the atoms in the crystallographic unit cell the same, you could extract the displacement from the phonon eigenvectors and the displacement from the normal modes. By projecting each normal mode displacement onto each phonon displacement, you can get a qualitative relationship between a molecular deformation and a lattice ...

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

When you say MCTDH, I am assuming you mean the vanilla MCTDH without employing the multi-layer structure. In which case 24 modes seem to be the best known result (higher modes can be done, I have tried things myself with more than 24 modes, but they are unpublished results!) However, the true power of MCTDH comes with ML-MCTDH, which is sort of adding ...

8

Firstly, a minor correction: a non-linear molecule has 3N-6 normal modes, not 3N-5 modes. Linear molecules have 3N-5 normal modes. GAMESS automatically prints out some values in normal coordinate analysis section with the labels TRANS. SAYVETZ and ROT. SAYVETZ. If the total value of ROT SAYVETZ is high, that mode can be identified as a rotation. You will ...

8

The developers of MCTDH from Heidelberg reported in the year 2000 [1] The largest system treated with MCTDH to date is the pyrazine molecule, where all 24 (!) vibrational modes were accounted for. The particular representation of the MCTDH wavefunction requires special techniques for generating an initial wavepacket and for analysing the ...

8

LocVib (part of MoViPac) I have never used VEDA before, but according to the paper, it decomposes the normal modes into vibrations of atomic groups, bond stretching, bending or something else. Something similar is LocVib, which localizes normal modes to localized vibrational modes by maximizing the "distances" between vibrational modes and "...

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 ...

6

Even in treating molecular vibrations, the Morse potential is not always the best, because: There's cases where the potential is more "harmonic" than "Morse-like", for example in the asymmetric stretching of water. It is the same case in solid state physics: considering the most crude approximation that we fix all the atoms in a solid ...

6

I cannot see your output file, but I am pretty sure that the program is running into an error when starting the optimization i.e. when it is trying to generate the guess hessian. You are using Cartesian coordinates for optimization, and GAMESS by default will attempt to eliminate the rotational and translational modes from the guess hessian, before the ...

6

The quantum number n simply represents the different energy levels given by the harmonic oscillator. $\mathbf{n=0}$ does not correspond to a given temperature, but its relative occupation to other energy levels does correspond to a given temperature. As a system rises in temperature, the higher energy levels can be occupied at greater numbers. Likewise, at ...

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 not a full answer, because it does not solve the problem. But I hope to shed some light on why you are not getting the correct frequencies. Short answer: I suspect there is a bug in GAMESS Long answer: First of all I would advise you to go through the manual of GAMESS. There are lots of problems in the input file, and most of them can be easily ...

5

I can see two major problems: CCD != CC2 and I'm not certain if CC2 is available in GAMESS. CC2 is an approximation of CCSD, which is available in GAMESS. You may be able to use this since $\ce{NH3}$ is a fairly small molecule, though I don't know how time consuming this will be relative to your initial CCD calculation. TZV != TZVPP. The def2-TZVPP basis ...

5

As has been stated in several other answers already, $n$ is only a number, and the population of the states with different $n$ depends on the temperature. However, an important point has not yet been mentioned. The quantum harmonic oscillator is often invoked for nuclear motion. It arises from the second-order Taylor expansion of the Born-Oppenheimer nuclear ...

5

Is $𝑛$ only a number? In short, $n$ is the energy quantum number of the quantum harmonic oscillator. If so then how does $𝑛$=$0$ have anything to do with temperature? In particular, $n$=$0$ means that the harmonic oscillator will stay at its ground state. Usually, the ground state of a quantum system is assumed to be lived at zero temperature. Therefore,...

5

Is $n$ only a number? $n$ is indeed a number. Is it only a number? Well it's a quantum number which means it labels the $n^{\textrm{th}}$ excited energy level of the system (i.e. the $(n+1)^{\textrm{th}}$ smallest eigenvalue of the system's Hamiltonian, with $n=0$ corresponding to the smallest eigenvalue, $n=1$ corresponding to the second smallest ...

5

I was able to figure out what was going wrong, but forgot to check back here and leave an answer if none were give. @ShoubhikRMaiti should be credited with helping me figure this out. From this comment Also, may I ask why you are using fully numeric differentiation? U-BLYP has analytic hessian programmed into the code. I was curious to try removing this from ...

5

You mention phonons, so I assume you are doing periodic structures which I am not entirely familiar with since I study mostly single molecules. Although, when I get imaginary frequencies from optimized geometries of single molecules this typically implies that the isomer in question is not a stable minimum on the potential energy surface (PES). This does not ...

5

In order to check if a geometry is a local minimum, it is a necessary and sufficient condition that the Hessian is positive (semi)definite, i.e. that the lowest eigenvalue of the nuclear Hessian is non-negative. Namely, expanding the energy $E({\bf R})$ around the reference point ${\bf R}_0$ you have the Taylor expansion $E({\bf R}) = E({\bf R}_0) - {\bf g} \... 5 Let$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

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 non sense, see SVP model of Hua Guo and Bin Jiang and related theories. To make things short, I will use ...

Only top voted, non community-wiki answers of a minimum length are eligible