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Disclaimer and warning: long and likely biased answer. Background: The Pople style basis sets were defined almost 50 years ago. The 6-31G was designed for HF calculations, the 6-311G for MP2 calculations. For computational efficiency reasons, the s- and p-exponents were constrained to be identical. Polarization functions were defined for 1d, 2d, 3d and 1f. ...

24

This is a very broad question, so I am going to give a very brief overview of typical exponentially-scaling problems. I am not an expert in most of these areas, so any suggestions or improvements will be welcome. Solving the Schrödinger equation In order to solve the Schrödinger equation numerically, you need to diagonalise a rank $3N$ tensor -- as you can ...

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This is an excellent question! Reversibility in MD is useful because: Time-reversibility in a numerical integrator leads to a doubling of the accuracy order (see Propositions 5.2 and Theorem 6.2 here). Reversible maps can be readily Metropolized, for example in a hybrid Monte-Carlo scheme. This gives an easy way to enhance the sampling efficiency and ...

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B3LYP is still a decent functional at its level of theory (single-hybrid functional), but you're right that there's a general criticism of it, which I largely hear in the form of people saying things like "all they did was B3LYP/6-31G*" to criticize non-experts that blindly use this combination which became the "default" in chemistry for ...

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Disclaimer: I'm the lead developer of Open Babel and Avogadro - and currently mentoring Google Summer of Code projects. The biggest question is more "what kind of topics" interest you and/or what kind of skills you want to learn. Data Science? Informatics? Visualization? Reaction Prediction? QSAR? etc. That would help you refine the possible projects to ...

17

I think this review¹ by Head-Gordon is a useful supplement to Nike's answer. Its combines a review of functional development, a benchmarking of various functionals, and an explanation of the design process for the $\omega$B97 functionals. Its also open access, so its a great resource if you are interested in DFT functionals in general. They benchmarked 200 ...

16

I don't have too much to add to the answers of Nike Dattani and Tyberius, but I think the crux is that its capabilities have been historically overestimated. One particular failing of B3LYP is that it tends to underestimate bond energies. However, since the small (and fast) 6-31G* basis set will lead to overbinding, the famous combination B3LYP/6-31G* ended ...

15

Disclaimer: This answer would have been better placed in a comment but since I have just joined the community I cannot write comments. Ironically, I was tipped about this community after answering a very related question in Physics SE to which I dare giving a link. The short answer here is that projected DOS is a somewhat ambiguous construction in the ...

14

OpenBabel And the related Pybel are excellent platforms for starting a project because they have well written C++ and python APIs, and are specifically designed for cheminformatics 101. For example, cheminformatics involves Storing a Molecule in various formats (e.g. smiles, twirlymol, 2d, xyz, etc) Finding exact molecule Substructure search Similarity ...

13

This is a question that is answered by a straightforward literature search, here's e.g. two review papers from the 1980s: J. Chem. Inf. Comput. Sci. 25, 334 (1985) J. Chem. Educ. 65, 574 (1988) as well as a more recent encyclopedia article Encyclopedia of Computational Chemistry 1998, pp. 1169-1190

12

The potential energy surface (PES) is a 3N-dimensional function for a bulk system containing N atoms (in reality 3N-3 to account for the trivial translational degrees of freedom). For a bulk structure, N typically represents the number of atoms in a simualtion cell with periodic boundary conditions, which is of the order of $10^2$-$10^3$, so the function is ...

12

Okay first some basics: For most reactions we do not need to run molecular dynamics Molecules are like springs and obey the principles of minimum energy. Therefore, normally the dynamics of a molecule will be distributed around the "minimum energy path" going from reactants to products. The maximum along this minimum energy path is the transition ...

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The curse of dimensionality is indeed a huge problem in quantum chemistry, since the possible ways N electrons can occupy K orbitals is a binning problem whose computational cost grows factorially (almost as fast as x^x!) with the size of the system. Moreover, for accurate results you need K>>N in order to account for the so-called dynamical correlation, ...

12

I would argue the main reason this is important is philosophical, linked to the history of science and determinism (as proposed by Laplace). Newtonian mechanics is mathematically reversable while any observation in a "real world" system is one of irreversibility and increasing entropy, which is why we end up with Loschmidt paradox. From a ...

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The 2006 variational calculation by Schwartz is lower (more accurate) than Nakashima & Nakatsuji's 2007 energy: 2006 Schwartz: -2.903724377034119598311159245194404446696925309838 2007 Nakashima & Nakatsuji: -2.90372437703411959831115924519440444669690537 The lowest variational upper bounds ground state energies for the first 6 elements, ...

12

I know it is easy to get the PES tabulated very neatly in MOLPRO with a command like: {table,r,scf,ccsd,ccsd_t head, R,HF-SCF,CCSD,CCSD(T) sort,1,2,3} which for a diatomic molecule like yours, gives the following output: R HF-SCF CCSD CCSD(T) 1.5 -108.3566620 -108.6007993 -108.6060512 1.6 -108.6053845 -108.8602358 -108.8662569 1.7 -...

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tldr; it depends on flexibility / number of rotatable bonds A while ago, I answered a related question - in general, molecules with fewer "rotatable bonds" need fewer conformers geometries generated to sample properly. Based on that, I would normally have said "50 is more than enough for up to 3-4 rotatable bonds" and beyond that, I'd ...

11

It's not a descriptive error message, but this occurs when you reach the max number of iterations for the Eigenvector Following (EF) algorithm and still haven't converged a lambda. While Gaussian uses a different approach (the Berny Algorithm) for methods which have analytical gradients, CCSD(T) is one of the few methods for which these still aren't ...

11

Your Octave code is trying to do the integral by quadrature, which makes very little sense since it will have a huge problems with the cusp. Since this is a one-center problem, the best approach is to use the Legendre expansion for $|r_1-r_2|^{-1}$, which decomposes the interaction into a radial part and an angular part: $r_{12}^{-1} = \frac {4\pi} {r_>} ... 11 I'd just briefly add that among other things, chemical graph theory is extensively used for computing so-called "molecular descriptors", which are used to capture some "common properties" of a certain class of molecules. Todescini and Consonni, Molecular Descriptors for Chemoinformatics already a bit dated, offers an extensive collection ... 11 We attempted to solve a similar problem when studying the (also highly symmetrical)$\ce{CH4}$and$\ce{CF4}$homo- and hetero-dimers. I found it easiest to use internal coordinates and fixed molecular geometries to generate the hypersurface, but we also had large computational resources at our disposal and we might have benefitted from using even more, ... 11 There is a long history of correlation between ab initio calculations for nuclear physics and ab initio calculations for quantum chemistry/materials. Take coupled cluster for example, remembering that a lot of people used to say "CCSD(T) is the gold standard in quantum chemistry": The method was initially developed by Fritz Coester and Hermann ... 10 The computations do include quantum physics, since the very bare minimum of electronic structure calculations involve the quantum mechanics of electrons. There's been quite a lot of development in computational chemistry in synthesis. While computational chemistry was pivotal already in the late 1980s in developing ozone safe alternatives to ... 10 Meta-GGA density functionals are dependent on the kinetic energy density $$\tau_\sigma (\mathbf{r}) = \sum_i^\text{occ} \frac{1}{2} \lvert \nabla \phi_{\sigma,i} (\mathbf{r}) \rvert^2$$ where$\phi_{\sigma,i} (\mathbf{r})$are Kohn-Sham orbitals.$^1$Certain spatial derivatives of this quantity will be necessary for the calculation of the Hessian and I ... 10 Note: This was a response I've originally written on Chemistry Stack Exchange, so it was intended to be very brief. Natural Bond Orbital Theory is basically (among plenty of other uses) providing an orbital localisation scheme to achieve similarity to Lewis structures. In some of my answers you have probably read the term 'Lewis-like' structures for these ... 10 The safe choice is to use diffuse functions on all atoms. It is quite rare to run into pathological overcompleteness with standard augmented basis sets, unless you're looking at very high-energy geometries. Overcompleteness may become an issue if you're using multiply augmented basis sets, such as d-aug-cc-pVXZ or t-aug-cc-pVXZ, but as I've recently shown in ... 10 The PDB file format has a strict specification on the number of columns, etc. (Consider that some proteins have very large sizes, so distances can be many Ångstroms.) Thus, the number of decimal places are generally given by the file format. Some people have asked why Open Babel doesn't give more decimal places, e.g., in the XYZ format, which is, in ... 10 You are probably running a combined optimisation and frequency job in Gaussian. (I discourage that, but that's a different issue.) The line means that the calculation preceding it has been run as a test calculation, see https://gaussian.com/test. An archive entry has not been created. The reasons may be multiple and depend on the actual input file. That's ... 10 I recently had the same question. After emailing Gaussian support I was informed that the units are indeed$\sqrt{\text{km}/\text{mol}}\$. From their reply I also believe that the derivatives are calculated with respect to the 3N-6 vibrational modes obtained through the application of the Sayvetz conditions as detailed in their whitepaper (Paragraph after Eqn....

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Indeed, due to the uncertainty relation, the electrons in a molecule do not have a definite potential energy, nor do they have a definite kinetic energy (yet they have well-defined expectation values of potential energy and kinetic energy). But, assuming that the molecule is in an energy eigenstate, the two uncertainties exactly cancel out, and gives an ...

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