35

One example that appears in many areas of physics, and in particular classical mechanics and quantum physics, is the two-body problem. The two-body problem here means the task of calculating the dynamics of two interacting particles which, for example, interact by gravitational or Coulomb forces. The solution to this problem can often be found in closed form ...


27

A famous example is the boolean satisfiability problem (SAT). 2-SAT is not complicated to solve in polynomial time, but 3-SAT is NP-complete.


26

In one and two dimensions, all roads lead to Rome, but not in three dimensions. Specifically, given a random walk (equally likely to move in any direction) on the integers in one or two dimensions, then no matter the starting point, with probability one (a.k.a. almost surely), the random walk will eventually get to a specific designated point ("Rome"). ...


21

Here's one close to the hearts of the contributors at SciComp.SE: The Navier–Stokes existence and smoothness problem The three-dimensional version is of course a famous open problem and the subject of a million-dollar Clay Millenium Prize. But the two-dimensional version has already been resolved a long time ago, with an affirmative answer. Terry Tao notes ...


20

In social choice theory, designing an election scheme with two candidates is easy (majority rules), but designing an election scheme with three or more candidates necessarily involves making trade-offs between various reasonable-sounding conditions. (Arrow's impossibility theorem).


15

Counterpoise correction is a method to limit an error that results when studying an intermolecular reaction using an incomplete basis set. Typically a basis set is not converged, and a calculation could always be improved with more basis functions. This is especially true for long range interactions, ie one often needs to add diffuse functions to the set ...


14

I personally have come the way from Gnuplot to Matplotlib with PGFPlots as an intermediate step. I will try to name all aspects of Matplotlib that I like. It is very versatile. You are not limited to line or scatter plots, you can easily do bar plots, images (matrix visualization!), basic 3D plotting and even some animation. You can use Matplotlib as a GUI ...


14

The link Godric pointed out under the question is exactly right. It gives a good overview of the many talents a computational scientist has to have. In general, the difference between being a Computational X (X=mathematician, civil engineer, materials scientist) and being a Theoretical X or Experimental X is that the former tackle problems with computers ...


12

My primary experience is with crystal structures, and there is only a finite number of point symmetries that show up in a crystal. So, the algorithm I would use is slightly different than what you'd use in a molecule. But, it is unlikely with a large molecule that the continuous symmetries will show up, like the axial symmetry in H$_2$ or CO$_2$, so the ...


11

For such a small simulation, I would strongly suggest looking into GPU-based solutions. This is probably what will get you the most ns/day/Euro. In my opinion, the fastest fully-featured GPU-based Molecular Dynamics (MD) software out there is ACEMD (see here for timings). The software, however, is commercial, but has a single-GPU free version that can be ...


11

Simultaneous diagonalization of two matrices $A_1$ and $A_2$: $$ U_1^T A_1 V = \Sigma_1,\quad U_2^TA_2V=\Sigma_2 $$ is covered by existing generalized singular value decomposition. However, when the simultaneous reduction of three matrices to a canonical form (weaker condition compared to the above) is required: $$ Q^T A_1 Z = \tilde{A_1},\quad Q^T A_2 Z = ...


10

There's old code for the purpose that's used in a few packages, called SYMMOL. The algorithm it uses is described in the following paper: T. Pilati and A. Forni, "SYMMOL: a program to find the maximum symmetry group in an atom cluster, given a prefixed tolerance", J. Appl. Cryst. 1998. 31, 503-504. Basically, it determines the centre of inertia, then ...


9

This is a pretty big topic, but the basic important qualities of an atom-centered basis set are: The number of separate, unlinked functions it uses at the valence level (the so-called *zeta* count), which allow the modeling of that many different electronic environments, practically speaking. Additional higher angular momentum so-called *polarisation* ...


9

A counterpoise correction is an a posteriori correction that may be applied to correct for the basis set superposition error (BSSE). More specifically, it uses mixed basis sets with "Ghost orbitals". For more information see, Boys, S.F. and Bernardi, F., "The calculation of small molecular interactions by the differences of separate total energies. Some ...


9

Your goal has a lot of challenges. I'll break them down into parts. SMILES is not a trivial language to parse, and the rules for aromaticity perception are not well defined. The detailed grammar definition from the OpenSMILES project should help some. SMILES defines the topology, but does not give 2D or 3D information. Making either is hard. (That is, if ...


9

There are plenty of examples in quantum computing, although I've been out of this for a while and so don't remember many. One major one is that bipartite entanglement (entanglement between two systems) is relatively easy whereas entanglement among three or more systems is an unsolved mess with probably a hundred papers written on the topic. The root of ...


8

No, there are several cases where the approximation becomes unphysical and inaccurate. To name a few I'm aware of: excited molecule states, basis functions are typically optimized to describe ground states. Configuration Interaction (CI) methods are rather used here. HF covers ground states best. electron correlation, especially if correlation changes with ...


8

Aesin already answered part of your question. I can provide you with some more information on GAMESS(US). It is possible to make GAMESS(US) use the same 'type' of B3LYP as Gaussian 03. For this, you need to specify "DFT=B3LYP1" as you already mentioned in your question. This selects B3LYP with VWN formula 1 RPA local correlation which, to the best of my ...


8

The most popular molecular dynamics codes are namd and gromacs, and maybe also desmond. These packages are freely available and "open source" in the sense that the source code is made available for free. Wikipedia hosts a list of software for molecular modeling which may contain other good links. These codes, however, are also quite complex and therefore if ...


8

Some of the algorithms are available from the source code for the different packages. PyMol is one such, and VMD's source is also accessible. I implemented VMD's ribbon algorithm in the 1990s. The first step is the structure determination - where are the amino acids? which are connected into a chain? where are the C-alpha atoms? Next, as Kyle said, is the ...


8

Many of us in scientific computing simply have well-equipped laptops for regular software development tasks, some multicore workstations for smaller-scale testing, and access to clusters for larger runs. To give you an idea: My laptop is a Dell M3800 (4-core Intel i7, hyperthreading, 16GB of RAM). This is good enough to regularly compile my software and do ...


7

ChemSpider (http://www.chemspider.com/) provides structures in mol format, which is simple enough to convert to XYZ, e.g. using OpenBabel (http://openbabel.org/wiki/Main_Page).


7

The Hartree-Fock equations are the result of performing constrained Newton-Raphson minimization of the energy with respect to the parameter space of Slater determinants (I don't have my copy of Szabo-Ostlund at hand, but I believe this is pointed out in the derivation). Hence, HF-SCF will converge if your starting guess is in a convex region around a minimum....


7

I oftem use Matlab and then save the result as an eps file via print -depsc2 -f1 fig. This saves figure 1 as an eps file named fig.eps. There is also the Plot2Svg from matlab file exchange that can save as svg. This is really nice since you can then open the files in Inkscape or other vector graphics software and edit them. If you are willing to learn new ...


7

If you're willing to overcome the learning curve of Gnuplot, you can generate top-quality figures with it (as exemplified in http://www.gnuplotting.org/). In particular, I'd recommend using the epslatex terminal as it allows you to use LaTeX to render all the text in the figure (including any mathematical notation that you may wish to input). If you want ...


6

The Gaussian implementation of B3LYP uses the VWN3 functional, according to the manual. Making Gaussian use the VWN5 functional instead for it is a bit tricky, but can apparently be done by adding all the following to the route line: bv5lyp - to specify which functional components - Becke exchange, and VWN5 local, LYP non-local correlation. iop(3/76=...


6

In short, (T) means a perturbative (non-iterative) correction to a CCSD calculation. From a talk demonstrating the derivation of the CCSD(T) method: The CCSD(T) method consists of a perturbative (noniterative) correction to the CCSD energy. • Utilizing the expressions from perturbation theory, approximate second order triples amplitudes & T(2)...


6

I'll take a stab at it. The protein cartoon (also known as ribbon) representation consist of three parts corresponding to the three types of protein secondary structure. Random Coil (shown in green) - A B-spline, usually of order 2 or 3, passing through the alpha-carbons of each amino acid residue. Occasionally the spline will also pass through the amino-...


6

To put it crudely, you will not be a good professional if you claim to do 'computational science' but do not know programming. To do computation, you need a tool. And computer is such a tool. Programming is the only way to teach computer how to do a thing. Therefore programming is an essential part of computational science. This is not to say that it is ...


6

You could install BOINC on those machines. When the computers become idle, the BOINC screensaver/client requests tasks from a server and computes them. See more information about it here. This is the software used by a number of projects such as SETI@Home. You can create your own project with BOINC and then put your desktop machines to work.


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