What is Gaussian: Definition and 771 Discussions

Gaussian is a general purpose computational chemistry software package initially released in 1970 by John Pople and his research group at Carnegie Mellon University as Gaussian 70. It has been continuously updated since then. The name originates from Pople's use of Gaussian orbitals to speed up molecular electronic structure calculations as opposed to using Slater-type orbitals, a choice made to improve performance on the limited computing capacities of then-current computer hardware for Hartree–Fock calculations. The current version of the program is Gaussian 16. Originally available through the Quantum Chemistry Program Exchange, it was later licensed out of Carnegie Mellon University, and since 1987 has been developed and licensed by Gaussian, Inc.

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2. B Row reduction, Gaussian Elimination on augmented matrix

Hi! Please, could you help me on how to solve the following matrix ? I need to replace the value 3 on the third line by 0, the first column need to remain zero and 1 for the third column. I'm having a lot of difficulties with this. How would you proceed ? Thank you for your time and help...
3. I Can a pulse from a laser be treated as a Gaussian?

I know a laser is generally treated as a coherent state (i.e. a plane wave). However, if a laser turns on and back off quickly, can the resulting light be treated as a gaussian multiplied by the plane wave that would have been emitted if the laser were continually active?
4. I Grating Resolving Power of Laser Beams with Gaussian Distribution

All resources I’ve found for grating resolving power assume uniform distribution on the grating and produce airy disks. Resolvance is determined by the Rayleigh criterion where the peak of one wavelength is at the minima of the adjacent one. This definition doesn’t seem applicable for Gaussian...
5. Probability involving Gaussian random sequences

How do I approach the following problem while only knowing the PSD of a Gaussian random sequence (i.e. I don't know the exact distribution of $V_k$)? Or am I missing something obvious? Problem statement: Thoughts: I know with the PSD given, the autocorrelation function are delta functions due...
6. POTW Gaussian Integrals in Two Dimensions

Let ##a, b##, and ##c## be real numbers such that ##a## and ##c## are positive and ##ac > b^2##. Evaluate the double integral $$\int_{-\infty}^\infty \int_{-\infty}^\infty e^{-ax^2 - 2bxy - cy^2}\, dx\, dy$$
7. B Sigma Multiplied Gaussian Distribution

Hi! Say i have two variables that have independent gaussian distributions of probability of being a certain value when i sample them, what is the likely hood that both will land on a 3 sigma value simultaneously? Is there an equation that easily determines that? Also for other combinations like...
8. Uncertainty of the Standard Deviation

Using this error propagation formula: I expressed the standard deviation (s) and the partial derivatives of s w.r.t. each data point as: This gives me an uncertainty of: , where m is the mean. Does this seem reasonable for the uncertainty of the standard deviation? I also found the thread...
9. Gaussian Elimination of Singular Matrix with partial pivoting

Part (A): The matrix is a singular matrix because the determinant is 0 with my calculator. Part (B): Once I perform Gauss Elimination with my pivot being 0.6 I arrive at the last row of matrix entries which are just 0's. So would this be why Gauss Elimination for partial pivoting fails for this...
10. What is the difference between DFT and TD-DFT in Gaussian 09 software?

Homework Statement:: difference between DFT and TDDFT in Gaussian 09 software? Relevant Equations:: hello , I hope this message finds you well Please I want to know what is the difference between DFT and time‐dependent density functional theory TD-DFT and why we use it in the measurement of...
11. I Calculate Gaussian Curvature from 4D Metric Tensor

I've been trying to find a way to calculate Gaussian curvature from a 4D metric tensor. I found a program that does this in Mathematica using the Brioschi formula. However, this only seems to work for a 2D metric or formula (I would need to use something with more dimensions). I've found...
12. C# How close to Gaussian a 2D Matrix percentage is in C#

Does anyone know a C# class that can return a value (0 - 100 percentage) of How close a perfect gaussian curve an 2D Matrix is? for example, these would all return a 100%:
13. Gaussian cylinder enclosing cylinder of charge

I am confused why we don't take into account the lids of the cylinder since the Gaussian cylinder is of finite height L as shown in the image
14. B Is this identity containing the Gaussian Integral of any use?

I found this identity: ##x\int e^{-x^2} dx - \int \int e^{-x^2} dx dx = e^{-x^2}/2## by solving the integral of ##x*e^{-x^2}## and then finding its integration-by-parts equivalent. Is this identity useful at all?
15. I A few questions about doing a Gaussian Fit

A few questions about doing a Gaussian Fit : 1) Is gaussian fit and gaussian regression the same thing ? 2) I have a gaussian function that will return a list of gaussian numbers giving an initial list length. So if you input 5 you will get: 1,2,6,4,1. My question is if I have an image and I...
16. Electric Field Inside a Gaussian Surface with Point Charge q

If I have a point charge q right outside of a gaussian surface, it makes sense that the flux is zero inside the surface because the electric field going in equals the electric field going out. However, how would the electric field be zero inside? Wouldn't it just take on the electric field of...
17. I How Is Uncertainty Calculated for the Mean of a Gaussian Function in MATLAB?

Hello! If I have N points (x,y) which I know they are described by a Gaussian i.e. y(x) is a Gaussian of unknown mean and standard deviation, and each y has an associated error of ##\sqrt{y}##, is there a general formula for the uncertainty on the mean of this function? Thank you!
18. I Diverging Gaussian curvature and (non) simply connected regions

Hi there! I have a few related questions on Gaussian curvature (K) of surfaces and simply connected regions: Suppose that K approaches infinity in the neighborhood of a point (x1,x2) . Is there any relationship between the diverging points of K and (non) simply connected regions? If K diverges...

31. Mutual Information from this Gaussian Distribution

Let us suppose we are given a Gaussian Distribution in the form of $$p(x,y) \propto exp(-\frac{1}{2}x^2 - \frac{1}{2}by^2 - cxy)$$ What are the equations that I need to use to obtain Mutual Information ?