Gaussian Definition and 772 Threads

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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  1. A

    Solving Gaussian Elimination Algorithm Problems (Matrices)

    I tried to solve this Gaussian elimination algorithm problem (matrices) but for some reason when I plug in the x variables it doesn't work. The problem is: Alright so the first thing I did was divide the 1st row by 1/3 (scaling). Then I made the entries below the first pivot equal to 0...
  2. A

    Solving Gaussian Elimination Algorithm Problem (Matrices)

    I tried to solve this Gaussian elimination algorithm problem (matrices) but for some reason when I plug in the x variables it doesn't work. The problem is: Alright so the first thing I did was divide the 1st row by 1/3 (scaling). Then I made the entries below the first pivot equal to 0...
  3. E

    Solve System of Equations via Gaussian Elimination

    I am not sure how to solve this: Given an augmented matrix, find conditions on a, b, c for which the system has solutions: -1 -2 3 b -1 -6 23 c -3 2 4 a so by Gaussian elimination, the matrix I ended up with is 1 2 -3 -b 0 4 -20 b-c 0 0 -35...
  4. G

    Convolution with a gaussian G(t)

    Hi. Suppose I have a function T(x,t), units are in Kelvins. I then do a convolution with a gaussian G(t), and the result is also in Kelvins. What are the units of the gaussian G(t)? Thanks.
  5. R

    How does the elimination method work for solving simultaneous equations?

    I need a math guru to explain why and how the elimination method of solving simultaneous equations works ? why do we add or subtract the two equations ?(I undertand in order to eradicate either term) but I need to know from the basics . For that matter, how/why does the substitution method...
  6. D

    Gaussian Optics / Paraxial Approximation

    Derive \frac{n_1}{s_o} + \frac{n_2}{s_i} = \frac{n_2-n_1}{R} for Gaussian optics from the following equation \frac{n_1}{l_o} + \frac{n_2}{l_i} = \frac{1}{R} \left( \frac{n_2s_i}{l_i} - \frac{n_1 s_o}{l_o} \right) by approximating l_o = \sqrt{R^2 + \left( s_o + R \right) ^2 -...
  7. T

    Gaussian normal distribution curve

    I am looking for a mathematical equation which is similar to the Gaussian normal distribution curve, but I need one which terminates at a finite x = X and not at infinity, ie, f(x \geq X) = 0, but, f(x \leq X) = a function which has a Gaussian shape-like curve. Is there one such as this that...
  8. B

    Truncating a Gaussian Beam: Effects on Intensity and Other Parameters?

    Hi All, I am just wondering whether there is any kind soul to help me out with the following problem: If a gaussian beam is truncated by the circular aperture situated at the beam waist just before the entrance of a microscope objective lens, what should be the intensity distribution of...
  9. S

    Line of infinite charge and a gaussian sphere

    Construct a spherical gaussian surface centered on an infinite line of charge. Calculate the flux through the sphere and thereby show that it satisfies gauss law. I know how i can do it for a cylinder, but a sphere? I know that the ends of the wire (one diameter) wil have zero flux at it's...
  10. R

    Plane wave limit of Gaussian packet

    \psi (x)= \frac{1}{(\pi\Delta^2)^\frac{1}{4}} e^(\frac{i<p>(x-<x>)}{\hbar})e^(\frac{-(x-<x>)^2}{2\Delta^2}) as \Delta\rightarrow\infty should approach the plane wave \frac{1}{(2\pi\hbar)^\frac{1}{2}} e^(\frac{i<p>x}{\hbar}) up to a phase factor. I guess this happens by setting the...
  11. E

    Maxwell related equations converted from MKSA units to Gaussian units

    So here is an example of what I am trying to do. We know that div of an E field=p/eo where p=charge density and eo=the permittivity of free space. This equation is expressed in MKSA units. In order to convert this into Gaussian units, we must multiply E by 1/sqare root of 4*pi*eo, and...
  12. K

    Integration of Gaussian equation

    Hi, Need help desperately! I am trying to figure out the area under a gaussian cone by finding the integral of 2PIArEXP[-(r^2)/(2sigma^2)] dr My supervisor thought it is 2PI [A sigma^2 EXP(-(r^2)/(2 sigma^2)] Between 0 and infinity and he came up with the...
  13. S

    Gaussian Discription of Dimension

    Nigel was polite enough to offer some discriptive views for extending awareness that I thought I too would indulge. To raise the issue, to include the GR perspective, one has to retain some comprehension and viewing of the hyperdimensional realities when it comes to the geometries? This...
  14. P

    Electric field and gaussian surface

    A small copper spherical BB of radius a is located at the center of a larer hollow copper spherical shell of inner radius b and outer radius R. A charge of +q is on the small BB. The hollow copper shell has zero charge on it. a) What is the electric field within the BB (for radii r<a)? b)...
  15. J

    Function of a random gaussian variable

    I'm having trouble showing the following relation: E(exp(z)) = exp(E(z^2)/2) where z is a zero-mean gaussian variable and E() is the avg anyone can help?
  16. J

    Function of gaussian random variable

    I'm having trouble showing the following relation: E(exp(z)) = exp(E(z^2)/2) where z is a zero-mean gaussian variable and E() is the avg anyone can help?
  17. P

    How Does Changing a Gaussian Surface's Shape Affect Net Flux?

    A positive test charge is placed at the center of a spherical Gaussian surface. What happens to the net flux through the Gaussian surface when the surface is replaced by a cube of the same volume whose center is at the same point? or When the sphere is replaced by a cube of one third the volume...
  18. D

    K-Delta Function in Autocorrelation of Gaussian White Noise

    hi, I would like to know why dirak-delta function is used in autocorrelation in a way that the following is true: <å(t)å(t')>=2Dä(t-t') where å(t)is Gaussian white noise and D is the strength of the noise. Dora
  19. Y

    Type(s) of charge distribution for spherical and cylindrical gaussian surfaces

    I have a new question: "In applying Gauss's Law describe the types(s) of charge distribution for which (a) a spherical gaussian surface is useful and (b) a cylindrical gaussian surface is useful" please help!
  20. S

    What is the Gaussian Quadrature?

    I am not sure of the spelling, but I heard of the 'gaussian quadature' (or quadrature). It was spoken, and was in a mathematical equation. What the heck is it?
  21. MathematicalPhysicist

    Is Gaussian Elimination Only Used for 3x3 Matrices?

    is this elimination used only in 3*3 matrix?
  22. E

    Gaussian Integration: Int(0,1000)g(x)[f(x)]dx

    I have some doubts about it..in fact when you want to calculate an integral numerically..i always use gaussian integration but what would happen if i use this technique to calculate: Int(0,1000)g(x)[f(x)]dx where [] means the floor function in fact it is a non-continuous function..would be...
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