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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  1. B

    Minimum Beam Waist of 655nm Gaussian Laser Beam

    Homework Statement A 655nm gaussian laser beam has a waist of 15mm located at a lens with focal length of 12 cm. What is the minimum beam waist and where is it located? Homework Equations Beam radius w = w0*sqrt(1-(z/zr)^2) w0 = min beam waist; z = distance, zr = Rayleigh range The...
  2. N

    Understanding White Gaussian Noise: Probability of Inclusion in [0.25A, 1.15A]

    Homework Statement Consider the random process X(t)=A+N(t), where A is a constant and N(t) is a white Gaussian noise with spectral density equal to 1. The process X(t) is filtered with a system with impulse response h(t)=u(t)exp(‐t/T). Compute the probability that X(t), once filtered, is...
  3. M

    Gaussian Summation - Find Out the Result!

    Hi, We know that the Gaussian integral is \int_{-\infty}^{+\infty}e^{-\frac{x^2}{a^2}}dx=a\sqrt{\pi} However, if the gaussian function is discrete in x, what is the result of \sum_{n=0}^{+\infty}e^{-\frac{n^2}{a}} = \\? where n is natural number, that is n=0,1,2,3....
  4. I

    How to rewrite 2D Gaussian eqn in terms of x?

    http://upload.wikimedia.org/math/1/9/8/1983171154842b0b061fc42aa5eb7642.png" How to rewrite this 2D Gaussian eqn in terms of x? i need to calculate the x and y values. let x0=0 and y0=0. is it complex?
  5. A

    Calculating ESP charges for a molecule fragment using Gaussian

    Hi there, I'm trying to reconstruct the ESP charges that have been determined in a paper using a Gaussian-like quantum chemistry program. While I understand the basic notion of the iterative procedures to approximate the wavefunctions etc., I'm not a chemist and so I'm having problems with...
  6. N

    Electric Field between two opposite, gaussian distributed charged spheres

    Hi, I understand how to get the electric field between two spheres of uniform charge, \vec{E} = \frac{\rho \vec{d}}{3 \epsilon_0} which is simplified because at a point \vec{r}, the vectors from each charge center combine to give the distance, \vec{d}, between centers (since \rho's can...
  7. L

    Geometry Optimization with GAUSSIAN 03W

    Hello, I am new in computational chemistry. I was calculating by "DFT and HF theory" (using GAUSSIAN 03W) molecular parameters of "2D coordination polymer, [Cd(μ-pydc)(2-mim)]n (pydc = pyridine-2,3-dicarboxylate, 2-mim = 2-methylimidazole)" . I have Crystallographic data are belong to this...
  8. H

    Intersection of two gaussian distribution functions

    Can you please give me formulas which give intersection of two gaussian function f(x, mu, sigma) = 1/sqrt(2*pi*sigma^2) * exp(-(x-mu)^2 / (2*sigma^2)) for the case variances are different. (Note: I think it is time I learn how to use "tex" tags, do you know a good tutorial?)
  9. N

    Taylor expansion of gaussian integral with respect to variance

    Hi everyone. The problem I have to face is to perform a taylor series expansion of the integral \int_{-\infty}^{\infty}\frac{e^{-\sum_{i}\frac{x_{i}^{2}}{2\epsilon}}}{\sqrt{2\pi\epsilon}^{N}}\cdot e^{f(\{x\})}dx_{i}\ldots dx_{N} with respect to variance \epsilon. I find some difficulties...
  10. I

    Computing the Integral of a Gaussian with a Cosine Factor in DTI Analysis

    Homework Statement Looking through this proof in my DTI(diffusion tensor imaging) book and they don't show the work on how to compute this integral (and I'll need to know it for a presentation): \int cos(\gamma G\delta x) * e^{-x^{2}/4D\Delta}dx I haven't really gotten anywhere yet...
  11. S

    Introducing Gaussian errors to data (Matlab)

    Homework Statement I need to introduce Gaussian errors to a set of velocity measurements. The errors should have mean zero and standard deviation .2. v = [4.6 3.8 7.2 9.7 6.4]; The Attempt at a Solution I tried to use Matlab's imnoise command (J=imnoise(v,'gaussian',0,.04), but...
  12. O

    Multidim. Gaussian integral with linear term

    Hey everyone, I know, lots of threads and online information about Gaussian integrals. But still, I couldn't find what I am looking for: Is there a general formula for the integral \int_{\mathbb{R}^d} d^d y \left|\vec{y}\right| \exp(-\alpha \vec{y}^2) where y is a vector of arbitrary...
  13. mnb96

    What is the result of a discrete Gaussian summation?

    Hello, If we are given a gaussian function which is continuous in x we know that: \int_{-\infty}^{+\infty}e^{-x^2}dx=\sqrt{\pi} What if the gaussian function is discrete in x? What is the result of \sum_{x=-\infty}^{+\infty}e^{-x^2} = \\? where x\in \mathbb{Z}
  14. P

    What is the formula for calculating the FWHM of a gaussian function?

    Hi, I have a gaussian of the form exp[-\frac{\pi*x^{2}}{A^2}]. I know that the FWHM=0.939A, but I cannot prove it. I Let exp[-\frac{\pi*x^{2}}{A^2}=0.5 (i.e. the half maximum part) taking natural logs I get rid of the exponential, but then which bit represents the full width?
  15. Shackleford

    Spreading of Gaussian Wave Packet

    We finally started modern quantum mechanics. I'm definitely feeling a bit lost or fuzzy, especially in the more rigorous book Quantum Physics by Gasiorowicz. At any rate, we have two more problem sets before the last exam. As for the problem, I'm not sure what to. Is it asking to calculate...
  16. I

    Complex gaussian, complete the square

    Homework Statement Evaluate this integral (in essence the Fourier transform of the Gaussian): \int_{-\infty}^{+\infty} e^{-ax^2} e^{ikx}\, dx 2. The attempt at a solution One way is to complete the square, so that -ax^2 + ikx = -a(x-ik/2a)^2 - (k/2a)^2 so the integral becomes...
  17. I

    Gaussian Curvature, Normal Curvature, and the Shape Operator

    Homework Statement Let u_1, u_2 be orthonormal tangent vectors at a point p of M. What geometric information can be deduced from each of the following conditions on S at p? a) S(u_1) \bullet u_2 = 0 b) S(u_1) + S(u_2) = 0 c) S(u_1) \times S(u_2) = 0 d) S(u_1) \bullet S(u_2) = 0...
  18. P

    Understanding Gaussian smoothing/filtering

    Hello, I was looking at the explanation for Gaussian smoothing found here: http://homepages.inf.ed.ac.uk/rbf/HIPR2/gsmooth.htm" Now, figure 3 shows a discrete Gaussian kernel approximation. I have 2 questions: 1: Why is there a scaling factor (1/273)? Is it so that the sum of the discrete...
  19. R

    What are the variables at the center of a Gaussian distribution problem?

    Q. (Something), (Something) and (Something) is at the centre of distribution.(bell curve) The mean? And i don't know - I've read through my maths book(s) and several other sources of information and can not find any information. Thanks.
  20. M

    Gaussian Elimination: Translating text into equations

    Hello :smile: I have a homework question regarding Gaussian Elimination, where I am supposed to use information in a block of text to get equations, and form an augmented matrix. There are 4 unknowns, but I can only seem to get 3 equations and 3 "checks", to see if the values I get are...
  21. K

    Solving Gaussian Problem: Cylindrical Shells w/ Radii R1 & R2

    Homework Statement A thin cylindrical shell of radius R1 = 5.0 cm is surrounded by a second cylindrical shell of radius R2 = 9.0 cm, as in the figure. Both cylinders are 5.8 m long and the inner one carries a total charge of Q1 = +4.2 µC and the outer one carries a total charge of Q2 = -2.4...
  22. C

    Solve Gaussian Integral: e^(-x^2)

    can some one tell me how to go about solving the gaussian integral e^(-x^2) I know it has no elementary integral . but i was told the improper integral from -inf to positive inf can be solved and some said that i haft to do it complex numbers or something and help would be great , this...
  23. M

    Gaussian Elimation with Partial Pivoting Algorithm by hand

    Homework Statement The Gaussian Elimination with Partial Pivoting algorithm when applied to the following matrix A[-3 0 4; 5 2 -6; 0 0 1] Will construct matrices P, L, and U 1- What are the defining properties of the matrices P, L and U? 2- What relation do P, L, U and A always satisfy...
  24. P

    Covariance of Gaussian Process

    This is probably a stupid question, but here goes: based on the covariance function of some (centered, stationary) Gaussian process - how can one determine non-degeneracy (here I mean for any choice of a finite number of sampling times, the resulting RV is AC). Ideas?
  25. Y

    Gaussian beam passing through a circular aperture

    Hi all, when I have a Gaussian beam passing through a circular aperture: What should be the far field (Fraunhoffer's) distribution? Thanks in advance, Yoni
  26. R

    Integration Involving a Gaussian Function

    This is a University quantum physics problem but I'm posting it in this section as what I'm having trouble with is the integration. Homework Statement Homework Equations Normalisation condition: \int ^{\infty}_{-\infty} \left| \psi(x)^2 \right| dx = 1 The Attempt at a Solution...
  27. D

    Exploring the Impact of Gaussian Elimination: A Comprehensive Analysis

    My linear algebra teacher is strange. This is proof, he wants us to write a 4 page essay about the strengths and weaknesses of the Gaussian Elimination method to solve systems of equations covering these four areas: accuracy, student understanding, preparation for higher-level mathematics...
  28. S

    Mean, squared mean and standard deviations of a gaussian

    Homework Statement find <x>, <x^{2}> and \sigma of the probability distribution; \rho(x) = \sqrt{\frac{\lambda}{\pi}}e^{-\lambda(x-a)^{2}} Homework Equations As shown above The Attempt at a Solution I know that I can simply take the mean value (a) and the standard...
  29. M

    Electric Force & Gaussian Sphere: Need Help Understanding?

    Our professor said that when a metallic body or a conductor is inserted inside a gaussian sphere, it will not experience anykind of electric force? But i don't understand why? Any help will be appreciable.
  30. D

    Solving linear systems + gaussian elimination

    Homework Statement http://img.rflz.net/problems.jpg Homework Equations The Attempt at a Solution Question 1 x4 = 1 + 4x5 but from there I am not sure where to go or if there is even a solution? Question 2 I eventually got the matrix down to this: 1 2 -3 1 4 1 0 1 1 0...
  31. J

    Pythagorean Primes and Gaussian Primes, divisibility question

    Here is an interesting problem that I've been thinking about for a while: Let p be a prime s.t. p = 4m+1 for some integer m. Show that p divides n^2 + 1, where n = (2m)! It comes from a section on principal ideal domains and unique factorization domains. It is well-known that p is the...
  32. P

    Linear Algebra / Gaussian Elimination

    Homework Statement Find coefficients a,b,c and d so that the curve of a circle in an xy plane, with points (-4,5), (-2,7) and (4,-3), is given by the equation ax2 + ay2 + bx + cy + d = 0. Not even sure where to start. Can anyone help me with this?
  33. K

    Is This a Standard Formulation of a Gaussian Beam?

    In the book "Fundamentals of Photonics", the form of the Gaussian beam is written as I(\rho,z) = I_0 \left(\frac{W_0}{W(z)}\right)^2\exp\left[-\frac{2\rho^2}{W^2(z)}\right] where \rho = \sqrt{x^2 + y^2} However, in some books (I forgot which one), the author use the following form I(R) =...
  34. M

    Understanding Gauss' Law in Cases with Charges Outside Gaussian Surface

    Gauss' Law only figures out the the total charge enclosed by the Gaussian surface and on it, I treid this in a few cases where charges were placed only inside the surface, and my answers were correct. But, when I tried imagining how to do this if there were charges present outside...
  35. A

    Problem involving Gaussian Integrals

    Homework Statement \int e^{-\frac{1}{2}(ax^{2}+\frac{b}{x^{2}})} dx from -\infty to \infty Homework Equations it says to solve this, given that, again from -\inftyto \infty: \int e^{-\frac{1}{2}x^{2}}}dx = \sqrt{}2\pi and suggests that the substitution u =...
  36. D

    Why are probabilities distribution of thermodynamic variables tend to Gaussian?

    The probability distribution for some thermodynamic variable x is given by P = N e^{-A(x)/KT} where A(x) is the availability, which can be replaced by Hemlholtz free energy F, Gibb's free energy G, etc depending on the conditions imposed. N is just some normalization constant. A(x) can be...
  37. N

    Gaussian curve, x is a log scale

    Hello! If I have the gaussian function, but x is a loarithmic scale. Can I infer that, if x was plotted using a regualr scale, that the function would be 'fairly' linear? At least initially? As the rate of change gradually increases befor slowing down again. I think this is reasonable... I...
  38. W

    Find integral using Gaussian Quadrature Method (numerical)

    Homework Statement approximate this integral: \oint e^(-(x^2)) from 0 to 4 using Gaussian Quadrature with n = 3 Homework Equations can be found at: http://en.wikipedia.org/wiki/Gaussian_quadrature The Attempt at a Solution n = 3 coefficients: c(1) = c(3) = 5/9, c(2) = 8/9...
  39. G

    I need to fit a tail-heavy Gaussian curve

    I need to fit a tail-heavy "Gaussian" curve Hi, it's been a long time since I've been around PF. Homework Statement This isn't a homework problem per se, but I've been trying to fit some scattering data using a Gaussian function using a least squares approach and it's not working so...
  40. E

    Diffraction: rectangular aperture and gaussian beam

    Is the Fresnel-Kirchhoff formula (FKF) valid also for gaussian beams? I a book starting from the gaussian intensity: U_0(x,y)=\sqrt{\frac{2}{\pi\omega_0^2}}\exp\left(-\frac{t^2+s^2}{\omega_0^2}\right) it said that using the FKF in free space the gaussian beam spreads (in far-field assumption)...
  41. deccard

    MATLAB Lorenzian and gaussian pdf-function fitting with Matlabs nlinfit, confidence interval

    I have data that I want to fit to both Gaussian and Lorentzian (Cauchy) distribution. I have been using Matlab's nlinfit as follows: gaus = @(p,xdata) (p(1)/(sqrt(2*pi*p(2)))*exp(-(xdata-p(3)).^2/(2*p(2)))+min).*weights; [g_pfit,g_residual,g_J]=nlinfit(data(:,1), data(:,2).*weights, gaus...
  42. A

    Relating chi-squared and gaussian curves

    Simple question: can a chi-squared be represented as a gaussian distribution? I'm wondering if I can take some chi-squared numbers that I have and represent them as increasing/decreasing widths of FWHM of a gaussian. Can I?
  43. LarryS

    Gaussian Wave Packets - Fiction?

    Forgetting about spin and polarity for the moment, do individual identical particles of the same type (electrons, photons, etc.) really have their own individual wave functions (Gaussian packets)? The mathematical definition of probability (relative frequency, etc.) has meaning only at the...
  44. P

    Question about Gaussian distribution

    Hello everyone, I am trying to understand situations under which Gaussian distribution would apply. For example, I read somewhere that if you have some ink drop on a porous paper, then the distribution of the displacement of ink particles is approximately gaussian. I am trying to figure...
  45. 5

    Fortran Gaussian Elimination in Fortran

    Hi, I am trying to recreate the naive gauss elimination method in fotran 95 but am having a few problems with it. The idea is to read in a nxn matrix of equations, so you can type in any number when u start the program and then the program will ask you to enter the relavant amount of...
  46. S

    Energy density expression of a Gaussian pulse

    Hi, Energy density of the ith annular section of a Gaussian pulse is written as F(r_i, r_i+1)=2*totalEnergy/[(r_i+1^2-r_i^2)*w^2]*integral(r*exp(-r^2/w^2),from r_i to r_i+1) where r spans from r=0 to r=r_n (theoretically infinity) in n steps, w is the waist size of the beam. This...
  47. P

    How Do Field Lines Represent a Hydrogen Atom in a Simplified Model?

    Homework Statement draw the field lines of a simple hydrogen atom model. A case is given where a proton is surrounded by an electron cloud. Without getting into quantum mechanics how would represent the field lines of this mini sphere inside and out. Homework Equations gauss's law The...
  48. N

    MATLAB Gaussian Fitting: Finding Error with MATLAB Output

    Hi I have fitted Gaussian function to some data in matlab. Now MATLAB gives me this: General model Gauss1: f(x) = a1*exp(-((x-b1)/c1)^2) Coefficients (with 95% confidence bounds): a1 = 2633 (2628, 2637) b1 = 1824 (1824, 1824) c1 =...
  49. K

    Gaussian Co-ordinates-background and derivation

    In Section XXV of Relativity we are introduced to Gaussian Co-ordinates. I can't seem to find much about this on the internet, perhaps there is another name? Can anyone link some background behind why this system was initially derived, and most importantly does anyone know the derivation of...
  50. P

    Gaussian Fitting: Get Help Now!

    I have a set of data for an absorption spectra that I plot the firtst derivative of and it gives me a gaussianish plot, I then want to fit it with a gaussian and what I've been doing so far is calculating the mean and variace of the spread and then using them in the equation. Although this does...
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