# Search results

1. ### Koopmans theorem

it is in gas phase
2. ### Koopmans theorem

Hi all, I am using Koopmans theorem trying to estimate excitation energy so I have calculated the homo/lumo for molecule A as well as for A- and A+(adding and removing an electron respectively). Then I would use the formula Egap = min[(E(n+1)-E(n)]-[E(n)-E(n-1)]] I get a energy gap...
3. ### Derivate of generalized function

Hi, I have to show that if the derivate f'(x) of a generalized function f(x) is defined by the sequence f'_n(x) where f(x) is defined f_n(x)[\tex] then \int_{-\infty}^{\infty}f'(x)F(x) dx = - \int_{-\infty}^{\infty}f(x)F'(x) dx I use the limits for generalized functions and...
4. ### Write as sum of real and imaginary part

Hi, I have to write the 1/(a+ib) as a sum of a real part and an imaginary part. I was thinking of using the complex conjugate (a-ib) and multiply with this (a-ib) / (a^2 + b^2) I am a little bit lost on what to do next - any help appreciated thanks in advance Best
5. ### Find a general formula

Thanks yes I have tried integration by parts but that got very messy. I don't quite understand how to rewrite the equation involving the anti-derivative? Best,
6. ### Find a general formula

Hi, I have to find a general formula for the function 1/(2n)!\int_{-\inf}^{\inf}x^{2n}*e^{-ax^2} I am a little bit lost in how to proceed - any hints appreciated thanks in advance
7. ### The Heisenberg Uncertainty Principle and bacteria

if you write up Heisenbergs uncertainty principle and plug in the numbers from the exercise you should see that the uncertainty principle is not so relevant for the bacteria. Try to write up the equation and put in the numbers...
8. ### Hamiltonian for homogeneous system

I can see that some of the exponents have vanished so the integral which gives me problems is - \int dr^{3} dr'^{3} \frac{n^{2}}{|r-r'|} which in scaled coordinates can be written as - \frac{3}{4*pi}\int d\tilde{r}^{3} \frac{1}{\tilde{r}}
9. ### When does the Hartree-Fock approximation fail?

just to ask - when would a mean field approximation fail? Non-adiabatic processes?
10. ### Coordinate transformation and multiplying with size of J

Hi, So if I transform and the volume of the transform is preserved the size of |J| is one?
11. ### Coordinate transformation and multiplying with size of J

Hi, I am using the book "Advanced Engineering Mathematics" by Erwin Kreyszig where I am reading on the transformation of coordinates - when changing from \int f(x,y) to \int f(v(x,y),v(x,y) it is necessary to multiply with the size of the jacobian, |J| - I cannot find the proof in the book...
12. ### Hamiltonian for homogeneous system

I have to show that the hamiltonian for a homogeneous system can be simplified in scaled coordinates. The first two terms I can convert to scaled coordinates <T>+<V> whereas I have some trouble for the last term -½* \int d³r d³r' \frac{n²}{|r-r'|} where n is the density. The scaled...
13. ### QM/MM vs QM/MD

Yes - that is my question. I would presume that in a QM/MM one would converge to structure when the QM part would converge due to some gradient tolerance but I am not quite sure about the QM/MD. Any advise appreciated - thanks
14. ### QM/MM vs QM/MD

Hi all, I have a general questions on which is the difference between these two methods QM/MM and QM/MD? Any hints appreciated - thanks in advance Best
15. ### Product of spin functions

Hi, I am looking at the product of two spin function (a_1,a_2) where I would like to apply the spin operator S² to them. 1. To express the S² operator I have seen different expressions either expressed as linear combinations of Pauli matrices or expressed as follows S²=S_1² +...
16. ### Convert N/m to kcal/(mol*m^2)

Hi, I have to convert my force constant from N/m to kcal/(mol*m^2) but I don't know where to start. Any help appreciated. Thanks
17. ### Chemistry Spring constant of molecule

Hi, I have to determine the spring constant for a diatomic molecule. I have the frequency in cm^-1 which is 1395. I know the relation between the angular frequency and spring constant so I use the following relation: omega = 2*pi*c*v = sqrt(k/mu) so I isolate for k = mu*(2*pi*c*v)^2 mu...
18. ### Chemistry Spectra of small molecule and computed spectra

yes it is this difference. Is there a way to determine if one is going to use DFT which functionals to use and the size of the basis set in order to optimise the calculation?
19. ### Chemistry Spectra of small molecule and computed spectra

Hi, I am calculating the spectra of a small molecule - benzen with nitrogen group attach. I have some experimental data of the molecule IR and raman. I use DFT B3LYP with TVZ as basis set when I compare the modes and are a lot of differences between the two. 1. Would it help to increase...
20. ### Non-Adiabatic versus excited state

Hi, I am reading about protons and their transfer mechanisms and often the words nonadiabatic and excited state are used in a way which confuses me. If I have a proton in a higher vibrating state (E1) I would called that an excited state for the proton - is this also a non-adiabatic state...
21. ### Question regarding hydrophobic forces

Hi, I am not an expert on thermodynamics but does the enthalpy not increase as well with temperature - the values you get from a table is at 298 K so ... By just raising the temperature your system is no longer in equilibrium this might be an approximation for certain temperature ranges -...
22. ### Size of imaginary frequency

thanks - I am a little puzzled how to interpret to values when they are imaginary - if you have a C-H bond with frequency of 1300 cm^-1 you can say something about the energy of the bond or mode but when you have -1300 cm^-1 what to say about it than? I mean the bond/stretch should have the same...
23. ### Size of imaginary frequency

Hi, In the transition state of a chemical reaction defined as one imaginary eigenvalue of the hessian matrix - the size of my frequency is 1000i what can one say about the size of the imaginary frequency - is it related to energy in some way ? I have not been able to find any documents...
24. ### Vdw distances

Hi, I am looking for table or something that gives a tumb of rule for van der Waals distances - I have some C C spatial interactions which I would like to determine if their interaction contributes to the total energy or should I calculate it with a Lennard-Jones potential to get an...
25. ### Lowering of activation barrier

Hi, It is stated that changing the medium - water to ethanol f.ex - the experimentally measured rate enhancement is 10^6 fold which leads to a lowering of the activation barrier of \approx 9 kcal/mol. I don't quite understand which parameters I am missing in order to calculate that? Any help...
26. ### Integral centers in Hartree Fock

Hi, I guess that centers are often atom coordinates when using gaussian functions but it is not necessary atomic coordinates when using Slater functions?
27. ### Peptide chains with ER sequences

Could you please expand on the ER - what is ER?
28. ### Integral centers in Hartree Fock

Hi, I am looking at the integrals in HF - I am a little puzzled about the use of the word center. F.ex. two electron integrals on different center - it that electron belonging to different atom A and B? Than it mentions three- and four center - how to interpreted center? Thanks in...
29. ### IR/Raman spectra and symmetry

hi, A character table - is it possible to find that online or does one have to consult a certain book?
30. ### IR/Raman spectra and symmetry

hi, I am trying to interpret some data which have been calculated for IR/Raman but I don't know how to interpret them exactly. The schema says mode \nu 1 b_u 82 1 a_g 216 2 b_g 239 I presume that the u/g are gerade/ungerade from the bonding/antibonding wave functions but how to...
31. ### Coulombic operator

what is that more exactly? I know from spherical geometry that the volume is calculate dV = \rho^2 sin \phi d\phi d\rho d\theta If I integrate over two wave functions representing two electrons how to interpreted it? Any help or advice appreciated Thanks in advance
32. ### Coulombic operator

Hi, I am trying to understand this equation where the coulombic operator is given by J = \int d\tau \phi(2) \frac{1}{r_{12}}\phi(2) so I integrate over \tau but what is tau and the number I get from the equation is the energy I pressume? Any hints or help appreciated. Thanks in...
33. ### Harmonic oscillator

Hi, I am approximating a proton transfer from one water molecule to another. I would to have a quantum mechanical description of the proton transfer as a wavefunction. So I have approximated a "transition state" and use this as a harmonic potential. Then I get some energy values around this...
34. ### Restriction enzyme math question

(1/4)^6 gives you the probability that your enzyme will read the string(tag) correctly and you know the length of your string so combine these number will give you an average length of a cut given that it consists of only this sequence - this is how I understand you.
35. ### Calculate the formula weight for values of X

I pressume that you want to know how many NH_3 molecules that coordinates to Cu - so assume that you are able to experimentally get the mass of the complex than you can determine X - so calculate the mass of the complex by using X = 1,2... (Or at least that is how I understand your exercise.)
36. ### Poisson_boltzmann equation

I think I have it here; the electrostatic potential \phi can be written as the reduced potential u. If one again assumes that q*u / kT << 1 than the hyperbolic function can be approximated as sinh(q*u/kT) \approx q*u/kT which than reduces to the equation.
37. ### Poisson_boltzmann equation

The problem is going from the Poisson-Boltzmann equation \nabla (e(r)*\nabla \phi(r)) - \kappa^2(kT/q)*sinh(q*\phi(r)/kT) = -4*\pi \rho(r) The equation is than rewritten in terms of a reduced potential u \nabla (e(r)*\nabla u(r)) - \kappa^2 sinh(u(r)) = -4\pi*\rho(r) The reduced...
38. ### Generating dipole vector

Hi all, I want to generate the dipole vector for a water molecule. I start by generating the dipole moment of the molecule by the formula \mu = \sum Q_a * R_ab but I don't know how to generate the dipole vector? Any help appreciated. Thanks in advance
39. ### Hydrostatic pressure

Hi Sorry if it is bit unclear. I should calculate the pressure difference with a nanotube and on water on both sides. So I will use the formula \Delta P = n*f/A where f = 0.4 kcal/mol/Å and the unit cell of the system is 23Å*19.9Å*30.4Å and the number of water is in the 5.4 Å thick layer...
40. ### Hydrostatic pressure

so this should be okay 0.4 kcal/mol/Å*1.37*10^-19 mol /(23*10^-10*19.9*10¯10)m² = 1.1988e-08 kcal/Å /m^2 and than convert this to Pa? Thanks in advance
41. ### Hydrostatic pressure

Hi I am to calculate the hydrostatic pressure difference - given by the \Delta P = n*f/A where f = 0.4 kcal/mol/Å. The unit cell has the dimension 23Å x 19.9Å x 30.4 Å and the number of water molecules are 5.4 Å in the z-direction with a molar volume of 55.5 mol/l. I start by...
42. ### Ground state energy

Thanks could there be a situation where an electronic excited state could be "ground state" for a molecule - having lower energy than a none excited state?
43. ### Determine symmetry group

I draw the molecule and determine the different groups; E - the identity C2 rotation of 180 degrees C2 horizontal 180 degrees I know the molecule should have D5h but I have some trouble finding the rest of the symmetri axis. Any help appreciated thanks in advance

45. ### Determine symmetry group

Hi, I have to determine the symmetry group of cyclopentadienyl(assumed to be planar and symmetrical) and I should use Huckel theory. Is there a systematic way to determine the symmetry group and is it possible to use software to determine the symmetry group. Thanks in advance
46. ### Computational chemistry

Hi, First I hope it is okay to post the problem here(?). I have some general questions regarding the use of software for chemistry simulations - my questions are more fundamental than software specific. I would like to simulate a chemical reaction - so I should be searching for the saddle...
47. ### Ground state energy

so the change will be given as E_1 = <psi_0|V|psi_0> where V is the small term?
48. ### Ground state energy

I am looking at a diatomic molecule where the Hamiltonian is given as H = l²/2I + F*d*cos theta where d is the dipole moment. The term F*d*cos theta is small. I write the energy of ground state as E_0 = \hbar*l*(l+1)/ 2I Than I have to determine how much the ground-state energy...
49. ### Variational theory

Hi, I am trying to understand the variational principle (E_n - E_0) >= 0 E_0 is the ground state of the system? E_n is nonground and will the nonground state than always have a higher energy than the ground state? Thanks in advance
50. ### Fock operator for closed shell system

N/2 is due to each orbital has to electrons hence 2*Coulombic.