Gaussian potentials

In Gaussian, potential energy surface scans are automated. Here is a sample input file fora simple potential energy surface scan ... 

These filler constraints can be represented by a Gaussian potential... 

The anharmonicity of the confining potential can be controlled by changing the depth of the Gaussian potential D with respect to >z and ojxy, respectively. The parameters coz and coxy represent the frequency of the harmonic-oscillator potential characterizing the strength of confinement of... 

Figure 1 Energy spectrum of the low-lying states of four electrons confined in a quasi-one-dimensional Gaussian potential with (D, a>z,a>xy) = (4.0, 0.1, 20.0) for different-size basis sets. Energy levels of different spin multiplicities are indicated by different colors (See the caption to Figure 2). The number in the round brackets specifies the total number of basis functions and the parameter v p specifies the extended polyad quantum number (See the text for details). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this book.)...

The Hamiltonian (1) for quasi-one-dimensional two-electron quantum dots is simplified by neglecting the x and y degrees of freedom and by approximating the confining Gaussian potential by a harmonic-oscillator potential with >z... 

The energy spectrum of two electrons confined in a quasi-fwo-dimensional Gaussian potential has also been studied for the same set of the strengths of confinement as the corresponding quasi-one-dimensional cases, and are compared to them. The energy spectrum of the quasi-two-dimensional quantum dot is qualitatively different from that of the quasi-one-dimensional quantum dot in the small confinement regime. The origin of the differences is due to the difference in the structure of the internal space. 

Figure 1. Critical temperature versus for the Gaussian potential with width y = 5 for S0 = 0.05jt, 0.3jr, 0.3jt full line Abrikosov-Gorkov, dashed hnes one-component OP, dot-(dash) hnes two-component OP (2). Inset A6/A2 versus for the same three values of S0 with the parameters of the pairing interaction chosen such that 7 + = 90 K, T = 30 K and A26/A22 = 0.1.

Figure 2. Left panel Gaussian potential with y = 5. Right panel Point like scatterers. Note the difference in scale. S0 = 0.49 r, = 0.2 MeV...

With the goal of exploiting at best the short computational time available, in [36] we also introduced a variant of the Gaussian potential defined in (13) ... 

Polymer chains in solution form a loose coil such that two coils can interpenetrate. The resulting effective interaction potential O(lrl) is repulsive and is well approximated by a Gaussian potential of strength Oq and with a range ro which is proportional to the radius of gyration Rg. The excess free energy functional for such soft systems can be approximated by a quadratic form... 

From vibrational analysis of the out-of-plane bending vibration assuming a harmonic-cum-Gaussian potential. Barrier height = 609 cm. ... 

Figure 4 A sketch of the process of metadynamics. First the system evolves according to a normal dynamics, then a Gaussian potential is deposited (solid gray line). This lifts the system and modifies the free-energy landscape (dashed gray line) in which the dynamics evolves. After a while the sum of Gaussian potentials fills up the first metastable state and the system moves into the second metastable basin. After this the second metastable basin is filled, at this point, the system evolves in a flat landscape. The summation of the deposited bias (solid gray profile) provides a first rough negative estimate of the free-energy profile.

The energy rate at which the Gaussian potential is grown and, for WTMetaD, the parameter AT that determines the schedule for decreasing it along the simulation. 

Here C d) is a prefactor that depends on the dimensionaUty of the problem (i.e., the number of CVs included), S is the dimension of the domain to be explored, 8s is the width of the Gaussian potentials, D is the diffusion coefficient of the variable in the chosen space, and co is the energy deposition rate for the Gaussian potential. This equation has several nuances that need to be explained, and here we will do it by considering alanine dipeptide as a real-life example. 

The deposition rate for the Gaussian potential can be expressed as the rate between the Gaussian height and the time interval between subsequent Gaussian depositions, that is, co = WqJtq. This rate can thus be tuned by adjusting both these parameters. 

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