# *LAPLCE¶

## Introduction¶

Laplace transformation module by B. Helmich-Paris.

The Laplace transform of orbital energies denominators can evaluated numerically by quadrature procedures. This is an interesting reformulation for perturbation-theory based approaches like Green’s functions methods, Møller-Plesset perturbation theory etc. Here the minimax algorithm is employed, which is very fast and gives also a good accuracy for vanishing HOMO-LUMO gaps. See also Ref. [Takatsuka2008] and [HelmichParis2016] for more details.

## Keywords¶

### .NUMPTS¶

A fixed number of quadrature points given by the user. If not given the number of quadrature points to reach a given accuracy TOLLAP is estimated.

*Default*:

```
.NUMPTS
0
```

### .MXITER¶

Maximum number iterations in the Newton-Maehly algorithm that searches for roots and extrema of the numerical error distribution.

*Default:*

```
.MXITER
100
```

### .STEPMX¶

Maximum step length of a line search part of the Newton-Maehly algorithm when far away from quadratic convergence region.

*Default*:

```
.STEPMX
0.3
```

### .TOLRNG¶

Tolerance threshold for the Newton-Maehly procedure that determines the extremum points. You should not touch that.

```
.TOLRNG
1.D-10
```

### .TOLPAR¶

Tolerance threshold for the Newton procedure that computes the Laplace parameters at each extremum point. You should not touch that.

```
.TOLPAR
1.D-15
```

### .XPNTS¶

You can start the iterative quadrature algorithm with some guess for the exponents. This only works if you are close to the final exponents. Also you have to provide the weights (WGHTS) and the number of quadrature points (NUMPTS).

### .WGHTS¶

You can start the iterative quadrature algorithm with some guess for the weights. This only works if you are close to the final weights. Also you have to provide the exponents (XPNTS) and the number of quadrature points (NUMPTS).