User Guide to the QUAD95 Program

v1.0

Online: June 2002

David F. Plusquellic

Optical Technology Division

National Institute of Standards and Technology

Gaithersburg, MD 20899-8441

A. Limitations of the current nuclear quadrupole programs

The nuclear quadrupole part of the program suite is limited to the calculation of hyperfine

splitting from one quadrupolar nucleus. Both first-order and second-order perturbation methods

are available to calculate the hyperfine components. However, only a single cross term of the

nuclear quadrupole tensor is currently available in second order. The calculation of hyperfine

intensities is based on the LS-coupling formalism for spin-orbit coupling in atoms.

B. Generating Nuclear Quadrupole Spectra from the Jb95.exe interface

The first-order nuclear quadrupole spectrum is calculated directly from jb95.exe. 

Hyperfine splitting are calculated from the expectation values of the squared angular momentum

components over the rotation wavefunctions generated by iar95.exe. As such, off-diagonal

quadrupole elements (eQqxz, etc.) are not possible since these expectation values average to zero

over the rotational wavefunctions. When the off-diagonal quadrupole tensor element, eQqxz, is

important (as might be expected for Cl atom in an planar asymmetric top molecule), then the
second-order program must be used. 

 To calculate and display the first-order quadrupole spectrum, a rotational spectrum must

first be calculated using iar95.exe and the simulation read into one of the nine simulation

channels. From the SIMULATION CONTROL DIALOG, check the quadrupole trackbar (TB)

dialog. The hyperfine components will be calculated and displayed for each rotation transition

according to the parameters values in the trackbar dialog. Change the nuclear spin to the desired

value. Select the symmetry axis and enter a value for eQqzz (eQqzz, is the component having the

largest magnitude and is often coincident or nearly so with a chemical bond axis). The symmetry

axis should be defined as the principal axis (a, b ,c) that makes the smallest angle with eQqzz

tensor component. Adjust the SYM PRM trackbar to automatically define the values of eQqyy

and eQqxx or modify the value for one of two parameters directly (see Gordy and Cook, p 254). 

Note that if the magnitude of eQqxx or eQqyy entered is larger than eQqzz, the symmetry axis will

automatically be redefined. Refine the magnitude of eQqzz and the symmetry parameter using the

trackbars to obtain the best match with the experimental data. 

To begin making experimental assignments, check the quadrupole quantum number (QN)

dialog box. Double clicking on or near a hyperfine component on the display (or by depressing the

CALL button in the QUADRUPOLE QN DIALOG) will select that line’s quantum numbers. 

Notice that the quantum numbers of the associated rotational line(s) will also be displayed and the

center frequency of the hyperfine multiplet will be displayed as a vertical line having a label J in

the center of it. If the multiplet center is not properly located, adjust the A, B, or C rotational

constant(s) using the ROTATIONAL CONSTANT TRACKBAR DIALOG (enabled from the

SIMULATION CONTROL DIALOG by checking the ABC RIGID box). If Doppler split profiles

are present, use the w, s and arrow keys to adjust the window size to match the Doppler splitting.
The ASSIGN and CLEAR buttons in the QUADRUPOLE QN DIALOG are used to define and

clear experimental assignments in memory. 

Quadrupole assignments should be saved to file using the WRT ASN button in the

Simulation/QUAD PRMS dialog. Prior to writing the file, select from the scrollable list (SIM

SEL) the simulation channel containing the assignments. Be sure to click within the box to select

it. In general, the proper channel selection must be made prior to performing other operations

available in this dialog as discussed below.

To refine the quadrupole parameters and rotational constants, the program QUAD95.exe

must be run from the 2ND ORDER QUADRUPOLE OPTIONS DIALOG. There is currently no

first-order least squares fitting procedure. To define initial values in this dialog, use the IAR-

>2ND button to copy the rotational constants from the ROTOR OPTIONS DIALOG and the

1ST->2ND button to copy the 1ST order quadrupole parameters. The assignments used in the

least squares procedure are read from the file named in the ASN FLNM field. Enter values for the

nuclear spin, the maximum K to use in the calculation and the number of least square cycles. 

Check the VAR STAT boxes for those parameters that are to be varied in the least squares fit.

Once all parameters have been defined, it is usually a good idea to save these parameters to an

INPUT FILE using the WRITE button. Notice that while the input and assignment file used by

IAR95.exe and QUAD95.exe both have “.in” and “.asn” extensions, the ASCII files used by these

two programs have different formats. Therefore, be sure to distinguish in the filename the type of

file saved.

A least squares analysis using the QUAD95.exe program will be performed when the RUN

button is pressed. Prior to execution, the user will be prompted with CALC 2ND ORDER

FREQS FOR ALL JKK LINES? If answered YES, the program will predict in second order all
hyperfine components of all rotational lines in the simulation. If answered NO, the program will

predict only the hyperfine components of the assigned transitions. Note that QUAD95.exe is a

FORTRAN program (written by Gerald Fraser) and does not dynamically allocate memory. The

maximum number of predicted transitions currently allowed is 5000 lines. If an error message is

given, try reducing the number of simulated lines using the ITN CUT option in the ROTOR

OPTIONS DIALOG.

Once the calculation is finished, an output file named quad_mod.out is created and may be

read using the RD button. The dialog boxes will be updated with the best fit results and the

second-order frequencies will be matched with the corresponding hyperfine transitions defined in

first-order. If satisfactory, save the new parameters to the input file and use the 2ND->IAR and

2ND->1ST buttons to update fields in the ROTOR OPTIONS DIALOG and 1ST ORDER

QUADRUPOLE TRACKBAR DIALOG. Rerun IAR95.exe and update the simulation. The

displayed spectrum will be the best representation of the quadrupole spectrum in first order. To

display the predicted energies from the 2ND ORDER calculation, check the 2ND ORDER box in

the QUADRUPOLE QN DIALOG. 

Another useful feature in the 2ND ORDER QUADRUPOLE DIALOG is the button WRT

CTR. When pressed, the center frequencies for all quadrupole multiplets having a least one

hyperfine component assigned are copied as rotational line assignments to the simulation. These

assignments must first be saved to file using the WRITE button in the SIMULATION CONTROL

DIALOG if they are to be used by IAR95.exe in a least squares fit. This feature is useful when

additional Hamiltonian parameters are needed for the calculation of rotational transitions as might

be needed for systems having a methyl rotor.
C. Restoring Nuclear Quadrupole spectra from file

The input and assignments files that were saved to disk are the two files needed to restore

the quadrupole spectrum upon restarting JB95.exe. From the Simulation/QUAD PRMS dialog,

first read the quadrupole input file. Select the simulation channel in which to restore the

quadrupole parameters and use the 2ND->1ST to restore the quadrupole parameters in the 1ST

ORDER QUADRUPOLE DIALOG. Finally, read the assigment file. 

Currently, there is only one generic output file called quad_mod.out that is created when

QUAD95.exe is run. This file contains the predicted second-order frequencies. Press the RD

button to restore these frequencies to memory. Note, however, that if this QUAD95.exe was later

used to fit another conformer or isomer, the quad_mod.out file will not have the correct secondorder frequencies. In this case, rerun QUAD95.exe before reading (RD) the quad_mod.out file.