Structure Solution with SHELXS
The reflections resulting from the x-ray diffraction experiment are in principle 'packages' of single waves, characterized by wavelength, phase and amplitude. These waves arise from the interaction between the incoming x-ray beam and the electron shells of the sample atoms in the crystal. This phenomenon is called x-ray scattering. Under certain conditions, the regular lattice arrangement of the atoms leads to constructive interference of the scattered waves - the result is known as x-ray diffraction. Mathematically, the electron density function and the reciprocal lattice of reflections are related to each other by Fourier transformation. To calculate the electron density function - describing the structural density map with the atomic peak coordinates we are interested in - from the experimental pattern of reflections, you have to perform a Fourier synthesis using amplitudes and phases of all reflections.
There is one decisive problem that makes the density calculation - theoretically - impossible: Only intensities (squared amplitudes) are measured during a diffraction experiment. The phase information however is lost, because the measurement is not time-resolved and the relative phase shifts of the reflections hitting the x-ray detector cannot be determined. Unfortunately, the phases are more important for Fourier synthesis than the intensities. This difficulty is known as the phase problem of crystallography. Solving the phase problem is not trivial at all, so that the crystallographic structure determination was not a routine method until about 20 years ago (and is still not a routine procedure for macromolecular structures). 
There are several approches to phase a structural data set, i.e. to determine phases for given reflections. There are non-standard three-beam interference experiments by which relative phases can be determined directly (i.e. physically) on special diffractometers. Much more common are methods that derive experimental phases mathematically from reflection intensity differences based on the anomalous scattering of non-centrosymmetric structures. Therefore macromolecules (which are always chiral) containing anomalous scatterers, i.e. heavy atoms, are well suited for these types of experiments. 
A different approach derives the phases ab initio from the measured intensities. This means, that the phase calculation is done statistically without any direct or indirect phase information available, but starting 'from scratch'. Only the intensities (as E-values) and a random starting set of phases are used. These so-called direct methods are very successful for small molecule structures with up to 100 (non-H) atoms, where they have become the standard way to solve the phase problem. Thanks to the use of direct methods as a fast and convenient 'black box' procedure, small-molecular structure determinations are nowadays a routine method like NMR. 
Another non-experimental phasing method for structures with heavy atoms present is the Patterson method. The Patterson function is based on squared structure factors (the intensities) and does not need any phases. The peaks in this function represent interatomic distance vectors, from which the positions of the heavy atoms can be derived. Knowing the type and the coordinates of the heavy-atoms, this part of the structure is already solved and the corresponding phases (as well as amplitudes) can be determined. Thus, compared to the other methods, this structure solution procedure works the other way around - first the coordinates, then the phases are calculated. The rest of the structure usually can be determined during the refinement process.

The structure solution program SHELXS either uses direct methods or the Patterson method for phasing. Depending on the method you want to use, the INS file must contain the command TREF or the PATT instruction, respectively. Direct methods are in general recommended for all small molecule structures, they may only have problems in rare cases, e.g. for some non-centrosymmetric spacegroups. The Patterson method only makes sense if the structure indeed contains heavy atoms. In such cases, it is sometimes superior to direct methods.
As seen in the XPREP chapter, the default command is TREF. Our structure does not contain any atoms heavier than oxygen, so there is no need to change that INS file line to 'PATT'. 

Start SHELXS with the command shelxs momo-new
Two files of the same name are needed, the HKL file for the intensities and the INS file containing essential crystallographic information plus the phasing instruction(s) - as explained in the previous XPREP chapter. Both files should exist. Having typed the SHELXS call in the terminal, the following output appears: 
In the section marked with (1) you find some internal program parameters, most of which are default values for the TREF mode and not interesting for you, as the program will be run in standard mode.

Section (2) lists some information about the direct methods results - for example, how many triplet phase relations (TPRs) have been found. From the TPRs, phases can be derived with a certain probability because in case of a reflection 'triplet', the reciprocal lattice vectors sum up to zero. Without going further into detail, it is the principle of direct methods that valid phases are calculated from a random starting phase set using TPRs and 'negative quartets' (NQRs), and then refined with the so-called tangent formula. SHELXS produces many solutions, not all of which make sense as chemical structures. Therefore, the phasing solutions are evaluated by applying the Fourier synthesis and checking the resulting electron density functions. 
The interesting part of the output is found in section (3), where for the best solutions, a code number and various figures of merit are given, followed by the distribution of CFOM values in a batch (here 128 tries). This line is read like a histogram, where the phase sets are divided into fractions. The leftmost columns are for the best phase sets, the rightmost ones for the worst. It will be seen that there are 2 correct solutions followed, after a small gap in CFOM, by a broad distribution of wrong solutions amongst the first 128 tries. The CFOM of 0.085 is acceptable and the final RE value, decribing how well the resulting electron density fits to the experimental data, equals 18.9 %, which is very good. (In general, if it is below 30 %, the structure can be expected to be solved).  
Now that SHELXS has been used, you have to check whether the structure has indeed been solved in the sense of chemically interpretable electron density peaks. This is done with the visualization program XP, where you also can prepare the structure refinement. The XP chapter therefore is the next step of this tutorial.