Can I inject HS samples as splitless using the 7697A HS autosampler?

HS may handle splitless injection and maybe not , it is all according to your flow rates and pressures .

in general when you want to apply splitless with HS you need to increase your column flow rate since HS flow maybe higher than your column so you system will not get ready .

but on the other hand GC MS needs slow flow rates which doesn't make sense

I recommend you first to adjust your ms method

try low resolution , maybe you need to change ion source temp or you EMV .

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then try to optimize your head space method , maybe longer or shorter injction time or higher filling pressure .

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also try splitless injection , if the system get ready so try to inject and watch your repeatability , but make sure to increase your purge time to make sure that every thing make its way into column 

good luck

Splitless injection with headspace isn't supported.  From the 7697 Advanced Operation manual: "With any inlet type, the HS supports only split inlet modes.
Splitless inlet modes are not supported."

Thank you, Mohammad! I'll work on improving the method in a way the splitless injection wouldn't be needed.

Thank you, Lance. I noticed it in the supporting documents. Could you tell me the theory behind this incapability?

you are welcome , yes try the MS and HS method

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theory of incapability is simple

Head space needs carrier gas flow to transfer sample from loop to inlet

flow differs from method to another 

but this flow is much higher than column flow 

for example : column flow is 1.5 ml/min while HS transfer line flow 30 ml/min

so splitless injection become impossible , and the instrument can't get ready status for injection

You want to sweep the sample loop quickly to prevent the components broadening in the transfer line.  Split mode means that the flow through the loop is much higher for injection.  If you need more sensitivity, the best way is to use a larger sample loop in the headspace sampler.  The default loop is 1 mL; we also have 3 mL and 5 mL available.