beta-lactamase inhibiting compounds

The invention provides compounds of formula I and IV:wherein R1-R11 and A have any of the values defined in the specification, and their pharmaceutically acceptable salts, are useful for inhibiting beta-lactamase enzymes, for enhancing the activity of beta-lactam antibiotics, and for treating beta-lactam resistant bacterial infections in a mammal. The invention also provides pharmaceutical compositions, processes for preparing compounds of formula I and IV, and novel intermediates useful for the synthesis of compounds of formula I and IV. The A can be, for example, thio, sulfinyl, or sulfonyl.