The first structure in the planned, seven-building Shady Grove Executive Center in Rockville has been completed. The center is located on a 45-acre site at the intersection of Interstate 270 and Shady Grove Road.

The 115,000-square-foot, four-story building has an exterior of silver reflective glass and brick. The interior surrounds a three-story atrium.

The Shady Grove Executive Center is part of an office park that will be developed over the next five years. The project, which will have a total of 800,000 square feet, is a joint venture of Spaulding & Slye Corp. and New England Mutual Life Insurance Co. It is being developed, leased and managed by Spaulding & Slye.

Other recent developments in commercial leasing in the Washington metropolitan area:

* DANAC Real Estate Investment Corp. has completed the second of four buildings in its office park project, located at the DANAC Tech Park on Gaither Road in Rockville. Construction of a third building is expected to begin early next year.

* Tracor Inc., a national research and development firm, is expanding its Rockville headquarters at 1601 Research Boulevard by 121,000 square feet. Construction of the project has begun and completion is expected by fall 1983.

* Construction has begun on Woodmont Place, a 101,500-square-foot office building located on the former Woodmont Country Club property along Rockville Pike. Completion is expected by the end of 1983.

The exterior of the six-story office building has been designed in a "serrated" geometric pattern.

The $15 million development cost of Woodmont Place is being financed by Union Trust Co. of Maryland.

* Mulligan/Griffin Associates Inc. has completed development of the Commerce Center 270 office building in Rockville. Sixty percent of the building has been leased. Tenants include General Electric Information Services, GTE's Sylvania Systems Group-Western division and the U.S. Chamber of Commerce. Mulligan/Griffin, owners and managers of the center, also occupy the building.

Ground has been broken for the first of 14 planned buildings in the Branches Office Park in Reston. The development is located on 40 acres in the 1000-acre Business Center.

The building, which is expected to be occupied by the American Federation of Information Processing Societies in July 1983, will be a two-level, 25,000-square-foot structure on 3.2 acres. It will have an entry-level waterfall and a glass-enclosed atrium with skylights.