Spirocyclic quinuclidinic ether derivatives

1. A compound of the formula (I):

or a pharmaceutically acceptable salt thereof, wherein:

n1 is 0, 1, or 2;

n2 is 0, 1, or 2;

X is selected from the group consisting of O, S, or NR 1 , or X is a bond;

Ar 1 is a group of the formula:

X 1 , X 2 , X 3 , and X 4 are each independently selected from the group consisting of N and —CR 2 ;

Y 1 , Y 2 , and Y 3 are each independently selected from the group consisting of N, O, S, and —CR 2 ;

Y 4 is C or N, provided that when Y 4 is C at least one of Y 1 , Y 2 , and Y 3 , is other than —CR 2 ;

Z 1 , Z 2 , and Z 3 are each independently selected from the group consisting of N, O, S, and —CR 2 ;

R 1 is independently selected from the group consisting of hydrogen, alkyl, alkoxycarbonyl, alkylsulfonyl, and arylsulfonyl;

R 2 at each occurrence is independently selected from the group consisting of hydrogen, halogen, alkyl, alkoxy, alkylcarbonyl, and —NR 3 R 4 ; and

R 3 and R 4 are each independently selected from the group consisting of hydrogen and alkyl.

2. The compound of claim 1 , selected from the group consisting of:

wherein Ar 1 is as previously defined for compounds of formula (I) and R 6 is selected from the group consisting of hydrogen, halogen, alkyl, phenyl, —O—R 7 and —NH—R 7 , wherein R 7 is hydrogen, alkyl, and aryl.

3. The compound of claim 1 , wherein Ar 1 is selected from the group consisting of:

wherein R 2 at each occurrence is as defined in claim 1 ; m at each occurrence is 0, 1, 2, or 3; p at each occurrence is 0, 1, or 2; and q at each occurrence is 0, 1, or 2.

4. The compound of claim 1 , wherein Ar 1 is phenyl or phenyl substituted with amino.

5. The compound of claim 1 , wherein n2 is 1.

6. The compound of claim 1 , or a pharmaceutically acceptable salt thereof, selected from the group consisting of:

5′-phenyl-3′H-spiro[4-azabicyclo[2.2.2]octane-2,2′-[1]benzofuran];

5′,7′-diphenyl-3′H-spiro[4-azabicyclo[2.2.2]octane-2,2′-[1]benzofuran];

3-(3′H-spiro[4-azabicyclo[2.2.2]octane-2,2′-[1]benzofuran]-5′-yl)aniline;

5′-phenoxy-3′H-spiro[4-azabicyclo[2.2.2]octane-2,2′-[1]benzofuran];

5′,7′-diphenoxy-3′H-spiro[4-azabicyclo[2.2.2]octane-2,2′-[1]benzofuran];

7′-bromo-5′-phenoxy-3′H-spiro[4-azabicyclo[2.2.2]octane-2,2′-[1]benzofuran];

N-phenyl-3′H-spiro[4-azabicyclo[2.2.2]octane-2,2′-[1]benzofuran]-5′-amine;

N,N′-diphenyl-3′H-spiro[4-azabicyclo[2.2.2]octane-2,2′-[1]benzofuran]-5′, 7′-diamine; and

5′-(1H-indol-5-yl)-3′H-spiro[4-azabicyclo[2.2.2]octane-2,2′-[1]benzofuran].

7. A pharmaceutical composition comprising a therapeutically effective amount of a compound of claim 1 in combination with a pharmaceutically acceptable carrier.

8. The method of treating a disease modulated by an α7 nicotine acetylcholine receptor, wherein the disease is Alzheimer's disease, comprising administering an effective amount of a compound of claim 1 , to a subject in need thereof.

9. The method of treating a disease modulated by an α7 nicotine acetylcholine receptor, wherein the disease is schizophrenia, comprising administering an effective amount of a compound of claim 1 , to a subject in need thereof.